Transport modelling: Sensitivity analysis and policy testing

Progress zn Planntng, Vol. 7, Pt.

3,pp. 153-237, 1977. PergamonPress,Printed in Great Britain.

Transport Modelling: Sensitivity Analysis and Policy Testing P.W.BONSALL,* A.F.CHAMPERNOWNE,* A.C.MASON* andA.G. WILSON**

Contents Acknowledgements

155

1. Introduction

157

1.1. 1.2.

Objectives The Approach Adopted

157 157

2.The Model 2.1.A Brief Description of the Model 2.2.Model Inputs 2.3.Model Outputs 2.4.The Usefulness of the Model in its Present Form for Policy and Sensitivity

3.The Choice of Parameter and Model Form Variations to be Examined Introduction The Policy Tests Tests of Exogenous Inputs Modifications of Model Form

177 177 177 177 179 179

The Indicators to be Examined The Combinatorial Roblem Analysis of Single Parameter Tests Analysis of Two-parameter Tests Analysis of a Multi-parameter Test

5. Description of the MLF Predictions and Comparison with the Base Year 5.1. 5.2. 5.3. 5.4. 5.5. “Instmte **School

171 171 172 173 174

4.Methods of Analysis 4.1. 4.2. 4.3. 4.4. 4.5.

158 161 165 169

Testing: Some Qualifications

3.1. 3.2. 3.3. 3.4.

158

Introduction Network Usage Trips and Trip Ends Expenditures and Costs Accessibilities

180 180 180 180 182 184

for Transport Studies, Umversity of Leeds of Geography, University of Leeds 153

154

Progress in Planning

6. Results

6.1. 6.2. 6.3. 6.4. 6.5.

185

introduction Single-parameter Tests - by indicator Results of the Single-parameter Tests (by input) The Two-parameter Tests The Multi-parameter Test

7. Conclusions 7.1. Z2.

185 185 198 216 220 224

and Recommendations

Summary of Conclusions Recommendations

Appendix

1.

Derivation

Appendix

2.

Convergence:

its Importance

Appendix

3.

Convergences

Achieved

References

224 224

of the Basic Model Form shown in Fig. 1 to Sensitivity

Analysis

226 231 232 236

Acknowledgements We would hke to record our debt to the following for their vanous contributions to the model and to the data base from which this study developed:Eric Cripps, Paul Goodman, Tony Ha&m, Roger Mackett, Ian Sanderson, Martyn Semor, Frank Southworth, Ron Spence and Huw Williams. Thanks also to Jean Dobson and Ian Swindell for their typing and drawing help. The research was funded by the Science Research Council.

155

CHAPTER

1

introduction 1.1.

OBJECTIVES

Much transport planning is carried out with the aid of computer models of transport flows to predict the impacts of alternative plans and policies. Until recently, it has been usual to carry out only a relatively smalI number of runs in any particular study. This has both limited the number of policy tests which were carried out and meant that the model’s sensitivity was not tested as thoroughly as was desirable. The main aim of the research described here, therefore, is to use advanced computer and programming capabilities to run a transport model many times in order both to mvestigate extremes of policy and to carry out sensitivity tests. The model used IS described in Section 2. Very briefly, it consists of a category analysis trip generation model, an entropy maximising combined distribution-modal split model, and a capacrty restraint assignment model of mcremental loading form. It was calibrated for a coarsely zoned West Yorkshire regton as part of a programme of research funded by the Science Research Council. The methods presented could, however, easily be used with alternative models.

1.2.

THE

APPROACH

ADOPTED

Sensitivity analysis is the examination and quantification of the stability of a model in the face of changes m its parameters. Some of these parameters can be seen as representing policy options In practice therefore there is no sharp distinction between policy tests and sensitivity tests. Broadly speaking, however, the runs of the model tested three kmds of variation: (a) of parameters representing policy alternatives, (b) of parameters which are normally regarded as fixed exogenous inputs, and (c) of minor modifications of model form. The specification of alternatives to be tested under these three headings is given in Section 3. For any given run, the model generates a number of outputs which can be regarded as indicators of the impacts of the policies and parameter values being tested in that run. There are five groups of these, relating to (a) network usage;(b) trips and trip ends, (c) expenditures and costs; (d) accessibilities, and (e) consumer surplus measures of benefits. They are described in Section 2.3. The methods of analysis actually used are described III Section 4. The key to the method adopted is to take one set of policies and parameter values which seemed to be the most Zikely future (MLF) and all variations are measured and plotted against this basis. All predictions are made in the context of the West Yorkshire Study Area though it should be emphasised that the methods are widely applicable. The results are presented in Sections 5 and 6. First, the ‘most likely future’ is described (Section 5) together with observations of changes from the Base Year and secondly, the main results of the whole range of tests (Section 6). The main tests involve the variation of a selected parameter keeping all others fixed at MLF levels. Some results concerning other tests with two or more parameters varying simultaneously are reported separately in Sections 6.4 and 6.5. Because of the high dimensionality of the parameter space, it is impossible to do this systematically, but it is hoped that the range of tests adopted will give the reader a good intuitive feeling of the impact of variation in the whole space. Some conclusions are summarised and recommendations made in Section 7. 157

CHAPTER

2

The Model 2.1.

A BRIEF

DESCRIPTION

OF

THE

MODEL

The main submodels are shown in Fig. 1.) which shows the model to be a conventional one using the four stages of trip generation, distribution and modal split (in this case combined) and assignment (including tree building and a routine for estimating intrazonal costs). The model is

Loop M i.(repeat x 3)

t Trip dlstrkutlon and modal spht

Intrazonal cost program

I

I r---------Evaluation programs

’ 1

FIG. 1. Flowchart of the basic model.

described in detail elsewhere (Bonsall et al., 1976) and only a brief description is grven here. Note that the definitions of variables used throughout thrs paper are given in Table 1. The trip generation model is based on the category analysis procedure originally developed by Wootton and Pick (1967) and as used in the SELNEC Transportation Study (197 1). The main task within the model is to estimate 2’: which is the number of households in each of 108 categories, h, in each zone, i, and then to multiply these by trip rates, ph, to give zpnal trip origins, OF, thus: 0;

=pFph

(2.1.)

The 108 categories are defined in relation to six income groups, three car ownership groups and six household structure types. In subsequent sta es of the model car availability (n) is the only categorisation of person types required and so 4;1 is summed to give:

0; =

zi 0;

hen

158

(2.2.)

Transport Modelling: Sensitivity Analysis and Policy Testing

159

TABLE 1. Definition of variables Balancing factor for zone i in dist~bution-modal

split model.

The coefficients of generahsed cost which convert the components trme-like umts. Balancing factor for zone

J in

distribution-modal

for mode k into generabsed

split model.

Deterrence parameter for person type n. General&d

cost (m time like unrts) of traveliing from zone i to zone j by mode k.

Total trip attractions at zone j. of journey by mode k between zones i and j (if subscripted by I rt refers to link

Dtstance component length). Exponent

Flow by mode k on link 1. Public transport fare incurred m travehmg from zone I to zone

J

Household category superscript. Ongm zone subscript. Destination zone subscript. Mode superscript (k = 1 private transport, k = 2 public transport). Lmk subscrrpt. Subscrtpt of dlstrtbution

convergence loop.

Subscript of assignment convergence loop. Person type superscript (n = 1 car available, n = 2 no car available). Total trip origins by person type n in zone z. Excess out of pocket costs component of journey by mode k between zones r and j Number of households of category IJ m zone i. Trip rate of household category h. Number of employees of activtty group t( m zone j. Trip rate of actinty

group I(

Bunning cost of private transport (mcurred on link 1 or between zones i and f as specified). Trips from zone I to zone k by person n. In vehicle tune component

of journey from zone i to zone j by mode k.

Activity group superscript. Excess cost component

of journey from zone i to zone j by mode k.

Trip attractions, D, for each zone,i, are estimated in a similar manner using the number of employees, Q, in each of six activity categories, U, in each zone, j. These are then multiplied the activity category trip rates, qU to produce total zonal attractions, thus: Dj = z @q”

Note that the six activity categories are related to six land use categories aggregated from twenty-four SIC groups.

by

(2.3.)

160

Progress in Planning

The combined 1970):

distribution-modal

split model is of the form proposed by Wilson (1967,

where n 4.

A: = l$k2nBpJe-P

‘11

(2.5.)

to ensure that

CTkn = @? I

(2.6.)

jk lJ and

BJ = I/ Z A;~~e-finc~

(2.7.)

mken

to ensure that

x Tnk=D

inken 11

J

(2.8.)

where ken means that the k summation is to be taken over modes available to people of type n. The modal spht M for persons of type n travelling from i to j implied by thrs model can be stated explicitly as

Tk”

j&n '1

=A!-=

e-0

nk

CB

(2.9.)

T,;”

The treebuilding submodels calculate minimum generahsed cost interzonal paths and cost matrices for each mode using network mformatron and the generalised cost formulation. The generalised cost is expressed in time like units as recommended in the SELNEC working papers (SELNEC Transportation Study, 1971, 1972) in order that the deterrence parameters m the Qstributron and modal split submodel (pn above) should refer to an immutable unit (time) rather than an inflatable one (money). The formulation of the generalised cost is: (2.10.) and its component variables are given in Table 1. The private transport treebuildmg program uses the D’Esopo algorithm (see Pollock and Wiebenson, 1960) to calculate the minimum cost paths. The public transport treebuild uses a special development (Bonsall, 1975a, 1976) of an algonthm due to Dijkstra (1959) to deal wrth the nonlinearity of public transport fares. The assignment method used in the basic model involves an incremental loading routine which includes a capacity restraint mechanism using speed flow relationships based on those used in the Sheffield and Rotherham Transportation Study (Vorhees ef al., 1974). The convergence of this assignment process was tested against the Wardrop eqmlibrmm criterion (Wardrop, 1952). When convergence is reached the interzonal cost matrix can be said to take account of congestion. The dragonals of the cost matrices (the intrazonal costs) cannot be calculated from the network descriptions since we do not have sufficiently detailed intrazonal networks. The diagonals have, therefore, to be calculated by a specral routme (Bonsall, 1975b) which bases the cost of travel wrthin a zone on the size of the zone and the travel costs m the nerghbourhood of the zone.

Transport Modelling: Sensitivity Analysis and Policy Testing

161

There are two convergence loops within the basic model. These are denoted as ‘Loop N’ and ‘Loop M’ in Fig. 1. Loop N 1s the assignment convergence loop wherem, for a given set of trip matrices, trips are loaded onto the network in N increments with recalculation of congested link costs and trees between each increment. Loop M is a distribution and modal split convergence loop (which recalculates the trip matrices on the basis of the new cost matrix produced by the converged loop N). After exhaustive testing, which is reported in Appendix 1, we decided to accept fixed values for N and M (4 and 3 respectively) for all our runs rather than incurring the computmg expense of convergence testing for each and every run. Appendix 2 contains a discussion of some of the consequences of tlus decision, and Appendix 3 a description of the convergences which were attained.

2.2.

MODEL

INPUTS

2.2.1. Introduction It will be recalled from Section 1 that our main concern in the work reported here is to vary model parameters around those of a state which we have termed the most likely future (MLF). We have taken 1981 as the time horizon for this work and the parameters input to the MLF run are therefore estimated for 198 1. Many of the input parameters, together with the basic model form described m Section 2.1, were denved in our calibration to 1966 data. The methods used and results obtained in this calibration are described elsewhere (Bonsall et al., 1976). It will be clear from the brief description of the model in Section 2.1 that the model requires a great number of inputs. These are hsted in Table 2. TABLE 2. Data inputs to the model Input number 1 2 3 4 5 6 7 98 10 11 12 13

14 15

16 17 18 19 20

Data item Zonal totals of residential population Zonal totals of population in prrvate households Zonal totals of employed resrdents Zonal totals of population m 0, 1 and 2+ car availability categories Zonal totals of employment by SIC Cross probabilities of car ownership and income Income distribution parameters (6 income groups) Base year mean zonal incomes Household category trip generation rates Activity category trip attraction rates Annual change m real incomes Annual change m car prices Network characteristics (by lmk) 13.1 network structure 13.2 hnk length (d) 13.3 link time (t) 13.4 link excess times (x) 13.5 lmk jurisdiction code Parking charges (o) Coefficients of generahsed cost 15.1 mode 1 in vehicle time coefficient oi 15.2 mode 2 m vehicle time coefficient u: 15.3 mode 1 runrung costs 0: 15.4 mode 2 fare structure a: 15.5 mode 1 excess time coefficient 0: 15.6 mode 2 excess time coefficient 0: 15.7 mode 1 parkmg charge coefficient n: Zonal areas Zonal contiguity relations Deterrence parameter (Beta) for each person type Network flow conversion factor Speed flow relationships

Submodels affected* TG TG TG TG TG TG TG TG TG TG TG TG TB+A TB TB TB TB+A TB+l TB TB TB TB TB+I TB+I TB+I I D,bS A A

*TG - Trip Generation Submodel, TB - TreebuIlding Submodel, A - Assignment Submodel; I - Intrazonal Cost Submodel, D/MS - Dlstributlon/Modal Split Submodel.

162

Progress m Planning

2.2.2. Notes on the lkrivation of MLF Values forthe Inputs Listed in Table 2

hzput numbers I-5. These zonal totals were estimated on the basis of trends derived from the censuses of 195 l-1971 inclusive. Input number 6. The cross probabilities were derrved by Wootton and Prck (1967) p(NlX), the probability that a household with mcome X possess N cars is taken to be

‘Nx

p(NIX) = aNXbNe-

for N = 0 or 1, the values of a, b and c are given in Table 3. TABLE 3. Parameters of income/car ownership cross probabilities (see text) Value of N

a

b

C

0

1.15 1.64

0.00 2.29

0.80 1.31

1

Source Wootton and Pick (1967).

Input numbers 7-8. Calculated from the cross probabilitres mentioned above together with 1966 census information on car ownership in West Yorkshire (see Senior, 1975). The income group distribution parameters are given in Table 4.

TABLE 4. Real income distribution parameters (in f’OC0s)

Lower income lrmit Upper income hmit Median income

1

2

3

4

5

6

0 00 0.50 0.25

0 50 1.00 0.75

1.00 1.50 1.25

1 50 2.00 1 75

200 2.50 2.25

2 50 15.00 2.15

Input ~~rnbe~ 9-10. These trip productIon rates were derived from the SELNEC Transportation Study (1972). Data was not available to produce tnp rates specifically for West Yorkshire but the SELNEC rates gave good results for the Base Year (see Senior, op. cit.). Input numbers X1-12. These values are required in order that the Base Year zonal mean incomes can be modified to produce best estimates of the mean residual real incomes for each zone in the design year. Values of 2.0 and -1.5% were chosen to represent the changes m real incomes and car prices respectively (see Semor, op. cit.). Input number 13. The pnvate and public networks are separate and distinct although they are both expressed as a series of directed links connected by nodes. (a) The prrvate network: has some 700 nodes and represents the major roads of West Yorkshue (although the network IS finer m the Leeds area). Network layout and link lengths were derived from maps and plans. Link times were estimated on the basis of a movmg car survey (Copley and Judge, 1972) supplemented by local knowledge. Link times in the Leeds area are assumed to be affected by congestion (see below). Link excess times are assumed to accrue at the beginnings and ends of journeys and represent time penaltres incurred in the business of parkmg (or un-parking) a car; the values were based on local knowledge of the locatron of parking places in each zone. A junsdiction code is defined for each link in order that appropriate speed flow relationship (see input number 20) can be applied; the junsdictron code relates to the type of road (width, number of lanes etc.) and was derived from a DOE congestion survey (Department of the Environment, 197 1) supplemented by local knowledge. (b) The public network. has some 500 nodes and is a service based representation of the publrc transport routes of West Yorkshire (again with a finer representation in the Leeds area). The network layout and hnk trmes were derrved from public transport trme tables whrle maps were used to calculate hnk lengths Link excess costs represent time spent walking and waiting at either end of a Journey and at an mterchange Walking times were estimated on the basis of

Transport Modelling: Sensitivity Analysis and Policy Testing

163

local knowledge of the location of bus stops and rail stations while waiting times were taken to be 10 minutes or half the service headway - whichever be the less. The link jurisdiction codes differentiate between bus services and train services. Input number I4 Parking charges were applied to the SIXmajor towns of the study area and were calculated on the basis of recent (1974) charges in each town together wrth the assumption that there will be no increase in parking charges relative to incomes between 1974 and 198 1. The parkmg charges were then discounted to mclude the fact that only a fraction of the private transport trip ends in a given zone will incur the full parking charge (due to free or subsidised parking of one kind or another). The parkmg charges for the six towns are given in Table 5. Znput number 15. The generalised cost c$ of a trip from zone i to zone j by mode k was given in equation 2.10. but, for convenience, is repeated here

For any given interaction the components t, d, e, and o, are derived from the network description see notes 13 and 14). Since c$ is expressed m time like units the components 6 &,ak 3 an d a4 must include a “behavioural value of time” (or more precisely, a “duration of money”). We accept the assumption in McIntosh and Quarmby (1970) that the value of time (VOT) is directly proportional to income (VOT = 19% earnings per time unit) and therefore that as incomes rise then so too does the value of time. We have chosen to express our value of time relative to 1974 pence. McIntosh and Quarmby quote a 1968 mean income for all workers 19 x 4.41 = 0.8379 old of 4.41 old pence per minute; this implies a 1968 value of time of 100 pence per mmute, (= 0.349125 new pence per minute). Given the 212.3% increase m mean incomes between 1968 and 1974 (Central Statrstrcal Office, Annual Abstracts, 1950 to 1975) we derive a 1974 value of time of 2.123 X 0.349125 = 0.7412 new pence per minute. Car occupancy is assumed to offset the behavroural valuation of monetary expenditures (two people can park as cheaply as one) and consequently two of the coefficients of generalised cost described below (15.3 and 15.7) are assumed to be affected by car occupancy levels. We derived our mean car occupancy value of 1.2 from that quoted in the WYTS study of West Yorkshire (Traffic Research Corporation, 1969). Input number 15.1: ai is assumed equal to 1 (see McIntosh and Quarmby, op. cit.). Input number 15.2 a: is assumed equal to 1 (see McIntosh and Quarmby, op. cit.). Input number 15.3. a: : the value of this coefficient 1s derived from the 3 old pence (= 1.35 new pence) per mile quoted by McIntosh and Quarmby for 1968 together with the average car occupancy, and observed trends in car running costs (see Bonsall and Champernowne. 1976). From these trends, and in the light of current forecasts, we conclude that the 1981 car runnmg costs (in 1974 pence) will be approximately 2.6 times the 1968 costs. Our calculation for the MLF value of ai is thus. 1.2 1.25 X 0.7412 X 2.6 = 3 ’658

Input number 15.4. a; : the relatronship between distance travelled on a public transport service and fares payable is not strictly linear but is represented by a polygonal approximation to the fare structures as shown in Fig. 2. The value of a; is read, by the treebuilding program, from these fare structures. The coordinates of the fare structures for bus and train services were drawn from observed fares in 1974 together with the assumption that 1981 fares will be about 6% higher than 1974 fares (relative to income). Input number 15.5: a: 1s assumed equal to 2 (see McIntosh and Quarmby, 1970). Input number 15.6. a: : McIntosh and Quarmby recommend a value of 2 but we found better calibration results by adopting 1.5 in the Base Year and we have preserved this value for the design year. Input number 15.7: The parking charges shown m Table 5 are divided by car occupancy (1.2) and the 1974 value of time (0.7412).

164

Progress in Planning

I

0

I IO

5 Serwce Bus

distance,

I I5

I 20 miles

Train

-

1 25’

-

FIG. 2. Public transport fare structure.

TABLE 5. Parking charges (1974 pence) 1974 observed

% of trip ends assumed to pay the charge

Discounted charge

Leeds (1)

37

50

18.50

Bradford (31) Wakefreld (56) Dewsbury (60) Huddersfreld (65) Halifax (7 1)

25 25 25 25 25

15 10 10 10 10

3 75 2.50 2.50 2.50 2.50

Town (zone)

Input numbers 16-I 7. These values are requrred in the formatron of mtrazonal costs (see Bonsall, 1975b). Input number 18. The deterrence parameters were calibrated on the mean trip costs of a lO%Journey to work trip matrix for the study area taken from the 1966 census. The values used were: /3’ = 0.005526 and 0’ = 0.006180. Input number 19. This 1s required m order that the 24 hour Journey to work trips generated by the category analysis model can be factored to represent total peak hour flows for use in the capacity restramt procedures. The value of the factor is derived from WYTS data on the composrtron, purpose and distrrbution in time, of traffic m West Yorkshrre (Traffic Research Corporation, 1969). Input number 20. The relatronshrp between flow and speed on a link for the purpose of capacity restramt 1s

If FL < FFL

(2.11.)

,dvQc-FF~(FL-FFL)+~~s IfFFL
(2.12.)

V= FFS

QC - FFL

v=

VQC

If FL > QC

(2.13.)

where the variables are V - Speed on the link, D - Length of the link; FFS - Free-flow speed on the link, VQC - Speed at hmrtmg capacrty of link; FL - Flow per lane on link; FFL - Free flow hmrt per lane; QC - Lrmrting capacity of link.

165

Transport Modelling: Sensitivity Analysis and Policy Testing

The values of these parameters, which are dependent on lmk type, are listed in Table 6 and are based on values from the Sheffield and Rotherham Land Use Transportation Study (Voorhees, et al., 1974). Speeds were converted to miles/hour for input to the capacity restraint program. Note that type 0 links are notional lurks to zone centroids and type 10 links are outside Leeds. Neither is subject to capacity restraint. There is no capacity restraint in the public transport network. TABLE 6. Link classification and capacity restraint parameters Free flow speed

(km/hr) Road type* 0

Notional

1

D2/D3 M

FFS

Free flow limit

(Pc%‘$~/lane)

Limiting capacity (pcu/hr/lane) QC

Speed of QC (k&u) VQC

80

1700

2400

66

65

1400

2200

56

Restrtcted Capacity 65 km/hr hmit

50

600

1100

30

52153 AP Outer area 50 km/hr limit

45

500

1000

25

5

52153 AP Intermedtate area 5 0 km/hr limit

35

350

600

25

6

52152 AP Central business area 50 km/hr hmtt

1

Major radtal routes or outer rmgroads with roadside assumed 65% developed Fast dual carriageways, part single carriageway (approx 5 01 50) 65 km/ hr hmit Out of Leeds

2

D2/D3 AP

limited access 80 km/ hr hmit 3

4

8

9

10

D2/D3 AP

25

250

500

15

No major intersections

65

0

2000

47

less than 1 intersectton per km

65

0

1700

21

1-2 major intersections per km

65

0

1200

20

no capactty restramt

Jurisdictron codes l-6 apply to urban roads, 7 -9 apply to suburban roads. *M = Motorway; D, = dual two lane carriageway; AP = All-purpose; S, = smgle two lane carrtageway.

2.3.

MODEL

OUTPUTS

The model as programmed produces a great number of outputs and the mam ones are listed in Table 7. Notes following the table give further information on the outputs where appropriate. The table shows the range of indicators and outputs available to us but it will be appreciated that we can present here only those which are of strict relevance to the task in hand. The choice of indicators for this sensitivity analysis project is detailed m Section 4.1. The columns in Table 7 indicate that outputs can be presented for the entire system, for zonal groups, for individual zones or for each link in the networks. In the case of outputs presented for zones or groups of zones we can express them from the point of view of the zone as an origin or as a destination. We choose to express some of the outputs for groups of zones in

166

Progress in Planning

TABLE 7. Model Outputs Availability

Variables are defined in Table 1 Subscript i indicates avadability per origin Subscnpt j indicates availability per destination

z

i

Ji

j

I

Network usage kn 1 Link flows by mode and person type Fr 2

Lmk speeds by mode df/$

3 Usage of specified links (see footnote a) hnks (where Ff > capacity)

4

Overcapacltated

5

Mean speed travelled on links with capacity restraint J

qF{*d;/qF;*tj

Trips and tnp ends 6 Trip origins by mode and person type Of’ 7 Trip destinations 8

9

kn by mode and person type Di

Trips by mode and person type l-% m column A we can dlstmgulsh between bus and tram%tps)

J

J J

J

J

J

J

J

Route characteristics of specified tnps by mode k b)

(see footnote

J

J

J

J

J

10 Choice modal split T/J! /TG’

J

J

J

J

J

11 Total modal split Ty /G*

J

J

J

J

J

J

J

Expenditures and costs (see footnote c) 12 Interaction costs by mode c$ 13

InteractIon distances by mode d$ (with differentiation between bus and train)

J

J

14

Interaction pubhc transport faresfo (with differentiation between bus and tram)

J

J

J

J

15

Behavioural expenditures by mode and person type (with differentiation between bus and tram) 7-k” cik 21 Y 16 Expenditure on car runnmg costs Ti* rg 17

18

J J

Expenditure on pubhc transport fares by person type (with dlfferentlatlon between tram and bus) qnflj Distance travelled by mode and person type (with differentiation between train and bus) 7% dk Y

II

J

J

19 Parkmg charge revenue T;

20

Mean expenditure by mode and person type z T&“&Z TIf” 1J

21

Mean expenditure

IJ

..

dk car rum&

1J

22

J

J

J

J

J

J

J

J

J

J

J

J

J

J

J

costs

Z T:; rijl? T; Ii

J

J

J

o;

P

Mean expenditure on public transport fares by person type (with differentiation between bus and train) x T,yfiilF Tly 0 0

J

Transport Modeling:

167

Sensitivity Analysis and Policy Testing

23 Mean distance travelled by mode and person type (with differentiation between bus and trainf J

J

J

J

J

J

J

J

J

J

J

J

d

J

J

24 Mean in vehicle times by mode and person type (mterzonal trips only)

25 Mean excess costs on public transport (differentiation walking and w~t~g) (interzonal only)

between

Accessibiiities (see footnote df 26 Hansen type accessibiiities (E& J

J

J

J

J

J

J

27 28

Accessibility of people with cars available to job opportunities 114; Accessibility of people with no car available to Job opportunities l/4!

29

Aceessibllity to labour from employer’s point of view l/B,

30

Accessbility advantage of car-availablepersons available-persons Af 0; -x0;

31

1

J

J

J

J

J

J

J

over non-car-

0; J

J

J

J

J

A; 0;

Accessibility to jobs relative to accessibility to labour Bi/(Af + A;)

Benefit measures 32 Consumer surplus benefit by person type (see footnote e) J z: (?‘p (old) + Tp 2 fjkn 33

(new)) X (et (old) - c$ (new))

J

JJ

J

Consumer surplus benefit based on balancing factors from the distrr~utlon model (see footnote r) 1 z 0;’ pl i

loge (4: (oldYAr! (new)) +

1 z 0;” loge (A; (old)fAf p2 i

(new)) +

2 L: Dj log, (Bi (old)/Bj (new)) P’ +P2 i 34

J

J

J

J

J

J

J

Consumer surplus based on balancing factors from the distribution model (see footnote g) l&l

-!. T@ bg, (A? (old) x BI (old)/A/r (new) X I$ (new)> a” I1

168

Progress in Planning

Footnotes for Table 7. a. A special routme draws a map of all the links used by traffic which uses a specified duected lmk (or a set of specifted drrected lmks) m the private or pubhc transport network and annotates those lurks wtth the flows of that traffic. It is also possible to draw a similar map for traffic arrsmg from mteractrons which use a specified link or set of lmks in another model run (e.g. a run m which a drfferent runmng cost has been specrtied). b. With this form of output we are able to specify a zonal interaction and output will be produced describing the links used, time taken, costs mcurred and flows encountered in making that interaction It wtll be appreciated that this output is of particular Merest when we wish to compare the characterrsttcs of an interaction under two different pohcy scenarios. c. Note that, unless stated to the contrary, the systemwtde expenditures and their components (time, distance etc ) have been calculated to mclude the mtrazonal expenditures which were calculated by a special routine. d. Of the accessrbihttes listed here tt wrll be apparent that the Hansen type accessibrhttes do not take account of the effects of competitton while outputs 27-31 do It is important to note however that due to the existence of an arbttrary multtpher, these accessibilities dertved from balancing factors can be interpreted only in relative terms (e.g. zone A relative to zone B); the absolute values of these accessrbrhtres do not have a ready interpretation. This 1s particularly true of output 31 where no sigrufrcance at all can be attached to the absolute value of the mdrcator. Note also that output 31 might be interpreted as a measure of the value to be placed on extra labour m the zone m question. e. This benefit measure 1s simply the “‘rule of a half’ apphed to the 6 matrix It mvolves a linearity assumption which breaks down for other than small changes of the system f This 1s an approxrmatron to the consumer surplus mtegral

The thrrd term 1s only accurate when pi = p* . Benefit 1s divided into three types. (1) Benefit at the origin for persons of type 1 (fnst term); (2) Benefit at the origin for persons of type 2 (second term); and (3) Benefit at the destination for both person types (thud term). The formula IS only meanmgful when there has been no change 1110: or Dj between (old) and (new) The apportronment of benefit between origins and destinations depends on the mitral values assumed for A? and B, m the distribution model and 1s therefore arbitrary. g This 1s another approximatron to the consumer surplus integral. It gets over the problem of apportionment of benefit between origin and destination by workmg out benefits for each mteractron but rt 1sdependent on the 0: and DI remammg constant.

zonetypes

FIG. 3. Categorisation of zones in the study area.

Transport Modelling: Sensitivity Analysis and Policy Testing

169

order that more general conclusions might be drawn than would be possible in the case of outputs expressed for individual zones because results for individual zones, though interesting, may be ~~uenced by local factors which are not of general app~cabili~ outside West Yorkshire. The zonal groupings are: (1) Central Leeds; (2) Suburban Leeds; (3) Medium sized towns of the West Yorkshire conurbation; (4) Rural zones and free-standing towns; and (5) Major towns (other than Leeds) in the conurbation. These five zonal groupings are illustrated in Fig. 3. Computer programs have been written which compare the outputs resulting from different model runs and calculate the absolute and percentage differences between them. Other programs can plot these differences, or the original values, in order that the spatial expression of the results can be made evident. Induces in column C of Table 7 (relating to individual zones) are plotted using the SYMAP or SYMW* packages (see Muxworthy, 1972) while indrces in column D (relating to links) are plotted using our own graphical display programs more fully described elsewhere (Bonsall er al., 1976).

2.4.

THE

FOR

POLICY

USEFULNESS AND

OF SENSITIVITY

THE

MODEL

IN

TESTING:

ITS SOME

PRESENT

FORM

QUALIFICATIONS

The model as used has a number of features which would have been avoided if better data and more resources had been available. We had to rely totally on secondary data and consequently had no observed trip matrices for purposes other than the journey-to-work. The prediction of trips for other purposes could therefore not be properly tested. We drd not feel confident enough to include untested predrctrons and consequently we ignore journey purposes other than work. The West Yorkshire Study Area, to wfuch all our predictions related was arranged to have a finer zoning system (and network) in Leeds than in other parts of the county. The coarseness of some of the zones outside Leeds means that great care must be taken with predrctrons relating to these zones. The study area does not have any external zones and although only 6% of the observed 1966 journey-to-work trips m the study area involved external zones care must be taken to recogmse the consequences of this omissron particularly for the peripheral zones. There were a number of approximations within the model itself. Certain global averages were assumed which are in practice subject to variation by mode, zone or person type. These included car occupancy, value of time, trip rates, perceived running cost per vehicle mrle and the proportion of morning peak vehicular traffic which IS taken up with the journey-to-work by car. Of these all but the value of trme and runnmg costs were assumed not to change over the period 1966-198 1. We had no realistic way to model journeys which took place withm a smgle zone. Firstly the network structure was not fine enough to grve dnect estrmates of mtrazonal costs and SO these had to be approximated from interzonal costs of travel to nerghbouring zones using a special program (see Section 2.1). Secondly we made no attempt to model anything other than motor vehicle traffic and so ignored walk and bicycle trips which would be mostly intrazonal. Of obvious relevance to sensitivity analysis is the degree of model convergence attamed, because elasticities and sensitivitres can only be calculated to an accuracy commensurate with that convergence. Appendix 3 gves some detailed results of the levels attained but it is sufficient, in the current context, to say that our convergences were generally good and that, as a result, we can usually quote elasticities to within confidence limits of substantially less than 1%. Note, however, that the detailed assignments predicted by the model are certainly affected by this problem of convergence and also by the coarseness of the network. The coarseness of the network is particularly marked outside the Leeds area and among the ‘notional’ links which load the traffic to and from each zone centraid through, typrcally, one or two nodes of the road network. Capacity restraint techniques were applied only to the links u-rthe Leeds area and even there, the feedback of congestion effects onto bus journey times was not incorporated. We assumed *aveloPd

by the Laboratory for Computer Graphics, Harvard,

USA

170

Progress in Planning

the constancy of calibrated parameters, for both generation and distribution and modal spht, between the calibration year of 1966 and the forecast year of 1981. This was the basis for the MLF estrmates, though all these parameters were, of course, varied as part of the sensitivity testing process. In spite of these shortcommgs, we feel that the MLF prediction described in Section 5 below 1s likely to give a reasonable description of the character of transport patterns in a large conurbation. But most attention should be paid to the general character of the results, they should not be seen as a detailed prediction for the West Yorkshire area.

CHAPTER

3

The Choice of Parameter and Model Form Variations to be Examined 3.1.

INTRODUCTION

The choice of tests reflects our aim to investigate systematically the sensrtivrty of model predictions to changes under three major headings. These are: (a) transport and land use policy; (b) exogenous variables whose values may be expected to influence the transport system; and (c) modifications of the basic model structure. There IS appreciable overlap between these areas of interest but it seems useful to draw the mam distmctions between them and we have therefore maintained the distinction throughout this account. The notes in Section 2.2.2, have indicated how the values of the various inputs were derived for the MLF prediction and the structure of the model used in that prediction was described in Section 2.1. Below (in Sections 3.2 to 3.4) we indicate the reasons for choosing to run particular tests of variation in parameter values and model form. Table 8 contains a catalogue of the resulting set of tests. TABLE 8. Tests carried out for comparison with MLF Parameters whose values are modified (ref. Table 2)

Symbol USdin

Details of variations actually investigated

Type of test Land use mputs

Offrcral land use plan Decentralisatron of Jobs from central Leeds

Network characteristics The TPP network Park and ride in Leeds Private vehicle running costs

The do nothing network

section 6

1,2,3,4,5 5

13 13 13

Zero runnmg costs 0.5 X MLF costs 2 x MLF costs 3 x MLF costs 4 x MLF costs 10 x MLF costs

F

15.3

Parkmg charges rn Leeds

Zero charge 2 X MLF charge 4 X MLF charge

G

14

Pubhc transport fares

Zero fares 0.75 X ML< fares 2.0 X MLF fares 4.0 X MLF fares

H

15.4

Time spent walking to public transport

0.5 X MLF values 1.2 X MF values 2.0 X MLF values

I

13.4 or 15.6

Time spent waiting for public transport

0.5 0.8 1.2 2.0

X MLF X MLF X MLF X MLF

values values values values

J

13.4 or 15.6

Trme spent travelling on public transport

0.5 0.8 1.2 2.0

X MLF X MLF X MLF X MLF

value value value value

K

13.3 or 15.2

171

172

Progress in Planning Mean car occupancy level (1.2 m MLF)

Car occupancy = 1 Car occupancy = 2 Car occupancy = 4

L

15 3,15.7,19

Behavtoural value of time

0.5 X MLF value 0 9 X MLF value 1 1 x MLF value 2.0 x MLF value

M

15.3,15 4,15.7

Design year real income wtth correspondmg changes m value of time

0.5 x MLF value 0.9 X MLF value 1.1 X MLF value 2.0 X MLF value

N

11,lS

Design year real mcome without correspondmg changes in value of time

0 75 0.87 1.06 1.34

value value value value

0

11

Design year real car prices

0.49 X MLF value 0.8 X MLF value 0 96 X MLF value 1 .12 X MLF value 1.25 X MLF value 2 09 X MLF value

P

12

Trip rates of highest income category

0 5 X MLF value 2 0 X MLF value

Q

9

Base year income of zone 17 (planned council housing expansion)

0.7 X MLF value 1.3 X MLF value

R

8

0.5 0.9 1.1 20

X MLF X MLF X MLF X MLF

value value value value

S

18

Deterrence parameter of people without car available (p2 )

05 0.9 11 2.0

X MLT X MLF X MLF X MLF

value value value value

T

18

Both deterrence parameters

Wytconsult values @’ = 1.810 X MLF value) (p* = 1.214 X MLF value)

U

18

Modtficatton of trip generatron submodel

Damped category analysts

V

Modtftcatron of trip drstrtbutton and modal spht submodel

Post distribution split

W

Modification of treebutldmg submodel

Burrel type

X

Modrfrcatton of assignment submodel

Dial type No capacity restraint

Y Z

Deterrence parameter of people with car available (p’ )

3.2.

THE

POLICY

X MLF X MLF X MLF X MLF

modal

3,15.4,15.7

TESTS

These tests reflect policies which, for various reasons, are of current interest. The choice was, however, constrained by the limitations of the model as descrrbed in Section 2.4. The distribution of populatron and employment is of major policy importance and one test relates to the “official land use” policies of the constituent authorities of West Yorkshrre (this land use pohcy 1s described m greater detail elsewhere (Bon&l er al., 1976)). However this policy does not differ from that of the MLF m any systematic manner and this makes interpretation rather complicated. We chose, therefore to run a simpler test of land use change reflecting the current planning debate on the dominance of Leeds in West Yorkshire. thrs is a test of decentrahsatron of employment from Central Leeds. The provision of roads is a live issue m West Yorkshire and we felt rt Important to examine the rnfluence on the model results of the network structure. For thus purpose we used three alternative network options. (a) a “do-nothing” option, representing the road system as it had

Transport Modelling: Sensitivity Analysis and Policy Testing

173

been in 1966 (that is, prior to the major motorway schemes): (b) an option contaming all the major schemes set out in the 1974 TPP document (West Yorkshire MCC, 1974); and (c) tests of local “Park-and-Ride” schemes in Leeds, representing, perhaps, a more realistic, low cost alternative given the current economic climate. Recent years have seen large changes m the costs of transport, both public and private and it is likely that more changes will occur in the near future (see Department of the Environment, 1976). We therefore felt it important to test the model under variations in the more obvious components of the transport cost, such as car running costs, parking charges and public transport fares. We decided to explore the effect of variations in the perceived duration of waiting, walking and in vehicle times for public transport since these clearly reflect the level and quality of the service and the level of provision of this servrce is a contmuing matter of current debate (see Department of the Environment, 1976). A test of the effect of changing car occupancy has been included since this is now being seen as a potentially cheap and effective method of reducing congestion and saving energy. The pohcy tests which we have therefore decided to run are those listed A to L m Table 8. Tests A, B, C, D and E require further explanation and this is grven below: Test A : This land use policy was defined during the earlier part of the project and is fully described elsewhere (Bonsall er al., 1976). It should be noted that this pohcy is an amalgam of the policies of the constituent authorities of West Yorkshire prior to reorganisation of local government and does not reflect a co-ordinated policy as might be expected in a structure plan. Test B: This policy involves the dramatic relocation of one third of central Leeds employment in an industrial suburb of Leeds (Hunslet) and the relocatron of another third in an adjacent town (Horsforth). Test C: This network was constructed by subtractmg from the MLF network all such lmks as represented roads built after 1966 and modifying other lurks to their 1966 status. A fuller description of thus network can be found elsewhere (Bonsall et al., 1976). Test D. This network was constructed by addmg into or modifying the MLF network to include all major road schemes mentioned in the Transport Polrcres and Programme (TPP) produced by West Yorkshire Metropolitan County Council (1974). It should be noted that this was the first TPP to be produced after reorgzmsation and as such did not represent a totally co-ordinated policy - rt even included varrous schemes which were mcompatrble and as such should not be represented as an optrmal drstribution of resources. Test E. This test simulated a “Park and Ride” scheme by mcluding in the private network a special link from the car park to the centre of Leeds. The costs associated with the lmk being based on the distance travelled and an average speed of 15 mph for the service buses, a 5 minute wait m the car park, a bus service right to the city centre (leaving 2.5 minutes to the average place of work in the city centre), no park charge and no bus fare. It will be appreciated that the decision to park and ride is here simulated wrthm the route choice submodel rather than m the mode choice submodel.

3.3.

TESTS

OF

EXOGENOUS

INPUTS

These tests undoubtedly include some which might be said to reflect policy decisions taken outside the realms of transport and land use plannmg. However these tests were not specifically chosen for any policy implications which they might have, rather they were chosen because we believed that the parameters involved were important m the determination of model results and we wished to estimate the degree of this importance. We were particularly anxious to discover the sensitivity of the model output to possible error in the parameter values used in the MLF prediction. There has been a great amount of research mto the question of the appropriate value of time to be used in behavioural predictions (see, for example, Mackintosh and Quarmby, 1970) but there is still no overall agreement. We therefore decided to test the effect of varrations in the value of time on the model predrctrons.

174

Progress in Planning

Prediction of future real mcome levels is a notoriously difficult process and we therefore felt it important to discover how sensitive the model was to variations in these predictions. We also wished to investigate to what extent the effect of variation m income was dominated by the corresponding changes m the value of time (taking the assumption that value of time is a function of real income). There is, similarly, great difficulty in forecasting real car price levels and we wished, in consequence, to examme how critical these forecasts might be to the model predictions. It is well known (see Pick and Gill, 1970) that one of the drawbacks of the standard category analysis model as described in Section 2.1 is that since the population “migrates” through the categories, it is often the case that a large number of households, m the design year, fall into a category for which there was relatively little observed data in the base year (this is particularly true for high income categories). We therefore chose to investigate variations in the imputed trip rates of the highest income category. It can be similarly argued that since the standard category analysis model assumes that the characteristics of the population of a given zone in the design year will reflect its characteristics in the base year then it will not adequately cope with land use changes which will manifestly change the characteristics of the zonal population (such as the building of a large council housing estate). In order to investigate the importance of this effect we ran tests which varied the base year income of a zone in which a large council residential development was planned. The fundamental parameters of the distribution and modal spht model as described in Section 2.1 are the deterrence parameters 0’ and 0’. This is not the place to enter a debate on the constancy of such parameters values through time, suffice it to say that although the MLF values for these were taken from the calibration run we felt it imperative to test the effect of varying such important parameters. The tests of variation in exogenous inputs which we have therefore chosen to run are listed as tests M to U in Table 8. Note that test U makes reference to “WYTCONSULT betas”. These are the deterrence parameters used in the initial stages of the WYTCONSULT study of West Yorkshire (WYTCONSULT, 1975). The values used were /3’ = 0.01 and /I2 = 0.0075 (after adaptation to our cost units).

3.4.

MODIFICATIONS

OF

MODEL

FORM

The research project, of which the work on sensitivity analysis is a part, has resulted in the development of a number of alternative versions of the submodels described in Section 2 .l . Given the existence of these alternative submodels we wished to take the opportunity to examine their effect on the model outputs. Details of each of the tests are given below. Our variation on the category analysis submodel is a response to the criticism that it is unrealistic to assume constancy of trip rates for a given category. We term it a damped category analysis model. Our variant of the joint distribution and modal split submodel as described m Section 2.1 is a post distribution modal split submodel. Finally, we have experimented with a number of variations within the treebulldmg and assignment sections of the model. These have been a Burrel-type tree burld, a Dial-type assignment and an assignment without capacity restraint. (This last test being particularly important because of the uncertainty about the validity of the DOE speed flow curves.) The modifications of model form which we have chosen to test are listed as tests V to Z in Table 8. Further information on each of these tests is given below: Test V: The damped category analysis model adopts the simple assumptron that the total number of trips generated m a given zone should be set equal to the average of two numbers. (a) the number of trips generated m that zone under the full design year assumptions; and (b) theanumber of trips generated from the design year land use for that zone but with the base year values of real income and car prices. This calculation reflects the hypothesis that those members of the design year population who have moved from one household category to another between the base and design years have a trip rate which 1s the average of the trip rates for the two categories. It has been said that the correlation between household category membership and trip rate arises from social group as

Transport Modelling: Sensitivity Analysis and Policy Testing

175

well as the economic characteristics of the household. In that case one might expect less change in overall trip rate in response to an overall increase in incomes and decrease in car prices than is given by the MLF generation model. Test W: The post distribution modal split model separates the calculation of modal split from that of distribution and modal split parameters h and 6 are then calibrated independently of the distribution model. We then have (3.1.)

(3.2.)

(3.3.)

c; = c?. ‘I

(3.4.)

where A: and Bj are balancing factors as before; T$ = the number of trips from i to j by mode k by persons of type n; Tty = Z: TV ; q = the number of trips from i by persons of k

type n; Di = the number of trips to j; c3 = the composite cost (as defined) of travel from i toj for person of type n as derived by Williams (1977); 0” = the “deterrence parameter for person of type n” (this is calibrated in the base year against mean trip cost); 6k = the “modal penalty associated with mode k” whrch is calibrated against overall modal split; X = the “modal deterrence parameter” which is calibrated against mean trip cost; and c$ = the cost of travel from i to j by mode k. Values of parameters used were 8’ = .005526;f12 = 0.006180; X = .0010875; 6 = 658.0. Test X. Our Burrel (1968) type treebuildmg involves the assumption that the behavioural cost of a link should be sampled from a normal distribution N(c,o) whose mean, c, is the observed cost of that lurk and whose standard deviation, u, is 40.75~. In our test we have substituted one assignment and capacity restraint procedure and one Burrel treebuild for the 4 capacity restraints and 4 treebuilds used m the MLF assignment convergence routine (loop N on Fig. 1). Test Y: Our Dial (1971) type assignment is of the single pass type (see Van Vliet, 1973) wherein the flow FI on a link 1 from i to j is:

(3.5.)

where: rj = the flow which is to arrive at j; L, = the set of alternative

ar = exp (0 (Pi -Pi -cl))

lurks to j,

ifP, Pj

(3.6.)

f3 = the route chorce deterrence parameter; Pi = the shortest path cost to j, Pi = the shortest path cost to i and cl = the cost of travel on link 1. In our test Y we have substituted one Dial assignment (with capacity restraint) and one shortest path treebuild for the 4 capacity restraints and 4 treebuilds used in the MLF assignment convergence routine (loop N on Fig. 1). Test Z. Our non-capacity-restrained assignment acts just as the all or nothing assignment described in Section 2.1 with the obvious exception that the times on links are not altered to reflect the flows (the link times thus remam equal to therr observed values as described u-r the

176

Progress in Planning

note on item 13 on Table 2. In our test Z we have replaced four capacity restraints and four treebuilds of the assignment convergence loop N in Frg. 1 with one assignment program. It will be appreciated that since there will be no change m the cost matrix we do not have to repeat loop M which IS the distribution and modal split convergence loop. This clearly leads to much shortened overall run time.

CHAPTER

4

Methods of Analysis 4.1.

THE

INDICATORS

TO

BE

EXAMINED

The great range of output indicators and methods of presentation which were available to us were outlined in Section 2.3 and Table 7. In choosing from these lists we have borne in mind that we are interested in the study area only as a test-bed for our sensitivity analysis at a general scale and that detailed examination of the effects of a given policy on a given zone or link would usually be out of place. We therefore concentrate on indicators in columns A and B of Table 7, though occasionally we do draw from columns C and D when appropriate.

4.2.

THE

COMBINATORIAL

PROBLEM

Sensitivity analysis and policy investigation is essentially a multi-dimensional exercise: that is, we would wish to sample the parameter space as comprehensively as possible. The variations in parameter values and model form which we wish to examine have been listed m Table 8. If we were to investigate all possible combinations of values given in that table the required number of computer runs would exceed two hundred thousand million. This is obviously not a practical undertaking! We have decided, therefore, to concentrate most of our attention on varying a single parameter at a time. we examine the effects of variation in each parameter in turn while keeping all other parameter values fixed at their MLF level. However a small number of runs representing two-parameter changes and one multi-parameter run have also been carried out and are reported on m Section 6.

4.3.

ANALYSIS

OF

SINGLE

PARAMETER

TESTS

Where possible, model outputs were calculated both as absolute values and as a percentage change from the MLF value. This facilitated the graphical plotting of the results as “percentage change in independent variable from MLF” on the horizontal axis against “percentage change m output indicator against MLF” on the vertical axis. This has the particular advantage that the slope of such a curve near the origin is the elasticity of an output indicator to the variation of a parameter, and also that curves for different indicators or runs can be plotted on the same set of axes. Two types of graph are plotted. Those in Section 6.2 take a smgle output indtcator and plot a number of curves, each one representing the effect of varying an input parameter. In this case, the directions and extents of a variety of policy or other changes on a particular output indicator can be examined at a glance. It also gives a measure of the possible trade off between different policies since often, a change m one diiection for a particular policy variable mvolves a change in the opposite direction for another. The graphs in Section 6.3 take a particular input variable and against it plot a range of output indicators. This allows the planner and the decision maker to appreciate whrch elements of a system are most sensitive to the effects of a particular pohcy or parameter change. The curves reproduced in Section 6 are based on points representing the results of tests listed in Table 8 and unless otherwise stated, we were able to draw smooth curves actually passing 177

178

Progress in Planning

through the appropriate points. We felt confident in drawing smooth curves because of our conviction that the mdrcators in question vary continuously. This conviction is of course tempered by the problems of convergence and a discussion of this point is presented in Appendix 2. The main area of interest with the graphs has been taken as a variation m the independent variable from -50 to +lOO% from MLF value although we have tested more extreme values m some cases. Such extreme values provide a preliminary explanation of corresponding pohcres and have helped m the interpolation of curves within the -50 to +lOO% area of interest. Similarly we have been able to do a certam amount of extrapolation based on deduction of the behaviour of indicators at the limits; for example we know that if the running cost of cars tends to mfinity then car usage must tend to zero. While the results of the majority of tests can be expressed m this graphical form and elasticities can be deduced from the gradients of the curves, some of the tests (predommantly the tests of vanatron of model form) cannot be located on the horizontal axis (because they cannot be seen as ansing from a continuous change from the MLF parameters and model). The results of these tests are presented as points on the vertical axis (as+m Frg. 4) in order that the influence of these tests on the model results can be compared m magnitude with other tests.

IRI ~0 3

w=-018

gradlent negative

2 = 37 8

J

= % change m test parameter from MLF value ~&A. from MLF value (20 603 m p.h ) Y = % change in XFL tL X

L

where FL IS the flow on hnk L dL is the length of link L. tL IS the time taken to traverse lmk L. Z are all road lmks m the Leeds area L

FIG. 4. Mean speed of private transport in the Leeds area.

Transport Modelling: Sensitivity Analysis and Policy Testing 4.4.

ANALYSIS

OF

TWO-PARAMETER

179

TESTS

As an example of two-parameter changes we chose a major policy test (the change to the TPP network as described in Section 3.2) and examined the effect of that network change on major indicators in the context of differing parameter values (representing differing scenarios of the price of petrol, public transport fare levels and so on) and in the context of variations of model form. These tests thus enable us to gauge the extent to which the results of a given pohcy test are affected by the form of the model used and by the scenario in which the test is made. The presentation of the results of these tests is by means of a table wherein the different effects of the network improvement on various major model outputs under a variety of scenarios can be easily compared. The results of these tests will be given in Section 6.4.

4.5.

ANALYSIS

OF

A

MULTI-PARAMETER

TEST

The tests described in 4.3 mvolve changing one parameter at a time only. It is clearly not the case that changes in the model output due to simultaneous change of more than one parameter can be exactly calculated from the results of separately changing each parameter involved since the combined influence of two or more parameters wrll be complicated by the interdependence of the various components of the model. A combination of public transport fare increase, value of time increase and public transport waiting time (H, 3 and M in Table 8) was taken as an example of a multi-parameter test and the results plotted in the same way as described in Section 4.3 for the single parameter tests except that in this case the horizontal axis represents a simultaneous percentage change in the three parameters chosen. On the same graphs were plotted the values wttlch would have resulted if the change in output had simply been the sum of the changes in output correspondmg to each component of the multi-parameter change. This provides the reader with an example of the degree to whrch parameters can interact with each other and the nature of this interaction. The results of this test will be given in Section 6.5.

CHAPTER

5

Description of the ML F Predictions and Comparison with the Base Year 5.1.

INTRODUCTION

The model described m Section 2.1 was run using the inputs described in Section 2.2 as being those of the MLF m 198 1. A brief summary of the model prediction is given below in order that the reader may become familiar with its main characteristics. Such familiarisation is necessary because the results of the sensitivity tests (m Section 6) are expressed and explained m relation to the MLF prediction. We also include in this section a description of the manner in which the MLF prediction (1981) differs from that for the Base Year (1966). These differences reflect the trends whrch one would intuitively expect and thus increase our confidence in the model’s predictive powers. The predictions are presented below m the order in which they occur in the table of model outputs (Table 7). But, as pointed out in Section 4.1 we are being very selective in our choice of whrch outputs to present here and we report detailed predictions only when they are of general Interest or apphcabrlity.

5.2.

NETWORK

USAGE

Comparrson of the network flows estimated for the Base Year (1966) with those predrcted for the MLF (1981) reveals a general increase in traffic on the prrvate network and a reduction of public transport usage. The varrous improvements in the private transport network appear to have diverted traffic from the roads whrch they replace or duphcate but the general increases in traffic due to increased car ownership and usage throughout the system means that the effects of by-passes and rmg roads on congestion have almost been cancelled out. The flows on some of the roads in central Leeds, for example, are almost as high in 1981 as they were in 1966 prior to the constructron of the mner ring road. The number of congested roads (where flow exceeds the Department of the Environment definition of limitmg capacity) has increased by 25% but, due to network improvements, the mean speed travelled on links in the Leeds area has rtsen from 19.7 m.p.h. to 20.6 m.p.h. Reduced public transport patronage is almost universal and appears to reflect increased car ownership rather than road improvements.

5.3.

TRIPS

AND

TRIP

ENDS

There are some 770,000 Journey to work trips predicted in the MLF and thrs represents an 8% increase on the Base Year figure. 60% of the trips are from car owning households compared with 40% in the Base Year. The percentage of trips that are by private transport has increased from 35 to 50% although the percentage of car owners choosmg to use their cars has fallen from 86 to 83%. Table 9 shows trap end information by zonal category. From this table we deduce the relatrve importance of the five zonal categories m the MLF and note that category 3 is the most important u-r terms of both orrgms and destinations. We also note that category 1 is very much 180

Transport Modelling: Sensitivity Analysis and Policy Testing

181

dominated by its destinations and that its level of car availability is by far the lowest of the five categories. We note in contrast that category 2 has twice as many origins as destinations and that category 4 has the highest car availability.

TABLE 9. Trip ends by zonal category: MLF and Base Year (Base Year values in brackets.)

1 (Central Leeds)

2

0.09 (3)

2 (Suburban Leeds)

19

3 (medium conurbation

37

10 34

(0.28) 1.39 (0.64)

(1.95) 1.44

1.10 (1.40)

(27)

(37)

(0.79)

towns) 20

26

4

(rural areas and free standing towns)

hrgc conurbation

1.97 (10)

(20)

0.65 (0.20)

l6 (17)

(21)

16

20 (19)

2.18

1.30

0.80 (28)

(1.04)

(1.17)

(18)

1.22 (0.70)

(0 60)

towns

*For map of these groupings see Fig. 3.

By companng the MLF values in Table 9 with those for the Base Year we note the trip origin shift towards the rural zones and freestanding towns (category 4) and away from categones 5, 1 and 2. We also note the shift in trip destinations within the conurbation away from the largest towns and towards the smaller ones. In addition we observe that population and employment movements have resulted in category 1 being increasingly dommated by destmatlons and category 4 being increasingly dominated by its origins. It should be made clear here that these shifts in the location of trip ends are model predictions only insofar as they represent the land use data input to the model which are based on trends derived from the censuses. By examining the modal split predictions in greater detail we found that, between the Base Year and 1981 (the MLF), the pnvate transport proportion of trips arriving in Leeds City Centre has fallen from 20 to 16%. These low figures reflect central area congestion and the fact that public transport services tend to focus on the city centre. The reduction m this already low proportion can be ascribed to the systemwide trend noted above and to the lmposltlon of parking charges. Table 10 shows the zonal category trip interactions (by mode) predicted for the MLF. From this table we can calculate that 23% of the total trips in the system occur between and within the medium sized towns of the conurbation (zonal category 3). Other important mteractlons are those within categories 4 and 5 (16 and 10% of system trips respectively). Note, however, the large number of trips by public transport to central Leeds (1) particularly from suburban Leeds (2). Comparing Table 10 with a similar one (not shown) relating to interactions in the Base Year we note a large increase in private transport trips between and among the medium sized towns of the conurbation and a substantial reduction in public transport trips most significant within the large towns of the conurbation.

182

Progress in Planning TABLE 10. MLF tnps: by zonal category 1

origin*

Destination category* 2 3 4

5

Mode of transport

1

1.7 8.1

1.0 0.8

0.7 0.2

0.1 -

0.1 -

Private Public

2

2.1 50.8

25.8 23.9

14.4 4.2

5.3 0.9

25 1 .o

Private Pubhc

3

8.7 20.7

9.7 3.8

91.7 87.9

11.9 5.2

24.4 25.0

Private Pubhc

4

5.1 9.8

7.7 1.7

2.4 7.1

66.7 57.3

13.4 9.1

Private Public

5

0.9 2.6

19.6 13.4

5.2 1.9

25.4 50.6

Private Pubhc

category

Trips are m thousands (there are 770 thousand trips in the system). *Categories as depicted in Fig. 3.

5.4.

EXPENDITURES

AND

COSTS

Table 11 shows systemwide totals of components of travel expenditure in various categones for the Base Year and the MLF. From this table we find that overall expenditure has increased

m lure with the populatron increases but there have been more complex changes m the components of these expendrtures. Expenditure on car running costs has increased by 54% in real terms whrle public transport fare revenues have fallen by 28%, the fall in bus fare revenues being more marked than that of train fare revenues. Expenditure on car running costs whrch were (in 1966) less than the bus fare receipts now (MLF) consrderably outstrip the combined receipts of bus and train services. Receipts from parking charges (which primarily come from central Leeds) are msigmficant beside these other expendrtures.

Table 11. MLF and Base Year components of travel expenditure - systemwide totals. (All values are expressed in units of thousands of 1974 pounds.*) Base Year 1966 &I NXlllillg COStS Bus fares Tram fares Total fares Parking charges Total general&d

expenditure

MLF 1981

39 44 14 59 -

60 31 11 43 4

274

294

*Throughout this work comparisons and conversion of currency from different years are based on the value of time (see Section 2.2), which reflects mean household income, rather than retail price.

Table 12 shows the systemwide mean behavioural expenditures in units of generahsed cost for the Base Year and the MLF. From this table we find that pnvate transport trips have a generahsed cost less than that of public transport trips and that, consequently, trips by people with cars avarlable are, on average, less costly than those of people without cars available. (Note that these generalised costs are as defined m equatron 2.10 and include time as well as monetary expenses).

Transport Modelling: Sensitivity Analysis and Policy Testing

183

TABLE 12. MLF and Base Year mean behavioural expenditures on travel: systemwide. (Cenerahsed costs expressed in units of 1974 pence.*)

All trips by private transport All trips by public transport All trips by people with cars available AU trips by people without cars available Au trips (mean cost of travel in the system)

Base Year 1966

MLF 1981

31.2 42.5 32.9 42.4 38.5

32.3 43.8 34.6 43.3 38.2

*Throughout this work comparisons and conversions of currency from different years are based on the value of time (see Section 2.2), which reflects mean household income, rather than retail price.

It can be deduced from Table 12 that the more costly public transport journeys are being made by people with cars avatlable. Compared to the Base Year we note that the MLF values show an increase in the mean perceived cost of all sub-categories of trips in the system. This can only be explained by the change in land use (the MLF land use being much more dispersed than that of the Base Year), because both private transport running costs and public transport fares per unit distance have fallen in real terms. The fact that the mean cost of travel m the system has fallen while that of all of the sub-groups has risen is due to the increased proportion of trips falling in the cheaper private transport sub-group. From examinatron of the predicted mean trip lengths travelled by car, by train and by bus, we note that mean tram journey length (7.5 miles) 1s greater than the mean car journey length (5.7 miles) which u-r turn is greater than the mean bus journey length (3.4 miles). Note that car-available-people travel further on both public modes than do non-car-available-people. These relationships are reflected m the fares pud. We note that all categories of trips are longer u-r the MLF than they were in the Base Year and we take this as a reflection of the facts that travel costs per unit distance are lower, relative to income, in the MLF and that the land use 1s more dispersed. Table 13 shows the cost breakdown of mean interzonal trips predicted for the MLF. From this table we notice the dominance of car running costs m the perceived cost of pnvate transport and the dominance of excess times in public transport. We find that the perceived costs of walkmg and waitmg make up 50% of the total perceived costs of pubhc transport. Furthermore, it must be remembered that the proportions quoted in Table 13 refer only to mterzonal trips and we would expect that the excess time component of intrazonal trips would be even higher than 50%.

TABLE 13. Components of the mean trip cost for the MLF. (As per cent of total mean trip cost.) a. Pnvate transport trips m vehicle time running costs excess time parking costs

% 32 48 17 3

b. Public transport trips in vehicle tune fares paid walking tune waiting tune

23 27 35 15

Given these statistics for the MLF (those for the Base Year were similar) we can speculate on the results of the sensitivity analysis to be reported m Section 6. We would for instance expect a given proportronal change in fares to have less effect than the same proportronal change in excess times -but this issue must await further enlightenment in Section 6.

784 5.5.

Progress in Planning ACCESSIBILITIES

Table 14 shows the Hansen accessibrlitres for the zonal categories (output number 26 in Table 7). From this table we deduce-that the Leeds suburban zones (category 2) are the most accessible zones especially for access to jobs and especially for car-avarlable-persons. We also find that the large towns of the conurbation (category 5) are the least accessible places for people with a car available while the rural zones and isolated towns are worst for non-car owners. The changes from the Base Year pnmarily reflect the land use changes noted u-r Section 5.3. As we would expect, a similar table showing the accessibilities with account taken of competition (outputs 27,28 and 29 m Table 7) show a much more even distributron of accessibilitres than those in Table 14.

TABLE

14. Hansen accessibilities by zonal categories in the MLF and Base Year. (See output number 26 in Table 7.) Zonal categories+ 1

Hi**l

2

462

781

114

123

*1

H*j

125

H%j

*z

67

449

12

23

437

31 (19)

24

208

(22) 61

(112) 8

(26)

(153)

(13)

(248) 25

(41)

152 (213)

(46)

(277)

(84)

5

258 (612)

(101)

(low

4

707 (844)

(536) Hi**2

3

(47) 8

(7)

(10)

Upper figures refer to the MLF; Figures m brackets refer to the Base Year *Categories are as depicted in Fig. 3.

When we examme the accessibrhty advantage of car-available-people (output number 30) we find it most marked in the rural areas where public transport is poor, and least marked m central Leeds and the large towns of the conurbation. These advantages are less marked than they were in the Base Year due to the greater number of people with a car available competing with one another in the MLF. When we examine the ratios of accesstbihty to jobs over accessibility to labour we found that the zonal categories are ranked 1, 2,3,5,4 with category 1 being the most accessible to jobs and 4 being the most accessible to labour. This reflects the land use pattern given m column 3 of Table 9 as modified by competitron. It implies that, m terms of accessibihty criteria alone, housing estates would give the greatest benefit if sited in central Leeds and least if sited in rural areas or (surpnsmgly) the larger towns of the conurbation. It 1s interestmg to note that while the MLF rankmgs are the same as they were in the Base Year the reduced population in central Leeds has increased the benefit to be derived from extra houses in that area. This completes our summary of the model’s predrctrons for the MLF, rt IS hoped that the reader now has a context m which to view the results of the sensrtivrty tests to be given rn Section 6.

CHAPTER

6

Results 6.1.

INTRODUCTION

This chapter is divided mto four sections which present the results of our explorations. In Sections 6.2 and 6.3 the results of our single-parameter tests (by indicator and by test repectively) are examined. Section 6.4 deals with the results of the two-parameter tests and 6.5 the test in which we varied several parameters simultaneously. Throughout this chapter we attempt to be selective in the detail we present, trying to bring the readers’ attention to those aspects of the results relevant to sensitivity analysis. Having pointed out the main features we then give an explanation or interpretation of the causal mechanisms where appropriate. In plotting the curves, we have, as indicated in Section 4.3, made best use of the points available to us and any extrapolatron is indicated by a broken line. Where two or more curves run together at the edge of the graph we list their code characters, as defined in Table 8, together (thus: J, L). In some cases the change in an output indicator due to change m a particular mput parameter 1s so small as to be comparable in magnitude to the convergence errors associated with that output indicator (see Appendix 3). In such cases the values for that parameter have not been plotted on the graph for that output indicator but the maximum change and probable gradient for output have been noted at the bottom of the figure. Srmilarly where a discrete test causes a change in an output indicator not within the scale of the appropriate graph the change is noted at the bottom of the figure.

6.2.

SINGLE-PARAMETER

TESTS

-

BY

INDICATOR

In the following subsections we describe the important features of the accompanying graphs as they appear. There are, however, a number of features which are common to all graphs and they will be reserved for Section 6.2.15. Also reserved for Section 6.2.15 is Table 16 giving the elasticities at the origin for all curves in this section. This table should be referred to rf the reader wishes to quantify the curves in Figs. 4-l 7. 6.2.1. Mean Speed of Private Transport in the Leeds area Results for this indicator are given in Fig. 4. This indicator was found to be prone to poor convergence (see Appendix 3) and as a result we have had to take some liberties in the drawing of these curves m order to make them pass through the origm’ Therefore, whrlst the general form of the curves ts considered to be correct the values and gradients near the orrgin cannot be regarded as being highly stgnificant. Many curves, in particular (J), showed a tendency to adopt inflections around the origin. Since most tests including (J) were concerned with only the top end of the speed flow relationship on most links, it is difficult to explain thus phenomenon other than by a lack of convergence. Unfortunately trme and resources did not allow a proper investigation of this point. It is disturbing to note that three of the largest changes from the MLF mean speed (20.603 m.p.h.) are due to changes in model form (X, Y, Z). Other large changes (L, N, 0, P) are clearly runs which will produce a large change in modal spht. Also note that changes in generalised cost parameters for both modes (H, I, J), and in the deterrence parameters for both the person types (S, T), all produce mean speed changes of the same order. 185

186

Progress in Planning

It IS useful to compare this graph with the results obtained for congestion rehef gven m Table 15. It can be seen that the values obtained there do, m general, correspond with the ordinal range of gradients at the origin of the current graph. Notlce the effect of the alternatlve networks (C, D) both of which include dramatic changes m the Leeds area.

TABLE 15. Rates of congestion relief Thousands of minutes of generalwed cost per percentage change

(rate of congestron relref)

Parameter (I)

Car runnmg cost (F) Zone 1 parking charge (G> Public transport fares (H) Car occupancy(L) Value of time (M)

Design year real income with no change in VOT (0) Design year real car prices (P) Trip rate of highest income category (QI Design year mcome of zone 17 (RI

-77.66 -2.63

80.80 3.05

0.0

0.0

0.0 0.0

-58.96

0.0

58.47

DO

-0.49

-86.10 -86.10 0.0

0.0

- 38.47

0.0 0.0

5.31 -2.21 -6.53

91.47 142.36 11.36

0.0

17.89

3.14 0.42

-4.50

00

0.0

-9.93

5.43

1276

0.0

0.0

14.18

-1.42

0.0

0.0

0 130

0.227

-0.097

6.2.2. Private Tra~s~art Trips from ~ab~rba~ Leeds to Central Leeds Figure 5 grves the results for this indicator The trips tn question are those from zonal category 2 to zonal category 1 as defined m Fig. 3. The strongest effects are due to changes m origins and destmatlons caused by the tests B, N, 0 and P. Next m effect come some tests that directly affect travel cost G, H, I. K and L. Notlce that although pnvate transport runnmg cost (F) might be expected to be at least as effective as any of these it appears that it causes two opposite effects which cancel out near the origin The negative effect is presumably due to increased general~sed cost of private transport deternng pnvate transport tnps whereas the decrease m trips to central Leeds for low runnmg cost is perhaps due to car-avalable-residents of Leeds suburbs being able to take advantage of reduced costs to travel to Jobs in other towns without a significant fixed car parking charge. The deterrence parameters j3’ and j3’ (S, T) also have a sqruficant effect. Note that although there is a large (20.8 minutes generahsed cost) parkmg charge m Leeds CBD (zone 1) proportionate changes m this (G) are less effective than proportionate changes in public transport fares (H).

6.2.3. Public Transport Trips from Suburban to Central Leeds Figure 6 shows the pubhc transport version of Fig. 5. As for private transport, the tests B, N and P have a large effect. Real income (0) has less effect on this indicator than does car price (P). This is despite the fact that an increase m real income has the same effect on car avallablhty m the category analysis model as a decrease by the same factor in real car prices. The difference arises from the increase in trip rates which is caused by shifting people mto higher Income categories m the category analysis model. The value of time (M) is much more Important than for private transport. Whereas car runnmg costs (F) have a virtually linear effect pubhc transport fares (H) and the non-car avadable deterrence parameter (T) show the reversal

Transport Modelling: Sensitivity Analysis and Policy Testing /N ,I-

*J -S -L _--________---

J.’

:

Ii

-R +

/1

‘G

L

S

I\&L^_

x

y

n_nn

*__*_

I_I = % change in test parameter from MLF value. = % change m Tli” from MLF value. (20,874) where i is all zones m category 2 (suburban Leeds) j IS all zones m category 1 (central Leeds) FIG. 5. Private transport N

trips from suburban Leeds to central Leeds Y

20

Other x

y

tests

0= -49

22

IRI < 06

prodlent

negotwe

= % change in test parameter from MLF value = % change m Ti;” from MLF value (50,765) where I is all zones m category 2 (suburban Leeds) j is all zones in category 1 (central Leeds)

FIG. 6. Public transport

tips from auburban Leeds to central Leeds

187

188

Progress in Planning

effect that car running cost did in Section 6.2.2. As might be expected car occupancy (L) is important. The components of public transport generalised cost (H, I, J, K) appear to be comparatively unimportant.

6.2.4. Systemwide

Modal Split

This IS shown m Fig. 7. The greatest changes are due to changes in car availabihty caused by changes in incomes and car prices (N, 0, P). Next come changes in car running costs (F), car occupancy (L) and the components of public transport generalised cost (H, I, J, K). These affect modal split through changing the difference in generahsed cost between the two modes. Value of time (M) has much less effect since it changes the generalised cost of both modes by about the same amount but increasing it slightly favours private transport since this 1s the cheaper mode. The deterrence parameter for people with a car available (S) has as strong an effect as the generahsed cost components mentioned above smce it causes car-available-people to be more sensitive to generahsed cost and therefore to choose to go by car. The deterrence parameter for people without a car available (T) cannot directly cause any modal switching of course. The small effect it causes is due to competition with car-available-persons.

Y

Other tests

x

E 8 0 IO x-021

Y-0 14

= % change rn t;t;?yameter

y

from MLF value MLF value (0.5009)

FIG. 7. Systemwide modal split. 6.2.5. Modal Split into Leeds City Centre The results are shown m Fig. 8. The curves in this figure are substantially similar to those for the systemwide modal split described m 6.2.4 above. We note however that the gradients are generally much steeper for trips mto Leeds City centre than they were systemwrde. We postulate that this reflects the mean length of trips into the city centre which means that

Transport Modelling: Sensitivity Analysis and Policy Testing

189

\ \

.

Ofher

tests

(RI c

I

0 gradlent paslttve

x

= % change in test parameter from MLF value

y

= % change m r

I

FT:i

z lkn

from MLF value (0.159) Ti:”

where zone 1 is Leeds City Centre

FIG. 8. Modal split

into

Leeds city centre.

changes in the various parameters (specifically the coefficients of generalised cost) act to magnify the absolute difference between the trip costs by private and public transport and since our model bases the modal choice on the absolute cost difference we find a greater modal switch in the case of trips into Leeds City centre than in the system as a whole. The most predictable difference between Fig. 7 and 8 rs, of course, the behaviour of(G) which reflects changes in parking charges in Leeds centre. Note that parking charges (G) have become a more significant determinant of the result than car runnmg costs (F). We note that the deterrence parameters (S, T) have the opposite gradients to those they had in Fig. 7. In the case of(S) which is the deterrence parameter for people with a car available, 8’ , this is because Leeds City centre is an expensive destination by private transport and therefore, although an increase in p’ will lead to an increased car usage systemwide it will cause a redistribution of private trips away from Leeds centre and thus a decrease there. In the case of the deterrence parameter for people without a car available, fl*, represented by curve (T), it is because Leeds City is a relatively expensive public transport destination and that an increase in /I* therefore causes non-car-available-people to change their destination from Leeds City (resulting in increased private transport usage there) and to concentrate on the cheaper destinations systemwide. The cheaper public transport destinations are thus taken up by noncaravailable-people making it less attractive for car-available-people to go by public transport causing, thereby, a decreased public transport usage systemwide. Note that the land use decentralisation (B) causes a reduction in modal split into Leeds City but an increase systemwide, The reasons for this are discussed in Section 6.3.2.

6.2.6. Tot@ Expenditure

on Private Transport Running Costs

The results are depicted in Fig. 9. We note the high elasticities at the orrgin of the two curves M’ and N’, depicting variations in expenditure (in money units) resulting from changes in the

190

Progress in Planning

Other

tests

E = -0 24 Ifil c 0 31 gradlent (TI c 0 6 gradlent m test parameter

positive posltwe

X=NA Y = 06 at orvgln

x

= % change

y

= % change m 2 T1;“r,* from MLF value (8.08 X lo6 n-mutes) W where r 1s car runnmg cost per trip

from MLF value

FIG. 9. Systemwide behavioural expenditure

on car running costs,

value of time. The explanation of this 1s that smce our model uses generahsed time rather than generahsed cost then an increase m the “value of time” IS more correctly a decrease m the “duration of money”. This point and the reasons for the contrary gradient when we express the indicator m time units rather than money units (compare M and M’) IS covered fully in Section 6.3 .12. The influence of changes in the deterrence parameter for people with a car available (S) is strong and contrasts obviously with the neghgible but complex effect of changes m the deterrence parameter for people wrthout a car available (T). This 1s also reflected in the discrete test U which mvolves changing both deterrence parameters. Tests mvolvmg the generation model (0, P, Q) have an important effect as do those involving the components of generalised cost for pnvate transport (F, L). The fact that the private transport running costs curve (F) reaches a maximum at about +75% is an interesting effect slmllar to the “law of dimmishmg returns” and is dealt with more fully in Sectron 6.3.6. 6.2.7. Expenditure on Public Transport Fares The results are displayed m Fig. 10. We note the Importance of the tests involvmg a value of time, it is interesting to note that in this case it is when the expenditure is expressed in time units (M, N) that the effect IS strongest (m 6.2.6 we found that it was strongest when expressed in money units (M’, N’)). We note that both deterrence parameters (S, T) are important and that for this indicator, they both act in the same directron. The high elastlclty to fare levels (H) 1s to be expected, but it 1s interesting to note the Importance of real car prices (P). 6.2.8. Mean Trip Cost The results for this mdrcator are shown m Fig. 11. We note that the value of this indicator is highly sensltlve to changes m the deterrence parameters (S, T, U) and this 1s comforting since

._

L.

-

N

E=-021 X=-O35 (Ri ~OZgrx&enen Y--O23

Y H

= % change IN test parameter from MLF value = % change m C T??f. from MLF value (5.85 X 10’ minutes) on V 11 where f is public transport fares

Other tests

M

_.

-

I

m

.

-

-

,,,

_.

_

-

._

_

FIG. 10. Systemwide behavioural expenditure on public transport fares,

x y

T

Y

x

IGI e OOSgrod~ent pos!tlve IRI c 0 01 gradtent poottlve

x=-o1

E=OO

-20

FE.

I

from MLF value (5 1.35 minutes)

II. Systemwide mean behaviourai trip cost.

‘I

E T&n

‘I

I: +,Fc (ikn ykn

= % change in

Y=O0

-----____-

c=oo

” A=-02

Y

= % change in test parameter from MLF value

Other tests

s

192

Pfogfess in Planning

these parameters are normally calibrated on time (M, N) IS, however less than comforting value. It is interesting to note m this context effect compared to that of these behavloural

mean trip costs. The Importance of the value of m view of the uncertainty about its appropriate that network changes (C, D, E) have a minimal parameters.

62.9. Ratio of the Mean Trip Costs for the Two Person Types Observe the reiationshlp between the results shown here in Frg. 12 and the systemwrde accessibility advantage of car-available-persons shown in Fig. 16. (Note that the vertical scale in Fig. 12 is more exaggerated than that in Frg. 16.) The runs tend to split similarly into two groups, those with a high elastrcrty contaming parameters wrth substantial effects on generalised costs and perceived costs (H, I, J, K, L, S and T) and those with a low elasticity containing generation model variables and localised variables (G, 0, P, Q and R). The curves showing the variation due to changes in the value of time come partway between the two.

T

y

S

JL

I

F

Other

tests

E = 0

0

IRI -Z 0 I gradtent

negottve

us371 X

=

%

v=oo X =0 0 Y=OO

1

change 1x1test parameter from MLF value

y = %change m

(.)

/

c:fifj

from MLF value (1 2519)

FIG. 12. Ratio of the mean trip cost for people with no car available to that for people with a car available.

6.2. IO. Mean Distance Travelled by Private Transport This is shown m Rg. 13. There is a clear three way grouping of the runs, Firstly we notice the large direct negative effect of changes m perceived car runnmg cost (F) and in 0’ which is the deterrence parameter for persons with a car available, (S). Similarly there is a large positive

Transport Modelling: Sensitivity Analysis and Policy Testing F

Other

S

tests

Y

II IJ 5%

LMN

I RI c 0 2 gradlent

E=-02 IGI

193

~Olgrad~entnegatm

zera

U=-343

( < 0 Pgradlent poshve X= N A I < 0 2 grodlent negatlw

change in test parameter from MLF value

X

=

y

= % changein’ -

x Tl; d,) from MLF value (5.6954

miles)

,y Tl+ FIG. 13. Mean distance travelled by private transport.

effect as a result of changes m the value of time (M, N) and car occupancy (L) which, in effect, devalue the money component for an increase m the parameter. All other effects are minimal but note the effect of generating a higher proportion of car available persons (P and 0) which produces a decrease in the mean distance. It is interesting to compare this graph with Fig. 15, the systemwide accessibility of car-available-persons to destinations, which shows a high degree of correlation for F, L, M, N and S. 6.2. Il. Mean Distance Travelled by Public Transport This is shown in Fig. 14. It can be seen that the most significant effect is that of the deterrence parameter for people without a car available (T). Next come those parameters which change the distance related items of generalised cost in public transport (H, K, N, M). Walking time and waiting time (I, J) are less effective smce they act (as do H and K) through changing the modal split, making all public transport trips less attractive, but do not especially penalise long journeys. Since only people with a car available have a modal choice, the curve showing the effect of changes in their deterrence parameter (S) displays greater effect here than that for people without a car available (T). The minimum which occurs in the S curve at about t50% 1s due to the two opposing effects of decreasing the length and number of car-available-persons’ public transport trips (which tend to be longer in MLF because 0’ is less than $) and increasing the tnp length of non-car-available-persons due to increased competition for short journey attractions, as /I’ is increased.

6.2.12. Systemwide Accessibility of Car-available-personsto Destinatkms As can be seen from Fig. 15 the variables which have the greatest effect are 8’ the deterrence parameter for people with a car available (S), those directly affecting the perceived travel cost by private transport (F, L) and those affecting the value of time (M, N). Those directly

= % change in Iln & Tin

y

-P -J

nj /-t

- a -F

,h

,F

from MLF value (3.7149 mdes)

from MLF value

/RI -= 0 05 gradlent posrtlve x=-o15 Y=-012

FIG. 14. Mean distance travelled by public transport.

= % change in test parameter

C = 0 26 D=-039 E=-014

X

Other tests

Y

X

l.,‘MN

Y ,

= % change

/

N/

--T------

t

: 4

3

8,

0

m Z Z Dj (e -O’ ‘4 + e-@ ‘b ) from MLF value (2.36 X 106) i j

from MLF value

F u=-786 W=O4 Y =0 25

N”L

S -30 E=0 5 IRI
".

20

30

1_

AnI

= % change m test parameter

I

s

FIG. 15. Systemwide Hansen accessibility of car-available-persons to all destinations.

Y

/

Other tests

\ ++.

F

Transport Modelling: Sensitivity Analysis and Policy Testing

195

affecting public transport costs (H, I, J, K) are also significant since car-available-persons have the choice of mode. Even the car parking charge, (G) although only acting on trips to Leeds City centre, has a marked effect. Those runs which affect the numbers of productions (A, 0, P, Q) would also be expected to have a direct linear effect proportional to the change in origins since the destinations are increased proportionally in each zone to match this change. This is clearly shown by curves 0 and Q. Tests involving land use changes (A, B) also change the distribution of destinations. Note that many of these effects are also reflected in the change in mean trip length by private transport (see Fig. 13) especially curves (F, L, M, N, S). 6.2.13. The Accessibility

Advantage of Gwwailable-persons

This indicator is shown in Fig. 16. Notice that the tests appear to divide into two groups, one group displaying higher elasticities than the other. lnto the first group fa! those parameters (F, H, I, J, K, L) which have a substantial effect throughout the study area on the generalised cost of travel by one of the modes, together with the two deterrence parameters 6’ and 0’ (S, T) and the discrete test U which also involves a large change in the deterrence parameters. The second group consists of those tests affecting the generation of trips (A, B, N, 0, P, Q, R) the transport network (C, D, E), the model form (V, Y), the parking charge in Leeds (G) and the value of time (M) (which has a substantial effect on generalised cost but tends to operate in the same direction for both modes). The positive slope of the graph for M reflects the higher perceived monetary cost of private transport.

F

T

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s

I

LH

K

J

8 G I

Other

tests

I

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=

y

= %changemL

F

A;Of

z Of

X -

I

z 0;

z A;O;

I

I

from MLF value (8.908)

FIG. 16. Systemwide accessibility advantage of car-availablepersons

196

Progress in Planning

6.2.14. System wide Consumer Surplus Arising from Change from MLF

Figure 17 shows the consumer surplus arising from some of the parameter changes. Those parameter tests which affect the output of the generation model (A, B, N, 0, P, Q, R and V) and of the distribution model (S, T, U and W) have been omitted since the concept of accruing consumer surplus has a different significance when there is a change in the size of the population or of the presumed process of choice of tripmaking behaviour of the population of the study area. For the same reasons, changes in the assignment model (X, Y and Z) lead to spurious changes in consumer surplus but only that arising from ignoring capacity restraint (Z) is significant. In order to measure the consumer surplus arising from a change in car occupancy (L) it is necessary to add to the values shown in Fig. 17 the consumer surplus associated with whatever is presumed to have caused the change in car occupancy. This has not been done since car occupancy was regarded as exogenous and no specific cause for the change was postulated.

Other tests

-0 08 <

E,Y,Xc

008

x

= % change In test parameter from MLF value

Y

_!_ Tkn = .z . ljkn p” ‘I

A;(MLF)

FIG. 17. Systemwide

h,

x B,(MLF)

A;xBI consumer

in millions of minutes

surplus accruing from change from MLF.

By far the most potent influences on consumer surplus are systemwide changes in the components of trip cost (F, H, I, J, K), change m car occupancy (L) which affects the monetary cost of private transport, and the value of time (M) which is in effect the reciprocal of the generalised cost of money Changmg the parking charge in Leeds City centre (G) has only local influence and 1s insigmficant systemwide. The effects of network change (C, D) are by no means as large as those caused by changes in car running cost. This is an important point in the light of the frequent use of transport models to test the effect of network change. In some cases it is possible to calculate rates of congestion relief from the rate of change of the consumer surplus measure. This is done as follows. Suppose the parameter to be changed is called I and the consumer surplus will be called S. Then by definition of consumer surplus

Transport Modelling: Sensitivity Analysis and Policy Testing

197

(6.1.)

Now c$ (the cost of travelhng from, i to j by private transport) is made up of a free-flow cost Jdwhich may be a function oft and a congestion cost, representing delays due to congestion, cr$ which is a function of the flows on the links traversed and only indirectly a function of C. The rate of congestion relief (CR) is. (6.2.)

and is therefore equal to. (6.3.) acff . 1ssimply the length of the route from i to j by

In the case of car-running cost for mstance ar

car since car runnmg cost is taken to be proportional to distance travelled and of course 1 Zk; = 0. The distance component of intrazonal trips, has to be calculated separately as ‘2, the

at

partial derivative of intrazonal private transport cost with respect to running cost. As has been said before our measure of consumer surplus (item 34 in Table 7) is unreliable as a measure of consumer surplus where a change in the output of the generation model is concerned. However it is possible to calculate the partial derivatives of the measure of surplus that we use with respect to changes in the trip origins q and trip destinations Di output from the generation model. It turns out that if the cost matrices are held constant then (6.4.) so that the rate of congestion relief may be estimated as (6.5.) Table 15 shows the calculation of the rate of congestion relief for some of the parameter tests. The answers obtained could not have been derived directly by calculating from values of 2

since the convergence of individual link flows is poor (see appendix 3) and it is impossible

to estimate a derivative at the origin. Since capacity restraint operates only in Leeds what is measured is in fact the rate of congestion relief in Leeds. Notice the small effect which the level of public transport fares (test H) has on Leeds congestion. 6.2.15 Some general comments Table 16 shows the elasticities of the output indicators considered in Section 6.2 to the parameters tested. The greatest effects seem to come from changing the deterrence parameters (S, T) and changing the components of generalised cost across the system (F, H, I, J, K, L, M, N). Systemwide changes affecting the output of the category analysis model (A, B, N, 0, P, Q and V) can also have a dramatic effect especially where the indicator reflects changes in trip making ~tribution . ln comparison, except for the mean speed in Leeds (Fig. 4), the network changes C and D had less effect than the parameter changes. The Park and Bide network (E) had very little

F

-0.05

T

0.22

-0.63 0.16 0.03 0.34

0.10

0.09 0.25 neg. 0.11

-0.04 -0.28 -0.20 -0.36 -0.16

0.01 0 09 -0.04

0.12 0.10

3

-0.01

-0.52 0.05 0.01 0.18

0.12 0.21 0.06 0.58 0.51

0.13 0.18 0.09

-0.17 -0.01

4

0.31

-0.89 0.07 -0.56 pos.

0.38 1.28 0.60 0.69 0.81

0.56 0.29 0.18

-0.33 -0.78

5

0.20 0.03 0.50 -0.36 -0.17 -0.35 -0.23 -0.81 -1.14 -0.37 0.52 0.06 neg. -0.31 -0.56 0.20 -0.14

0.13 -0.33 -0.52 0.09 0.57 -0.54 0.17 pos. -0.58 zero 0.49 1.09

7

0.42 -0.03 0.14 0.19 0.09

6

0.01 0.48 0.46 0.42 -0.03 0.03 0.02 0.00 -0.81 pos.

0.01 -0.02 neg 0.58 -0.54

-0.41 neg. 0.00 pos. neg.

10

0.07 0.17 0.06 0.06 -0.00

-0.15 0.08 0.10 0.21 0.12

9

-0.05 0.01 pos. -0.15 -0.66

-0.36 -0.06 0.31 0.19 0.05

0.03 0.02 -0.36 -0.02 -0.08

11

pos. 0.09 pos. -3.04 neg.

-0.15 0.92 1.03 1.10 0.05

-0.38 -0.09 -0.16 -0.24 -0.12

12

0 15 0 10 0.00 --2 85 4.69

0 88 0.96 0 30 0.21 -0.10

-1.05 -0.07 -0.84 1 04 0.56

13

0.05 0.13 pos. -

0.11

-0.50 0.90 1.52

-0.74 -0.03 -0.59 -0.75 -0.38

14

1. Mean speed of private transport in the Leeds area; 2. Private transport trips from suburban Leeds to central Leeds; 3. Public transport trips from suburban Leeds to central Leeds; 4. Systemwide modal split; 5. Modal split into Leeds city centre; 6. SystemwIde behavioural expenditure on car running costs; 7. Systemwide behavioural expenditure on public transport fares; 8. Systemwide mean behavioural trip cost; 9. Ratio of the mean trip cost of people with no car available to those with a car available; 10. Systemwide mean trip length by private transport; 11. Systemwide mean trip length by pubhc transport; 12. Systemwlde Hansen accessibdity of car-available-persons to all destinations; 13. Systemwlde accessibility advantage of car-available-persons; 14. Systemwide consumer surplus accruing from change from MLF (100,000’s of minutes).

0.07 pos. pos. -0.37 -0.22

0.01 -0.11 -0.12 -0.20 -0.07

0.08 pos. 0.06 0.10 0.05

8

- see footnotes

of output indicators

Output indicator

16. Elasticities

neg. - negligible and negative; pos. - negligible and positive.

-0.09 0.23 neg. 0.14

: !

0.27 0.30 -0.09 0.54 0.69

0.33 0.29 0.16

-0.11 -0.12 -0.02

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0.08 -0.26

2

0.12 0.07

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8)

Test code he Table

TABLE

Transport Modelling: Sensitivity Analysis and Policy Testing 1ABLE 17. Some results of test B % change from MLF vahre Systemwide car running expendrture Systemwrde bus revenue Systemwide train revenue Mean private transport speeds in Leeds Modal split into Horsforth Modal split into Hunslet Parking revenue in Leeds Mean cost of trips into Horsforth: by private transport by public transport Mean cost of trips into Hunslet: by pnvate transport by public transport Mean trip cost systemwide Mean trip cost systemwrde n = 1* Mean trip cost systemwide n = 2* Mean trip length by car Mean trip length by bus Mean trip length by train Accessibility advantage of persons with cars available

3.40 1.858 -26.59 -9 .o -1.38 -13.91 -71.4 12.8 22.0 6.0 2.2 -0 4 -0.8 0.0 1.23 -1.146 -6.265 10.041

*n = 1 persons with cars available; n = 2 persons without cars available.

r-7 Horsforth

FIG. 18. Map of links whose flows increase by at least 20% due to the decentralisation policy test (test B).

199

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Transport Modelling: Sensitivity Analysis and

Policy Testing

201

6.32. Test B (The Decentraiised Land Use Pi@ Table 17 and Figs. 18 and 19 show some of the results of this test. Note that the reduction in parking revenue in beds City centre (71%) is greater than the 66% reduction m trap ends implicit in this land use policy. We conclude that this rs due to the increased congestion (note 9% reduction m the mean speed within Leeds) resulting from a travel pattern at odds with the road pattern which was designed to carry traffic ra&alIy (to the city centre) rather than circumferential& (between suburbs). Figure 18 shows those links where traffic volumes have gone up by at least 20%. There is a large reduction in train revenues (26%) resulting from the fact that the rail network focuses on the city centre and ISnot so attractive a mode on whrch to travel to or wrthin the suburbs. This result IS assocrated with the increased bus revenues and the increased expenditure on petrol. The increased employment in the two suburbs (Hunslet and Horsforth) increases their catchment area and thus increases the mean cost of tnps to these zones. This increase 1smost marked for pubhc transport trips to Horsforth (22%) which prevrously had a very small public transport catchment. There is a 9% reduction in the accessibility advantage of caravailable-people pnmarily because the decentrahsation of jobs to Hunslet has proved a great benefit to the many people without cars avarlable resrdent there and who used to have to travel into Leeds. Note also the 14% reduction m the modal split into Hunslet (see Table 17). Figure 19 shows the change m the mean cost of private transport trips onginating m each of the zones of the study area. This shows the spatial expression of the effects of the land use change and shows the different sensitivities of different zones. The largest decreases occur, of course, in the two zones to which jobs have been decentralised. Large decreases are also evrdent in those zones raddly further out from the crty centre (because the journey has, as rt were, been intercepted en route. There are slight decreases m other radtally distant zones. Large increases are found in central Leeds where many jobs were previously available locally and in zones which used to be dependent on Leeds City centre but have poor communications with Hunslet and Horsforth. Other zones with poorrsh ,communicatrons wrth Hunslet and Horsforth display medium increases in mean trip cost. Very small increases are characterrstrc of the most distant zones which are httle affected by the land use change and in zone 26 where improved job opportunities in Hunslet and Horsforth and decreased opportunities in Leeds Crty centre almost cancel out. 6.3.3, Test C (The f965 reworks We do not include detailed results of this test because the pomts are covered elsewhere (Bonsall et al., 1976) in much greater depth than would be possible here and in general are similar to those in Sectron 6.3.4 below. 6.3.4. Test D (T&e TPP uncork} Table 18 shows some of the results of this test. We note the large increase in mean speed (22%) and the switch to private transport which is most marked m central Leeds presumably because of congestion relief. The switch away from public transport appears to affect trains more than buses because the new and Improved roads are prrmarily for long distance travel and trains are more sensitive to this kind of competition than are buses. In this context we note the increase in trips by private transport from the rural areas and free standing towns into central Leeds. 6.3.5. Test E (Park and Ride) Figure 20 shows those hnks used in connection with the two park and ride schemes. It will be noted that only those zones radially removed from the parking stations find them worth using. Other zones are sensitive to the scheme because of the changed competrtion pattern and a marginal reduction in congestion in Leeds (the mean speed in the Leeds area rises by 1.04%) but actual usage of the scheme is highly localised.

202

Progress in Planning TABLE 18. Some results of test D Indicator

% Change from MLF value

Mean speed m Leeds Trips by private transport from rural areas and free standing towns to central Leeds Trips by pubhc transport from rural areas and free standrng towns to central Leeds Trips by private transport within the suburbs Trips by public transport withm the suburbs Total modal spht systemwide Total modal split into Leeds crty centre Total expenditure on car running costs Total bus revenue Total train revenue Mean trip cost systemwide Mean distance by car Mean distance by bus Mean distance by train Accessibility advantage of car available people

+ * + * + Park and ride bus route Real road links - - - - - Centrold connectors , ,’

Flows are annotated

22.09 10.79 -3.99 -1.3

1.18 3.77 5.46 -1.49 -1.64 -0.25 4.21 -0.38 -0.06 6.7

Li?/

on the left hand side of

FIG. 20. Map of usage of park and ride facilities (test E).

v

Transport Modelling: Sensitivity Analysis and Policy

Testing

203

6.3.6. Test F (Gv Running Costs)

Car users respond in two ways to increased perceived running costs. The first is to change job location or home location, while the second is to start using public transport. Changing job or home location would presumably not be a short term response, whereas changing mode might be. However, we are modelling a long term equilibrmm and responses should be seen in that context. In Fig. 2 1, a perceived car running cost of zero corresponds to a scenario in which the car user is deterred only by the time taken to complete his journey by car and any parking charges he may have to pay. In this situation the mean speed in Leeds (a) and the public transport revenue (d) are lower than for the MLF, the former because of congestion and the latter because the car usage (b) is higher than for the MLF. Trip length (F) is twice the MLF value and there are even greater increases m systemwide accessibrlity advantage of car-avarlablepeople (g) and total car passenger mileage (e). Figure 21 also shows that as car running cost increases from zero there is a steep rise in expenditure on private transport running costs (c) reflecting the high total car passenger mileage. The mean trip length by private transport (f) declines steeply and the number of car trips (b) begins to drop slowly, reflecting the fact that most of the initial reactions to the increase 1s in destination switching rather than modal switching. Both effects combine to reduce the total private transport mrleage (e) which in turn decreases congestron and so increases the mean speed m Leeds (a). The modal switching causes an increase in public transport revenue (d). When the car running cost reaches twice its MLF value the rate of decline of car passenger mileage causes the increase of expenditure on car running costs to reverse reaching the MLF value again at a running cost of three times MLF and declining thereafter. Mean trip length by car levels off to about 30% of the MLF value. This value simply reflects the coarseness of the zone structure in the model. Car passenger mrleage continues to decline, however, due to the continuing drop in the number of car trips. Public transport revenue and mean speed in Leeds continue to increase but begin to level off at around 400% increase in car running costs since the modal split is by then very low for all but mtrazonal and short interzonal Interactions.

% change in car running costs from MLF value. % change in indicator from MLF value. mean speed of private transport in the Leeds area. number of trips by private transport (modal split). expenditure on private transport running costs. expenditure on public transport fares. total mileage by private transport. mean trip length by private transport. accessibility advantage of car owners. FIG. 21. Some results of test F (1).

204

Progress in Planning

Ftgure 22 shows the changes in the number of private transport trips from each of the five zonal categories (as defined m Fig. 3) mto central Leeds (zonal category 1). The increase in running cost has a greater impact on longer trips and is reflected in the mitral rates of declme of trips from categories 3,4 and 5 (c, d, e). Due to changes in job competltlon trips within category 1 (a) and from category 2 (b) actually increase imtmlly, the number of trips within category 1 only regaining its MLF value when running costs have increased by 350% from MLF. Thus reflects the systemwide tendency for long trips by car to decline durmg the mitral part of the rise in runn~g costs but for short mterzonal and intrazonal pnvate transport traps to survive quote large increases in runmng cost before they are reduced by modal swrtching.

d

e

Y

b

% change in car runnmg cost from the MLF value. % change in mdlcator from the MLF value. private transport traps withm zone group 1 (central Leeds). private transport trips from zone group 2 (suburban Leeds) to zone group 1 (central Leeds). private transport traps from zone group 3 (medium sized towns of the conurbatlon) to zone group 1 (central Leeds). private transport trips from zone group 4 (rural areas and free standmg towns) to zone group 1 (central Leeds). pnvate transport trips from zone group 5 (large towns of the conurbatron) to zone group t. (central Leeds). FIG. 22. Some results of test F (2).

Figure 23 shows mean trap lengths by tram and by bus for each person type. The change m running cost have very little effect except on car-avarlable-persons’ trips by bus (c). The change m mean trip length of car-available-persons’ journeys by bus reflects the trap length of the interactions by private transport which are declming. Thus there is an initial rise as the longer pnvate transport trips are in steep decline while the number of shorter trips is stdl rising and followed by a decrease m mean trip length as the short private transport trips also decline. An outstandmgly unrealistic feature of this test IS that although the model simulates a long-term equrhbrmm there is no attempt to feed back the influence of car runnmg cost on car ownership or car occupancy. if this were done there would surely be a further reductson m private transport mileage at mcreased car running costs. 6.3.7. Test G {Parking Charges) This test IS included to show the effects of a zone specific test. We note in Frg. 24 that as parking charges increase there IS an increase m public transport trips mto central Leeds - the

Transport Modelling: Sensitivity Analysis and Policy Testing

205

Y

x y a b c d

% change m car running costs from MLF value % change in value of mdicator from its MLF value. mean trip length by train (car-available). mean trip length by train (no-car-available). mean trip length by bus (car-available). mean trip length by bus (no-car-available). FIG. 23. Some results of test F (3).

increase for car-available-persons being more marked than that for non-car-available-persons (d). These changes are m response to the massive decrease in private transport trips (b) to Leeds City centre. The effect of these changes is felt throughout the Leeds area which experiences a slight increase in the mean speed travelled (a). Note that the curves alI flatten off somewhat -when the parking charge reaches about double its MLF level. Curves b, c and d have shown the effects on trips into zone 1 where the parkmg charges are levied. Curves e to i show the effect on private transport trips to that zone and its neighbours m zonal grouping 1. Note that car trips to this zonal grouping behave m a broadly similar manner nomatter where they originate. At the left hand edge of the graph we find that the rankmg h, i, g, f, e implies that the more distant origins are more sensitive (in % terms) to reduced parking charges than are the near ones. This reflects the model assumption that changes in distribution and modal split are a function of absolute rather than proportional changes in cost. The model produces the pattern observed because the direct effect of the reduced price of private trips to zone 1 is equal throughout the study area but differentiation is introduced via the balancing factors. The reduced costs of travel to zone 1 cause a reduction in zone l’s destination balancing factor (Bf) and,through the iterative processes in the distribution/modal split model, produces reductions in the car-available-persons’ origm balancing factors (A:) especially for zones near zone 1, and produces increases in the non-car-available-persons’ origin balancing factors (A:) again especially for zones near zone 1. If we interpret the balancing factors as measures of accessibility, then we have increased accessibility for zone 1 as a destination and increased accesslbihty to destinations for car-available-persons living in or near zone 1. Now since accessibility is, in the current context, a relative term we can say that car-available-persons living far from zone 1 have a reduced accessibility to destinations and thus, to redress the balance, they have a strong tendency to travel to zone 1 being the only destination zone which has become more accessible to them.

206

Progress in Planning b

Y

h I B

e,f

b $6 change

m Leeds city centre park charge from MLF value. % change III rndrcators from MLF value. mean prrvate transport speed 111the Leeds area private transport destinations in Leeds crty centre. public transport destinations rn Leeds city centre by people with cars available. destinations in Leeds city centre by people without cars available. private transport trips wrthm central Leeds (zone group 1) prrvate transport trips from suburban Leeds (group 2) to central Leeds (group 1). private transport trips from medium sized towns of the conurbatron (group 3) to central Leeds (group 1) h private transport trips from rural areas and free standmg towns (group 4). i private transport trips from large towns of the conurbatlon (group 5). FIG. 24. Some results of test G. 6.3.8. Test H (Public Transport Fares) Figure 25 shows that pubhc transport users respond to increased fares by changing then job location and their transport mode. The percentage change m mean pubhc transport trip length (g) due to changes m job location is consrderably greater both for reduction and for increase in pubhc transport fares than is the percentage change m the number of persons travelling by car (b). With zero public transport fares there are less people travellmg by car, hence less congestion and a higher mean speed in Leeds (a), there is a higher pubhc mean trip length and proportionately even higher total public transport passenger miles (f). Of course there is a reduced accessrbrhty advantage for people with cars available (e) and zero pubhc transport revenue (c). As fares rise, public revenue rises steeply but leveis off a httle as the reduction in mean public transport trip length combined with modal switching reduces the number of pcbhc transport passenger miles. Whereas, for rising private transport running costs the expenditure on private transport (curve c in Fig. 21) reaches a peak and then declines the expenditure on pubhc transport (curve c in Frg. 25) for changes in fare does not. This 1s because

Transport Modelling: Sensitivity Analysis end Policy Testing

b,c

-25

207

-

% change in public transport fares from MLF value. % change in indicators from MLF value. mean private transport speed in the Leeds area trips by prwate transport. public transport revenue. expenditure on private transport running costs accessrbihty advantage of car-available-persons. mrleage by public transport. mean length of public transport trips. FIG. 25. Some results of test H (1).

there is a limit to the number

of people using public transport who can switch modes and a limit to the extent to which the remainder can reduce then mean trip length. As fares continue to increase, therefore, a residue of public transport trips remains, consistmg of those made by people who do not have a car available to them, and the total number of public transport passenger miles does not tend to zero but stops short at something less than half of its MLF value. The model therefore predicts that public transport revenue may be increased mdefimtely at the expense of persons who do not have a car available .x-;* by -asing fares. In practice, . presumably, public transport passenger miles would be reduced by people walking to work or in some way gaining access to the private mode. Notrce that Fig. 25 shows very little difference between the percentage change in the number of trips by private transport (b) and the percentage change in perceived expenditure on car running cost (d). The mean private transport trip 1s hardly affected by the change in fares. Figure 26 shows the percentage change in the number of traps by public transport to the centre of Leeds (zonal category 1) from each of the five zonal categories in the study area. This illustrates the changing of job location and transport mode and the correspondmg reduction in the mean trip length for public transport due to increasing fares. Thus while trips from zonal categories 3-5, (c, d, e) which are further from central Leeds, have a negative elasticity to fare change whatever the fare, trips from zonal categories 1 and 2 (a, b) show positive elasticity for low fares as job relocation increases the shorter public transport interactions.

208

Progress in Planning

x y a b c

% change m pubhc transport fares from MLF value. % change m indicator from MLF value. public transport trips wrthin central Leeds (group 1). pubhc transport trips to central Leeds (group 1) from public transport trips to central Leeds (group 1) from conurbatron (group 3) d public transport trips to central Leeds (group 1) from (group 4) e public transport trips to central Leeds (group 1) from

suburban Leeds (group 2) medmm sized towns of the rural areas and free standing towns large conurbation

towns (group 5)

FIG. 26. Some results of test H (2).

6.3.9. Test I (Walking Time) The results test H (public graphs shown changes in the K.

of this test, like tests J and K below, are similar in many respects to those of transport fares) described above. This similarity may be confirmed from the m Section 6.2. The similarity 1s due to the approximate correlatron between components of generalised cost which are being investigated m tests H, I, J and

6.3. IO. Test J (Waiting Time) See 6.3.9 above. 6.3. II. Test K (Public Transport in Vehicle Times) See 6.3.9 above. 6.3.12. Test L (Car Occupancy) The mam effect of mcreasmg car occupancy is to reduce monetary costs to car users. The most important such cost 1s the car running cost and so test L is roughly similar to test F (car

Transport Modelling: Sensitivity Analysis and Policy Testing

209

running cost). The other monetary cost to car users is the charge for parking. However, test L is not simply a combination of tests F and G (parking charge) since the ratio between passenger miles and vehicle miles is a function of car occupancy. Unlike tests F and G, therefore, test L leads to a direct reduction in congestion. This statement is supported by the congestion relief rates given in Section 6.2.14. 6.3.13. Test M (Value of Time) The model which we are using has costs expressed in units of generalised time (see Section 2.1). The deterrence parameters (~3’ and 0’) were calibrated on the basis of this generalised cost formulation. Our “value of time” is thus more correctly interpreted as a “duration of money” - an increase in the value of time being, in fact, a decrease in the duration or time-value of money. In Fig. 27 we note the fact that increases in the value of time lead to increases in the overall distance travelled (b) and the time taken for that travel (c). These increases reflect the reduced monetary costs of travel. The larger increases in distance travelled compared to time taken reflect the fact that monetary costs are dependent on distance rather than on time and that route switching therefore occurs m response to lower monetary travel costs. The overall reduction in travel costs leads to a systemwide benefit (h). The increased accessibility advantage for car-available-persons (f) resulting from an increase in the value of time reflects the greater monetary element in private transport journeys than in public a

Y

e

h

h % change in value of time from MLF value. % change in indicator from MLF value. systemwide total monetary expenditure (in tune units). systemwide mileage travelled. systemwide time expended. total modal split. ratio of bus miles to train miles travelled. accessibility advantage of car-avarlable-persons. systemwide total monetary expenditure (in money units). systemwide consumer surplus benefit (ir#ne units). _ FIG. 27. Some results of test M (I).

210

Progress in Planning

transport journeys (Table 13). This results m a modal switch towards the use of cars (d). But even more dramatic is the decrease m the proportion (on a passenger-mile basis) of pubhc transport trips which are by bus (e) Thus reflects the greater time/money ratio in bus trips compared to train trips. Note that as one would expect, decreases in the duration of money (increases in the value of time) lead to decreases m the systemwide total expenditure of money expressed m time units (a). However, expressed m money units (and thus not discountmg for mflation), the expenditure (g) increases approxtmately proportionately to distance (b). The fact that these lures (g) and (b) are not identical reflects the existence of monetary travel costs which are not strictly a function of distance (parking charges and minimum fares). If the model had had a formulation of generahsed cost based on money instead of time then the effects of an increase in the value of time would have been different. Increases m the value of time would have led to overall increases in the costs of travel and consequent systemwide disbenefit. Curve (h) would thus slope m the opposite direction. The relationship between the curves displaying systemwide distance and time (b and c) would alter in an interesting manner. They would both have negative gradients at the origm, that for curve c being more negative (1.e. steeper) than for curve b. The curve of systemwide expenditure of money in money terms (g) would be co-related with that of distance (b) (being slightly less steep). Curves f, d and e, car-available-persons’ accessibility advantage, modal spht and submodal spht respectively, would retain their form since they reflect the time/money ratios of the various modes and these are constant whether we express cost m time or money units. It 1s hoped that the importance of the difference between a generahsed cost formulation in time units and one in money units IS established and that our reasons for choosmg the former (set out m Section 2.1) will be appreciated Y

b-

x

Y a

% change m value of time from MLF value. % change m mdxator from MLF value. . _ private transport trips tram rural areas anc~ tree standmg

(group 1). b private transport transport C pubhc (group 1). d pubhc transport

towns

(group

4)

to central

trips from suburban Leeds (group 2) to central Leeds (group 1). trips from rural areas and free standmg towns (group 4) to central trips from suburban

Leeds (group

FIG. 28 Some results

2) to central

of test hi (2).

Leeds (group

1)

Leeds

Leeds

Transport ModeDing: Sensitivity Analysis and Policy Testing

211

Figure 28 shows a spatial expression of the effects of a change in the duration of money. As the duration of money decreases (value of time increases) we find a decreasing use of public transport for both long (c) and short (d) journeys (this reflects the change in modal choice (d) noted in Fig. 27). We also note a much smaller decrease in short journeys by car (b) and a very large increase in long journeys by car (a). A continued reduction in the duration of money causes all these trends to continue (albeit at a reduced rate) with the exception of the curve depicting long trips by public transport (c) which changes direction and begins to increase. The change is due to the fact that of the two influences acting on the curve (modal split and distribution) the former, whrch acts towards decreased use of buses, is most marked at the left of our graph while the latter, which acts towards increased trip length, is predominant on the rest of the graph. 6.3.14. Test N (Income Levels)

As was pointed out in Section 6.2 the results of this test are dominated for test M (above). We will not, therefore, reproduce the re&ixere. eb

1 x y a b c d e f g h i

% change in real car price from MLF value. % change in mdicators from MLF value. mean private transport speed in Leeds. origins by car-available-persons. ongins by no-car-available-persons. choice modal split. total mileage by private transport. total mileage by public transport. mean trip cost by car-available-persons mean trip cost by no-car-available-persons. accessibility advantage of car-available-persons. FIG. 29. Some results of test P.

by the effects noted

272

Progress in Planning

6.3.15. Test 0 (Income Levels (Without

Value of Time Correction))

The major results of this test are that income increases without the appropriate changes in the value of time lead to an overall Increase in trips made, an increase in congestion levels and a reduction in public transport patronage. It is interesting to note that the mcreased car availability causes an increase m the total modal split but that there is a reduced choice modal split (a decreased proportion of the mcreased number of car owners choose to travel to work by car). A similar effect is the reduced accessibility advantage of car-available-persons who now suffer more competition from their car-available-fellows.

63.16.

Test P (Car Prices)

We note, in particular, the effects of this test on car ownership, availability and use as shown in Fig. 29. Mileages by private and public modes (e and f) are not as elastic as are trips by car-availability category (b and c), this is due to the change in choice modal spht (d) (the more car-available-people there are in the system (b) the less of an advantage rt is to be one and choice modal split decreases (d)). The value of being a car-available-person may-be seen as reflected in curve (i) or in the mean costs of travel for car-available-persons (i) and no-caravailable-persons (h). Note however that these findings may not reflect real world activities because, as car avatlabihty increased so public transport services would almost inevitably decline (due to economic pressures) and land uses and facilities become increasingly adapted to the private car. Our model does not include these effects and may thus be said to be deficient in that respect. A case is then made for a more comprehensive urban model reflecting the adaptations of land use and transport services to travel demand. Finally we note the decelerated responsiveness of the mean speed travelled on Leeds roads (a) to changes m traffic volumes (e).

6.3.17. Test Q (High Income Trip Rates) The general effect of this test is to produce more private transport trips and as such the effects are similar to those m P above. But we note that high income zones are more sensitive to the test than are the rest.

63.18.

Test R (Base Year Income)

Figure 30 shows the changes in a number of indicators for that zone whose base year income was varied in this test series. Note that the increase in total origins (a) is masking a larger decrease in origins by no-car-available-persons (d). Note also a very marginal decrease in the choice modal split (c) (due to a reduction in the competitive advantage of cars resulting from increased car availability and concomitant congestion). The number of private trips (e) made to zone 1 (the main centre of employment) increases less than the total number of private origins (b) but decreases more than it. This clearly reflects the importance of second order effects such as those caused by competition and congestion. It will be recalled from figures in Section 6.2 that this test series did not have much effect at the systemwide level. Figure 3 1 shows how the effect of this parameter test, which was specific to one zone (17) diffuses through the system with its effect becoming weaker at the more distant zones. It is interesting to note that the effect of increased base year income is to create a reduction in the modal split of Journeys from neighbouring zones to the city centre; this is due to increased competition and congestion. We observe that, for all three zones for which results are given in Fig. 3 1, the proportionate effects on the private mode (a, c, e) are stronger than those on the public mode (b, d, f). This is merely because of the much smaller absolute number of trips by private transport (compared with pubhc transport) to Leeds City centre. Not only does increased distance from the zone of disturbance cause the intensity of the effects to decrease (compare the gradients of a, c and e and those of b, d and f), but the effect on the public mode becomes proportionately less than the effect on the private mode and the complexity of the effect appears to mcrease. This is a further reflection of the increased relative importance of the second order effects at increased distance from the zone of disturbance.

Y

f

2G

-15 -

.10 -

-5-

5-

IO -

15 -

zJ+-

d

FIG. 30. Some results of test R (1).

% change in the base mcome of zone 17 from MLF value. % change in indicator from MLF value total orrgins at zone 17. total origins by private transport at zone 17. choice modal split of trrps from zone 17. total origms by no-car-available-persons from zone 17. private transport trips from zone 17 to Leeds city centre (zone 1).

d

0

25-

b

d,f

cx e

FIG. 3 I. Some results of test R (2).

% change in base year income of Halton from MLF value. % change in indicator from MLF value. private transport trips from zone 17 to Leeds city centre (zone 1). public transport trips from zone 17 to Leeds city centre (zone 1). private transport trips from zone 12 to Leeds city centre (zone 1). public transport trips from zone 12 to Leeds city centre (zone 1). private transport trips from zone 11 to Leeds city centre (zone 1). public transport trips from zone 11 to Leeds city centre (zone 1). Note: Zone 12 is 3 miles from zone 17. Zone 11 is 4.5 miles from zone 17.

e-

fd-

c,

214

Progress in Planning

6.3.19. Test S (Coravoiloble-persons ‘Deterrence Parameter)

Figure 32 shows predominantly high elasticities in response to changes in the deterrence parameter for people with a car available. It also shows that reductions in 0’ have stronger effect than do increases. The curves for car mileage (a) and public transport mileage (b) behave similarly for decreases in P’ but increases have greater effect on car mileage than on public transport mileage (because modal split away from public transport means that the effect of changes on public transport are reduced). Changes in car-available-person’s mean trip cost (d) is not quite matched by changes in private transport mean trip cost (c) (again because of a modal switch). Comparison of curves g and h shows the spatial expression of the effects of the change in 0’ (because long journeys by car (h) become less frequent and short ones (g) more frequent). Finally note that long trips by car-available-persons by public transport (i) are more sensitive than long trips by private transport (h). Note also that decreases in long trips by car-available-persons corresponds to an increase in such trips by no-car-availablepersons (j) resulting in an overall increase in long trips by public transport.

I

h

dC

a

% change in the deterrence parameter for car-available-persons. % change in indicator from MLF value. mileage by private transport. mileage by public transport mean trip cost by private transport. mean trrp cost of car-avarlable-persons. mean trip cost of no-car-available-persons. chorce modal split (trips by private transport). private transport trips wrthm suburban Leeds (zone group 2). private transport trips from rural areas and free standing towns (group 4) to central Leeds (group 1). car-available-persons’ pubhc transport trips from rural areas and free standmg towns (group 4) to central Leeds (group 1). no-car-available-persons’ public transport trips from rural areas and free standing towns (group 4) to central Leeds (group 1). mean private transport speed in Leeds. FIG. 32. Some results of test S.

Transport Modelling: Sensitivity Analysis and Policy Testing

215

h.3.20. Test T (No-car-available-persons‘Deterrence Parameter) The mechanisms operating in this test, as in test U below, are similar to those 111the test of the car owners’ beta {test S above). tl.3.21. Test U (Wytconsult Deterrence Parameters) See 6.3.20. 6.3.22. Test V (Trip Generation Modelj Some results of this test are shown in Table 19. We note that the 8% decrease in origins of people with cars available and the 7% increase in origins of people without a car available, are not quite matched by the changes in expenditure on car running costs and public transport fares respectively. The fact that fare expenditure is up only 3% taken together with the TABLE 19. Some results of test V Indicator Mean private transport speed in the Leeds area Car-available-person’s orlgms No-car-avadabie-person’s orlgms Private transport expenditure on running costs Expenditure on pubhc transport fares Chotce modal spht Total modal split Mean trip cost systemwlde Accesslbihty advantage of persons with cars available

% change

from MLF

3.1 -8.061 7.24 -1.56 3.132 0.25 -5.9 0.6 0 34

reduced accessibility advantage of car-available-persons suggests that the additions origins of no-car-available-persons are located in the more accessible parts of the study area. It will be apparent that this test of minor modification of model form has had results of a magnitude and complexity equal to many of the parameter tests described above.

6.3.23. Test W (The Post~istrib~tio~ Modai Sp~itj Table 20 gives some of the results of this test. Note that two models, calibrated to the same base year data and testing the same policy can give answers which differ, in some cases, by a large amount even at the systemwide level. (e.g. public transport fares paid by people with a car available). Note also that the various differences though mutually consistent, behave in a way which would perhaps not have been intuitively obvious - such as the different effects on train and bus. These results should make us more cautious about accepting ‘calibrated’ values and show the danger of accepting imported calibrated statistics.

6.3.24. Test X (The BurredAssignments Some results of this test are given in Table 21. We note the great effect on the mean speed in Leeds reflecting great changes in individual link flows. Other effects are most marked in the Leeds area where the network is finest and where we have capacity restraint and, conversely, least marked in rural areas. Note that effects on public transport do exist and are due to competition. This assignment method gives increased benefit to ear-available-persons but reduced speeds (suggesting a less satisfactory convergence).

216

Progress in Planning TABLE 20. Some results of test W Indicator

% changes from basic model MLF

Systemwtde choice modal spht Expenditure on private transport runnmg costs Pubhc transport revenues from car-avarlable-people Pubhc transport revenues from no-caravailable-people Mean trip cost systemwide Mean trip cost private transport Mean trrp cost public transport Mean trip cost (car-avarlablepeople) Mean trrp cost (no-car-avarlablepeople) Mean trip length by private transport Mean trip length by bus Mean trip length by tram

-11.43 -15.04 73.13 -0.10 3.63 -3.00 1.05 6.66 -0.05 -5.3 1.98 -0.92

TABLE 21. Some results of test X Indicator

% change from MLF model

Mean prrvate transport speed m Leeds Total modal split into central Leeds (Zone category 1) Total modal spht Total modal split mto rural areas and free standing towns (category 4) Total mrleage by prrvate transport Total mtleage by public transport Mean trip length by pub& transport Systemwrde accessrbrhty advantage of car-avarlable-persons Accessibrhty advantage of caravarlable-persons in central zones Accessrbrlrty advantage of car-available-persons in rural zones

-15.58 3.26 0.86 0.46

0.63 (mterzonal trips only) -0.36 -0.15 0.466 1.79

0.84

6.3.25. Test Y (The Dial Assignment)

Shows results which, for the purposes of the present paper are similar to those noted for the Burrel assignment above. 6.3.26. Test Z (No Capacity Restraint) The results of this test are most interesting when we wish to compare alternative Detailed consideration is therefore reserved for Section 6.4 below.

6.4.

THE

TWO-PARAMETER

networks.

TESTS

As indicated in Section 4.4 the two-parameter tests are intended to show how the results of a given policy change (in this case a road network improvement scheme ) are sensitive to the values of other inputs to the model (seen as changes of scenario) and to modifications in the form of the model. Table 22 shows, for comparison, the actual change (upper half) in a number of indicators, for a selection of tests, caused by the introduction of a network change

Transport Modelling: Sensitivity Analysis and Policy Testing

217

to test D in Table 8 (the “TPP” network). The lower half of the table shows these changes as a percentage of the values of the indicators for the original (1974) network. When evahrating the effect of some policy change it is comforting to presume that whatever errors have been incorporated in the “before” projectron have been duplicated in the “after” projection and that since, except for the policy change itself, one is comparing like with like, the changes observed in system indicators will be relatively insensitive to these duphcated errors. Table 22 shows that this is only true to a limited extent. Although the direction of change of the various indicators shown is almost entirely independent of gross parameter cfianges the magnitude of change is not. In particular the variations in the predicted consumer surplus arising from the policy change are very large even after allowing for the magnitude of the parameter changes considered. This is particularly serious in view of the importance often attached to benefit measures by decision makers. The effect of the network change is to reduce delays to private transport in Leeds by the completion of an inner ring road of quasi-motorway standard and to speed inter-urban private traffic by upgrading existing trunk routes and burlding motorways. (Note that these changes are particularly beneficial to through traffic.) These changes cause time savings to existing users and encourage switching to private transport. They alsocause changes of job or home location to take advantage of opportunities which can now be more quickly reached. Table 22 shows the change in various indicators due to the network change under a number of different scenarios. The general effects of the network change are similar in all scenarios, though they differ in magnitude. The time savings cause trip costs for private transport to decrease giving a benefit to persons with a car avaiiable (there is a comparatively small disbenefit to persons with no car available due to the effects of job competition). This time saving also causes an increase in both the Hansen accessibility and the accessibility advantage of persons with a car available. The time savings lead to job, mode and route switching by commuters who take advantage of the reduced trip cost. This causes modal split, mean car journey length and expenditure on car running cost to go up and the number of trips from suburban to central Leeds to go down, not only for users of public transport but also private transport. The increased modal split and trip lengths would tend to increase congestion in Leeds but nevertheless the mean speed in Leeds goes up due to the network improvement, The time saving to traffic in Leeds depends on the level of congestion present before the network change. The influence of Leeds congestion is evrdent from a comparison of the changes caused by network improvement in the absence of capacity restraint (Z) with those for MLF. The changes due to network improvement are less when there is no capacity restraint than for MLF (and most other scenarios). Those scenarios which involve low traffic volumes (e.g. double petrol price, F) also tend to show less effect than MLF but notice that, although doubling the parking charge in Leeds City centre (G) might be expected to show a similar reduction of change due to reduced congestion, there is a larger increase in the mean speed in Leeds in this scenario than in the MLF. This is because, due to the expense of city centre parking in test G, a hrgh proportion of the road traffic in the Leeds area is in fact through traffic and, as noted above, the network improvements are particularly beneficial to through traffic. The benefits of the network change depend mainly on the volume of private trips, being high for example with double fares (H) or a car occupancy of two persons per car (L) and low for double car ~n~ng cost (F) or double car prices (PI. When the deterrence parameter for people with a car available, 0’) is doubled, (S), less advantage IS taken of the interactions which have been made cheaper because these tend to be fairly expensive ones by the nature of the improvements made and, for this reason, less benefit accrues. The largest benefits are those associated with a high value of time (M, N). This is because a high value is put on the time savings due to the network improvement and a low value is put on the extra monetary cost involved. We should point out here that the already large benefits shown for tests M and N in Table 22 would have been twice as large, relative to the other tests, if expressed in money units rather than time units. The reduction in mean trip cost due to the network change in a given scenario depends firstly on the degree of congestion associated with the unimproved network, and secondly on the mean trip length of private transport trips (the higher the degree of congestion and the greater the mean trip length then the greater will be the reduction in mean trip cost). However, a corresponding

I

: T V W X Y Z

2

-0.18 -0.28 1 46 0 32 -1.48 -0.73 -2 63 -3.32 -2 89 -0 09 3.14 -0.31 -0.17 -1.41 -122 -0 16 -0.84

- 31 - 55 219 53 -406 -174 -589 -618 -808 -10 730 -80 -32 -326 -261 -34 -186

tnps

26 m Table 7

22.09 26 02 18 14 25 23 27.08 22 89 23 76 24 11 24.52 1997 19 24 21 82 23.08 20.86 33.18 44 00 11.50

MLF A F G H

:. M N

4.55 5.26 4.2 1 5.41 4.93 4 48 5.56 4 87 4.05 5 04 4.38 4.14 4 90 4 29 5 77 6 57 3 27

MLF A F G H J

m.p.h.

**Opportunity umts, see exprewon tResults not awlable

*See key

Percentage change vewon of above

Change In mdlratol caused by change from “1974” road network to the “TPP” road network

Code’

Test

lndlcator Code’

-1 56 -1 72 -0 84 -1.53 -1.24 - 1.56 -1 42 -168 -3 12 -0 62 -1.48 -1 63 - 142 -0.81 -1 14 -133 -0 33

-792 -829 -415 -834 -599 -763 -641 -754 -1443 -368 -786 -784 -732 -397 -574 -670 -160

tnps

3

0.54 1.22 1 06 0.22 1 20 100 0 79

J.oo

1 20 1 22 1 23 1 21 0 73 0 75 0 93 1 35 165

006 006 005 006 004 .004 005 007 01 I .003 003 006 005 .oo I 006 005 004

(ratlo)

4

3 77 1 37 0.00 6 25 2 38 3 21 1.95 1 90 5 03 1 35 6 76 4 08 3 47 0.00 180 366 1 I1

006 002 000 .004 006 006 .005 004 016 001 005 010 005 000 003 006 002

(ratlo)

5

5.46 5 47 3.32 5.58 4 63 4 89 6 78 7 91 8 21 4 95 3 23 5 36 5 25 3 67 t t 4.45

365

441 459 303 441 411 423 436 435 616 238 178 429 392 257 :

Ill,” x IO’

6

-1.52 -1.46 -1.07 -1.46 -1.16 -2 10 -137 -1.86 -3.19 -0.60 -0 87 -2.18 -1 33 0 04 -148 -148 -0 99

-89 1 -89 4 -76.1 -87 0 -97 7 -108.7 -72 9 -62 2 -97 2 -47 0 -45 4 -97 7 -80 5 27 -86 1 -86 3 -57.3

mm x IO’

7

-0 26 -0.24 -0.14 -0 23 -0 32 -0 27 -0.53 -0 68 -0 89 -0 17 -0 32 -0.36 -0 25 -0 I2 -0 28 -0 2s -0 09

-1 34 -1 25 -0 78 -121 -1.72 -I 47 - 2.60 -3 26 -4 07 -091 -1 36 -168 -1 30 -0.65 -I 43 -1.29 -0 45

mm

8

0 29 0.35 0 14 0 31 0.30 0.30 0.84 1.13 1 05 0 31 0.15 0 58 0.31 -0 02 0 33 0 27 0 12

3.62 4.24 I 56 3 84 4 08 4 25 II 38 14.89 1372 3 85 3.07 5.37 3 92 -0 23 4.13 343 I 53

XIV

(ratlo)

9

i,6

4 21 4 16 2 05 4.28 3 96 4 04 5 77 6 32 644 3 89 2 74 3 98 4 02 3 22

.240 236 081 .244 226 .230 405 414 476 .227 .096 .229 .230 .I73 :,05

nnles

IO

-0 38 -0 28 -0 23 -0 26 -0.48 -1 58 -0 31 -0 29 -0.54 -0 19 -0.30 -1 19 -0 33 0.55 -0.38 -0 39 -0 17

- 0140 -.OlOO -.0088 - 0097 - 0136 -0 556 - 0114 - 0131 -.0256 - 0070 -.0114 - 0320 - 0121 0218 - 0141 - 0145 - 0063

mdes

II X

5.74 6.25 1.91 6 07 6 67 6 58 7.99 9.23 9 56 4.79 443 5 67 5 74 5 63 5 16 5 75 3 87

136 154 26 136 140 142 294 392 419 114 17 133 134 134 124 136 96

IO’

opp. umts**

I2

TABLE 22. Effects of variations in input parameters and model form on the results of a network policy test

13

4 26 4 02 3 34

t

4 35 4 96 1 73 4.23 4.40 4.80 6 55 8 09 10 93 5 21 7 66 2 22 5 21

533 so2 .426

t

542 636 105 .505 1.280 I .044 I 336 1.151 1.425 699 086 16 786 .640

(ratlo) x

14

5 50 6 00 2.38 5.48 6 33 6 05 7.70 842 11 86 2.96 2.69 5.53 5.04 4.58 6.23 5.29 4.20

(ratto) IO’

15

5 99 2 38 5.49 6 34 6.06 171 843 11.87 2 97 2.11 5.53 5.05 4 58 6.24 5.29 4 20

s 51

mm x IO”

I6

_ 0074 -.0083 _ 0036 -.0082 _ 0095 0087 I.0084 -0109 - 0094 -.0046 0200 10032 - 0076 - 0062 -.0107 - 0068 - 0028

min x IO”

9 3 ?. 2

8 5

-0 2 q

u G

“Most likely future” Official land use plan Private vehicle running cost = 2.0 X MLF value Parking charge in Leeds = 2.0 X MLF value Public transport fares = 2.0 T MLF value Time spent waiting for public transport = 2.0 X MLF value Mean car occupancy level (=2) = 1.67 X MLF value Behavioural value of time = 2.0 X MLF value Design year real income and value of time = 2.0 X MLF value Design year real car prices =2.0XMLFvalue Deterrence parameter of people with car available = 2.0 X MLF value Deterrence parameter of people without car available = 2.0 X MLF value Damped category analysis submodel Post distribution modal split submodel Burrel type freebuilding submodel Dial type assignment submodel No capacity restraint in assignment submodel

MLF A F

V W X Y Z

T

S

P

N

M

L

J

H’

G

Details of test run with and without the “TPP” network changes

Test code

Key to Table 22.

16

15

14

13

12

11

10

3

2

1

Code

Jndicator

Mean speed travelled on finks with capacity restraint Trips from suburban Leeds to central Leeds by private transport Trips from suburban Leeds to central Leeds by public transport Total modal split systemwide Total modal split into Leeds city Expenditure on private transport running costs Expenditure on public transport fares Mean trip cost systemwide Mean trip cost of people without a car available divided by that for people with a car available Mean distance travelled by private transport Mean distance travelled by public transport Hansen accessibility to destinatrons for people with a car available Accessibility advantage of people with a car available over people without a car available. Consumer surplus benefit systemwide Consumer surplus benefit for people with a car available Consumer surplus benefit for people without a car available

Indicator Code in

34

34

34

30A

26A

23A

23A

20A

20A

17A

16A

11A 11c

8B

8B

SA

Table 7

220

Progress in Planning

doubling of the deterrence parameter for people with a car available, I?’ , shown m Table 22 as test S, is an exception to this rule, despite the small amount of congestion and the short mean trip length, the network improvement reduces the mean trip cost as much as it does for the MLF. This is because, although less time is saved by trips already using the improved interactions, there is also less diversion of traffic to the new roads (a process which tends to increase the mean trip cost in the MLF case) Factors which lead to a large increase in the total modal spht are firstly a large number of people with cars available using public transport and secondly, a high mean trip length for those who do travel by car. Very little change in modal split was found usmg a post distribution modal spht model. This is not a feature of all such models but came about because the value of, h, the modal split sensitivity parameter, was small in comparison to 0’. The change m private transport trips from suburban to central Leeds caused by the network improvements is not large. The reason that the change is negative in most cases IS that pnvate transport users are changing their job or home location to take advantage of the quicker longer trips. Where the scenario deters long trips the change is positive due to the slight improvement in the private transport accessibility of central Leeds. The increased private transport accessibility of central Leeds and the overall reduction of the generalised cost of private journeys due to the network improvement tend to reduce the number of people travelling by public transport from suburban to central Leeds. One result which initially caused us some alarm was that, with a post distribution modal split model (test W), the network improvement actually caused an increase in public transport revenue and mileage (columns 7 and 11). This counter mtuitive prediction is a result of the modal split deterrence parameter A being smaller than the distribution deterrence parameter for car-available-persons @I). The decrease in private transport costs, resulting from the network improvement, causes a change both in modal split and in distribution. Since 0’ 1s large there is a relatively large change m distribution leadmg to increased trip lengths by car-available-people. However, X IS much smaller than 13’ and the change m modal split is relatively small. The net result is that public transport passenger mileage increases overall. The counter intuitive behaviour of the model is made more dramatic if we verbalise the implied decision process. “I am a car owner and so the reduced cost of carjourneys affects me. I shall travel further in consequence of this reduced cost. I travel by bus and don’t mind much whether I travel by car or by bus, I shall therefore continue to travel by bus”. This extraordinary consequence of using a post distribution modal split model with a pi larger than the X becomes more serious when we consider that it is quite normal to find, on calibration to cross sectional data, that the implied 13’ is indeed larger than the implied A. (See for example WYTCONSULT (1975) and Dorrington’s (1971) recalibration of the SELNEC model). Senior and Williams (1977) find that, with a variety of formulations of the composite cost, X is consistently lower than P’ . Williams (1977) gives good theoretical reasons which require /3’ < X. Thus, we would expect new forms of post-distribution modal split models to be developed to remove the anomalies reported here. Our test of the post-distribution modal spht model has shown that the change in model form causes the results of the policy test to vary in sign as well as in magnitude. 6.5.

THE

MULTI-PARAMETER

TEST

As explained in Section 4.5 it would be wrong to assume that the changes in output due to a simultaneous change m a number of input parameters would simply be the sum of the changes which would have resulted from changing each input parameter separately. Results in Section 6.2 suggest an approximately additive relationship between the results of tests M and 0 to produce the results of test N but in order to investigate more rigorously the relationship between a number of the input parameters we ran a test in which a number of parameters were varied simultaneously and compared the results of this test with the results one would have expected had the effects of varying each of these parameters independently been simply additive. The results of this test are shown as the solid lines in Figs 33-36. The dashed lines on these figures represent the results expected if the parameters were independent and additive. The test involved the simultaneous variation of public transport fares, public transport waiting times and the value of time (tests H, J and M respectively).

Transport Modelling: Sensitivity Analysis and Policy Testing

221

From Fig. 33 which depicts the number of trips by private transport, we at once see that the effects of parameter changes are not additive. For example a doubling of public transport fares, waiting times and the value of time separately produce increases in the number of private transport trips of 9,7 and 3.4% respectively (adding up to 19.4%) but the simultaneous variation of these parameters causes an increase of only 13%. Figures 34 and 35 depict mean trip costs in time units and in money units respectively and the difference between the two reflects the inclusion in our test of changes in the value of time.

I = % change In Input parameters y = ----

from their MLF level

% change resultmg from simultaneous parameter % change expected If effects

test

were addltwe

FIG. 33. Multi-parameter test: change In total number of tnps by private transport. .Y 10

L \ \ \ \ \ \ \

5-

\

-5

I = % charqs In Input parameters from thev MLF level y = % change resuttmg from simultaneous parameter test ----

% change expected If the effects

were addltwe

FIG. 34. Multi-parameter test: change in mean trip cost (in time units).

222

Progress in Planning

Near to the origin the two lines show almost identical behavlour on all four graphs This IS consistent with our assumption that the behaviour of the model outputs is contmuous and has continuous derivatives (appendix 2) and demonstrates that for small changes of input parameters the combined effect of changing 3 number of parameters can be accurate!y estimated as the sum of the individual effects of changing each parameter separately. For large changes, however, this estimate is evidently unreliable. In three oi the four cases shown the two curves

100

75 -

25 -

/

I

I

I

I

25

50

75

x = % changs I” mprrt parameters tram thew MLF level y = % change resultq tram slmultarxaus parameter test ----

% change expectedif effects

FIG. 35. Multi-parameter

were additive

test: change in mean trap cost (in money

I 25

I 50

I 75

x = % change In Input parameters from thew MLF level y =% change resultmg from stmultaneaus parameter ---

FIG. 36. Multi-parameter

units).

lO(

test

% change expected of results were addltlve

test. change in the total number of trips from suburban central Leeds.

Leeds to

Transport Modelling: Sensitivity Analysis and Policy Testing

223

diverge for large changes in either direction from the MLF, the divergence bemg roughly proportional to the square of the magnitude of the change. This is the behaviour that might be expected on the basis of the general argument that in examining the behaviour of an output of the model m the face of changes in a number of parameters (a,, a2, . . . an say) the error involved in estimating the effect of a simultaneous change by adding the effects of separate changes of each parameter will be mostly due to the cross derivative terms a2b . That is, the divergence wrll be mostly due to a term of the form: &li aa,

which will be proportional constant of proportionality

to the square of the magnitude being

of the simultaneous

change. (The

per (percent change)*). For larger changes still it is possible that higher order derivatives will become effective and that the two curves may converge again or cross each other. Indeed it seems likely that this would occur to the left (more negative) of the region depicted in Fig. 33 since as the value of time tends to zero car owners would tend to surltch completely to the cheapest mode in money terms, which is public transport for the MLF and SO one would expect a 100% decrease in private transport trips to which would have to be added the decrease due to fares and waitmg times of zero so that the dashed line on Fig. 33 would go below -100% while the solid line (since it must correspond to a positive number of private transport trips) should not go below -100%. In the particular case examined (simultaneous changes in fares, waiting times and the value of time) the principal reason for divergence between the solid and dashed lutes is the multiplicative involvement of fares with the value of time in the evaluation of generalised cost. For example the effect of the fare increase on mean trip cost m time units shown in Fig. 34, is less if there is also an increase in the value of time since fares are divided by the value of time when they are incorporated in the generahsed trip cost (see Section 2.3) and similarly the effect of the fare decrease is greater in the presence of a low value of time. Thus the solid curve in Fig. 34 is lower than the dashed one both for increases and decreases. Car usage varies with the difference in trip costs between public and private transport and so a similar effect is shown for this variable. The changes (dashed and solid) in mean trip cost in money terms shown in Fig. 35 are dominated by the effect of changing the value of time so that the apparent good fit is misleading. In this case the divergence seems to be due to combining the effects of value of time and waiting time. That is an increase in waiting time has a greater effect in money terms in the presence of a high value of time and similarfy a decrease in waiting time has less effect in the presence of a low value of time. No detailed explanation for the quantitative behaviour of the number of trips from suburban to central Leeds (Fig. 36) can be given since this is influenced both by the trip costs on both modes and competition effects at either end of the trips involved due to changes in other trip costs. Notice, however that near the origm a deviation proportional to the square of the change of input parameters may be observed although for very large changes the influence of higher order derivatives can just be detected. One rmght tentatively conclude that for changes of up to 25% in the input parameters the effects of change are roughly additive in this and probably most other cases but that the additive estimate becomes increasingly unreliable for larger changes. Obviously the acceptable degree of error must depehd on the use to which the estimate is to be put. To obtain a better next step in an iterative process, for instance, this estimate would.do.

CHAPTER

7

Conclusions and Recommendations 7.1.

SUMMARY

OF

CONCLUSIONS

Three types of general conclusion can be drawn from the work reported here. First, the method itself, involvmg the execution of a large number of model runs and the presentation of results by comparison with the most likely future, 1s a useful means of gaining insight into the transport characterrstics of an area and the way these are represented in a model. The method allows such results to be extended by curve fitting (albeit of an informal kind) and extrapolation and their presentation, graphically, in an orderly manner. This method proved to be an extremely useful technique for comparing policies one with another and for comparing the effects of policy with those caused by exogenous changes or model variation. The next two types of conclusion relate to the kinds of insights gained - in relation to the model and to pohcy respectively. Some of the results of model sensitivity testing are disturbing. In Fig 4, for example, the mean speed of private transport in the Leeds area was shown to be extremely sensitive to the method of assignment used. Other indicators, however, were relatively insensitive to this and thus, the method shows those indicators which should be used wrth particular caution in relation to particular model design characteristics. In other cases, a greater range of indicators were sensitive to model parameters, such as the deterrence parameters or the value of time. In such cases, again caution must be exercised because it is clear (see Section 6.4) that the same policy change can give very different results depending on the model used and on the pohcy environment. This all serves to illustrate the importance of carrying out the best possible empirical work for the estimation of such parameters in modelbased transport studies. Most of the detailed conclusions on policy making have been drawn in Section 6 above. At this point, however, it is useful to emphasise that the model does give an apparently sound “quantified common-sense” view of transport system characteristics m relation to many possible policy changes. However, for some policy changes, particularly those of great magnitude, the model’s predictions are clearly not sensible. This is because certain aspects of behaviour (such as car occupancy levels) are beyond the predictive scope of the particular model which we used. Further, it turns out that major system changes mainly relate to variables which are largely outside the control of policy makers - such as income levels, value of time or car ownership; and also that system characteristics are relatively insensitive to variables which can be changed as a matter of policy.

7.2.

RECOMMENDATIONS

We would recommend that the method described here should be widely used in urban transportation studies. The necessary “runs” could often be accumulated durmg the standard procedures of a study and graphs of the form presented here could be easily formulated. This indicates the need for careful prior consrderation of the (almost certainly long) lists of model inputs and outputs which are to be related to each other and measured against a “most likely future”. In this sense, our own study illustrates the method only. It will usually be relatively easy to modify our own input and output lists to reflect other features of transport systems and associated policies. 224

Transport Modelling: Sensitivity Analysis and Policy Testing

225

If such a recommendation was accepted, this should lead to pohcy debate taking place in a more reahstic climate: a sense can be gained quickly of what can be achieved with what resources for a particular area, and of what problems are likely to persist over a long period if resources are unavailable. Two kmds of questions are asked by pohcy makers: how can I best achieve X, Y, Z . . . ? and, what are the general effects on the system if I implement policies A, B, C . . . ? The method which we have presented in tlus paper can be used to answer these questions. The effects of policies can be compared wrth one another and, for small changes, the effects of different policies can be assumed to be additive. We recommend the use of models for the exploration of policy options all the more strongly in the light of the steady fall in computing costs. One final recommendation follows a preliminary remark. Most models have been used m the past in relation to much more detailed questions than posed here. Some aspects of the methods presented can be used in this way. However, we have emphasized the study of system-wide indicators using transport models. In many areas, time series data on some such indicators and system variables are available, even though detailed model-based studies have not been carried out for several time cross-sections. This suggests, therefore, that a useful research project would be to construct graphs relating such indicator-changes to other variables which would be comparable to our own model-based ones. This would provide a further perspective on the credibility of model-based predictions.

1

APPENDIX

Derivation

of the Basic Model Form shown in Fig. 1

It was decided that, prior to our sensitivity analysis tests we should optimise the form of the model suite which we would use for these tests. In the time available we concentrated our attention on the assignment and distribution convergence loops. The model which we had inherited from our previous work (Bonsall ef al., 1976) was essentially that shown in Fig. 1 except that it had used four equal increments for the assignment and had gone through the distribution model twice only. We wished to discover whether any substantral improvement of convergence could be achieved by adopting a different assignment/distribution convergence procedure. We had available, within our own modellmg suite, programs to achieve multirouting of the Dial or Burrell types. Despite the fact that multi-routing can be expected to speed up the assignment convergence we decided not to use these programs because we wished to retain, as far as possible, the form of the model as used previously in order to facilitate evaluation and comparison of results of our sensitivity tests with those of the earlier work. We have, however, included tests of the Dial and Burrell multi-routing procedures in our tests of variation in the model form and it is apparent (see Table 24) that, for a given computer budget expenditure, our versions of these procedures produced less satisfactory convergence than did the incremental assignment procedure. It will be noted that we do not, in this appendix, include any results of tests of iterative assignment procedures. This reflects our shortage of resources and the fact that we had reason to believe that incremental assignment would be more convergent than would iterative (see Van Vliet, 1977). In our mitral tests, we investigated the relationship between the number of equal sized increments loaded m the assignment and convergence to Wardrop’s first equihbrium criterion (Wardrop, 1952). Our convergence parameter, A 1s defined as: L: F/cl - C T;;c; A=

1

I]

(Al.l.)

XFlCl

I (m Leeds)

where Fl

-

the flow on link 1 of the prrvate transport netwo.k the generalised cost of link 1 Cl T?’ are trips from zone i to zone j by private transport - the mimmum generalised cost of travel by private transport from zone i to ,:’ ‘J zone j and the sum m the divisor 1s taken over just that part of the network in which capacity restraint operates.

Figure 37 shows, among other things, the relationship of A to the number of equal sized assignment increments. Note that progress to convergence slows down after about five equal sized increments so that, Judging from the slope of the curve, this method of assignment seems unlikely to reach a real equihbrmm without an extremely large, and thus impractical number of increments. It is interesting to note that we obtained a better convergence when the first load was assigned to a congested network (this type of assignment will be called CN as opposed to putting the first load onto an empty network EN) except when we have a small number of increments. This IS probably a function of the network, and in this case can probably be explained by the fact that, m the context of few increments, the first increment is large and 1s wrongly assigned to secondary roads (because the main roads appear congested already). 226

Transport Modelling: Sensitivity Analysis and Policy Testing

mi4.2,

0

L

’

’

4

3

N (number

of mcrements

2,

I, 11

’

’

6

5

227

’

7

’

6

In osslgnment)

F f~ CL-(T T, C,, DeltoCA) =

FIG. 37. Convergence

2 f‘ C‘ L

of different

assignment

methods

to Wardrop’s criterion.

We must bear in mind that the delta values we have derived from these tests, and the conclusions which we draw, have been greatly influenced by the configuratton of our test network (1974, West Yorkshire), the speed flow curves and the volume of trips being loaded onto the pnvate network. This latter point is borne out by the fact that when we ran a test involving a large parking charge in the centre of Leeds which caused a large modal change away from the private car, and a consequent massive reduction m road traffic, we achieved delta values of approximately 0.8% with four equal sized increments. In our sensitivity analysis we intended to vary the values of M and N in Fig. 1 in order to reach a similar level of convergence for all tests. But: (a) While variation in loop M is quite simple to achieve, appropriate variation in loop N during the run involves a complex procedure and canbe expensive in computer time. (b) Since N and M have discrete values we cannot expect to obtam identical degrees of convergence in different tests. (c) For operational reasons it is preferable to have fixed values of M and N. We concluded that although it would have been preferable to vary M and N, our constraints of time and computing budget meant that we had to adopt fixed values for these parameters. In choosing a value for N we noted the results shown in Figs. 37 and 38 and decided on N = 4 with unequal sized increments. The appropriate number of distribution loops required (the value of M) was more difficult to estimate but Ftg. 39 suggests that we reach a point after 3 or 4 loops where further loops have little effect on the trip and cost patterns. However, if we are concerned with flows we should, perhaps favour 5 or 6 distribution loops. Since we intended to run the model many times we had to seriously consider the “cost” in time, of every complete loop and therefore we opted for a combination consisting of 3 completed loops, (M = 3) that is 4 distributions in total, each consisting of 4 loads (N = 4) of unequal sized shares of the trip matrix in the ratios (5 : 2 : 2 : 1).

228

Progress in Planning 3( I2: j2C I-

IC >-

Private transport flows

1

IC)OE I-

Index

x = ‘j

ABS (&a,/“) z ‘,

02

01 008

006

I

‘r

I

I

I 4

3

----

where u,y =element of the 1, matrix after a loadlng of N equal wwements

a,y“

I 5

I 6

N = No of equal Increments

Starting Starting

Prwate transport trips

In osslgnment

from a conjested network from an empty network

* Computer problems at the time of calculotlon suggest some doubt about the precise values at these points

FIG. 38. “Incremental”

convergence

y*

z

of the tnp flow and cost matrices.

Ad,:

-~$I00

11

.Y a,: ‘/

M-NO

FIG. 39. “Endpoint”

of completed

convergence

dlstrlhrtlon

where a,: IS an element of the IX/ matr!x corresponding to the Mth d!strlbutlon loop

ICoPs

of the trip flow and cost matrices..

Transport Modelling: Sensitivity Analysis and Policy Testing

229

The next set of tests we ran were to examine the benefit to be gained from having unequal sized increments. Results of these tests are also shown in Fig. 37. From these results we deduce that judicious proportioning of the increments can Improve delta values quite substantially. More specifically we note that we obtain delta values commensurate wrth those derived from 7 equal sized increments by using only 4 unequal sized increments (ratios 5 : 2 : 2 : 1). During our tests of the effect of differing numbers of increments we recorded an index of change in the trip, cost and flow matrices caused by havmg (N) increments instead of (N-l) increments: 100 x Z&S

(ri;“_’

- $j

(A1.2.)

Change = Z TN-’ ‘J

for trips, and similar expressions for costs and flows. The results for the private transport matrices are illustrated graphically in Fig. 38. We note that, comparing (N-l) increments with (N) increments the flows change more than the trips which in turn change more than the costs. We are concerned wrth assignment and it is therefore no surprise to find flows changing most rapidly. The fact that trips change more rapidly than the costs on which they are dependent is a function of the deterrence parameter (/3); we would expect the percentage change in trips to be -1OOp times the absolute change in costs, and this is consistent with our findings. In comparing the curves for the congested network case with those of the empty network cases we note that in all instances the CN values are changing more than the EN values. Taking this fact in conjunctron with the lower deltas obtained from the congested case we conclude that the results of the CN runs “wobble” more than do those of the EN. This is, perhaps, because with our trip matrix and our network the size of the first increment m the CN case can be critical and unstabling since the roads to which flow is being assigned tend to be the secondary routes with low capacities. At this stage we consrdered that rt was necessary to construct a run consisting of several distribution loops, (loop M in Fig. 1) each usmg a large value of N in order to obtain an approximate standard with which to compare other runs. We decided on seven complete distribution loops (M = 7) each consrstmg of seven equal sized mcrements (N = 7) (before we realised that we could have achieved the same accuracy from four unequal sized mcrements!), the first increment m each loop being loaded onto a congested network. Similar comparrsons to that shown in expression (Al .2.), were performed as well as a version of this expression comparing each intermediate trap matrix etc. with the fmal trips, costs and flows obtained. These are displayed m Fig. 39 from which we conclude that after four complete drstributlon loops there is little further progress towards convergence. The delta values for each loop of loadings (based on Wardrop’s first principle, see above) were as follows (M being the number of completed distribution loops)

M

1

2

A

0.0108

0.0089

3

4

0.0101 0.0099

5

6

7

0.0102 0.0102 0.0099

These values of delta, being similar, indrcate that the approach to a convergence of the distribution loop is having no appreciable effect on the convergence of the assignment. This should be expected since any link between delta and the trip drstribution convergence would be very small and only srgnificant for wildly changing trip patterns. We wished to compare the effect of changing the number of drstributron loops (M) wrth that of changing the number of assignments (N). This was important because m order to maximise efficiency (with respect to computer time) we needed to have commensurate accuracy in the assignment and distribution loops. In making this comparrson we looked at values of the expression Al .2. u-r respect of the private transport trip matrices and found that varying N from 5 to 6 (with M = 2) gave a value of 0.13 whde varying M from 2 to 7 (with

230

Progress in Planning

N = 6) gave a value of 0.35. We conclude that, with such values of M, to use six equal increments is probably more than adequate. During this testing phase was also experimented with two new methods of achieving faster convergence to a final state. Basically these consisted of putting the distribution inside the loading sequence, such that the distribution is being continuously updated after each assignment and treebuilding. The flows at each point are made up of fractions of previous flows plus a fraction of the newly assigned trips (to make up a total over both modes which remains constant). The two methods were different in the way that these fractions were made up. In the first method the flows were halved and then quartered, and then “tumbled” 1.e. the earliest quarter of flows were replaced by the new quarter and so on until some convergence should be obtamed. In the second, all the previous flows were continuously retained but in equal, decreasing proportions at each stage. Preliminary results for these methods were encouragmg in terms of deltas and tendency to convergence of the trip and cost matrices, but we did not have the resources to pursue these tests. Interested readers are advrsed to consult the work of Evans (1976) which deals in some depth with the combination of the convergence problems for assignment and distribution models and proposes a Rockafellar-type mathematical program to achieve stmultaneous solution. After running the tests described in this appendix we had to decide on the form of the model for the policy testing sensitivity analysis. Despite the encouraging results from the “tumblmg fractions” and “decreasing fractrons” runs it was decided not to adopt these methods of reaching a convergence because they rest on behavioural assumptions about adaptation to change which are different from those used in earlier phases of our work. Since we intended that our results be compared with this earlier work we had to abandon this line of research and to adopt a model form similar to that already used. We decided therefore to maintain the form of the model shown in Fig. 1.

APPENDIX

2

Convergence: its Importance

to Sensitivity Analysis

It will normally be the case that there is no point in striving to achieve an accuracy in the calculation of results greater than the uncertainty implicit in the input parameters. Convergence need thus be no finer than the uncertainty of the inputs. In the case of sensitivtty analysis, however, we are, by definition, concerned with the rate of change of the equilibrium (converged) state of the model in response to changes in the input parameters and therefore we need to be able to calculate the value of this equilibrium whatever the uncertainty in the input parameters. Our approach to this problem has been to monitor the degree of convergence (by examining the change in a variety of indicators from one iteration to the next - results are given m Appendix 3) and to ensure that the ratio of the percentage change in the input parameter (I) to the expected degree of convergence (C’) is sufficiently large. An alternative approach might have been to consider a small change, as it propagates from one stage to the next of the iterative process, as a series which converges to the difference between two equilibria. To do this we would have had to compare like iteration numbers with like lest the difference from one iteration to the next swamp the propagating effect we would have been trying to observe. There is, however, an important uncertainty which led us to reject this approach: notwithstanding that the equilibrmm values may all be continuous functions of the input parameters, we have no reason to believe in such continuity at any stage of the iteration. The equilibrium state is the limit of a series of approxrmations in an iterative procedure and the problem is to estimate the limit from an initial segmentof such a series and to determine confidence limits for this estimate. To estimate rates of change we must be confident that the model’s behaviour is a continuous function of input parameters. To establish that the total model behaves in this way we examine its constituent submodels. The generation model is mathematically simple since no iteration or approximation is required. All functions involved are continuous and so the resultant origins (Oi) and destinations (Dj) are a continuous function of the model inputs. The distribution/modal split and assignment models are iterated with one another to achieve consistency. The distribution/ modal-split model is a doubly constrained entropy maximising model (described in Section 2.1) and is solved by the Fumess method. The assignment model attempts to achieve Wardrop’s first equilibrium criterion (Wardrop, 1952) by the incremental loading method (described in Section 2.1). Evans (1976) described a Rockafellar-type mathematical program which combines the assignment and distribution models to give simultaneous solutron to both. Since our distribution model gives a very good solution to its implicit mathematrcal program and the assignment model comes tolerably close to Wardrop equilibrium (typrcal A being 0.01 - see equation Al. 1.) then we can assume that we are very close to the solution of Evans’ programme. Now since Evans’ programme is of the Rockafellar type the solution is a smooth function of the parameters in the problem definitron such as the coefficients of generalised cost and the deterrence parameters. Results given in Appendix 3 indicate that trip and cost matrices are changing only very marginally between subsequent iterations while the flows on individual links (particularly links with low flow) vary wildly. It seems, therefore that the trip and cost matrices are very close to the continuous function of input parameters implied by Evans’ programme but that link flows are not.

231

APPENDIX

3

Con vergences Achieved Table 23(a) shows the percentage change from one iteration to the next of a number of outputs of the model for the last four iterations of the MLF. The last four iterations at double car running cost are shown in Table 23(b). The iterations referred to are complete circuits of the loop M in Fig. 1. The source of change from one iteration to the next is the assignment of private transport in the Leeds area. Starting from one assignment, trip costs are recalculated on the basis of new link times which are calculated from link flows on the basis of the capacity TABLE

231. The convergence process: various indicators The MLF run

The MLF run Iterations

Indicator*

10 11 12 13 14 15 16

17

18 19

Mean speed in the Leeds area Trips by private transport from suburban Leeds to central Leeds Trips by public transport from suburban Leeds to central Leeds Modal spht (systemwide) Modal spht mto Leeds city centre Expenditure on car runnmg costs Expenditure on pubhc transport fares Mean trip cost Mean trip cost for non-caravadable-persons dlvlded by mean trip cost for caravailable-persons Mean trip length by pnvate transport Mean trip length by pubbc transport Hansen accesslblllty of caravadable-persons to destmatlons Accessibtirty advantage of car-avadable-persons Flows on hnk 2143 (Private network) Flows on link 313 (Prnate network) Private transport trips from a suburban zone (Zone 9) to Leeds city centre (Zone 1) Private transport mtrazonal trips for a freestandmg town (Zone 41) Matrix of pubhc transport trips by car-avadable-persons Private network flow matrix

7th & 8th

compared 8th & 9th

-2.76 -1.09 0 19

1.91 041 -0.12

-0.030 -0 97 0.12 0 063 0’0174 -0.0082

0.017 0 65

9th & 10th -0.68 -0.47

Value of mdrcator m 10th iteration 20 603 20874

0.17

50765

-0.021 -0.69

0 501 0 159

-0.15 -0.039

-0.004 0 043

80798 58469660

-0 0099 0.0023

00135 -0 0091

513.543 1.2519

0 153

-0.167

0 016

5.6954

0.038

-0.024

0.322

3.7148 2362636

-0 047

0.030

-0.030

-0.088

0 048

-0 040

12457

-0.126

79 5

3 571 17.88 -4.56

0

-1.970 -10

25 4.906

-0.008

5.357 -4 197

0.008

0 251

0.239

0.242

4.229

3.6044

3 1334

3144 6 7 99

11839

*For mdlcators 1-17 we show the percentage mcrease m the mdrcators value resultmg from the change from the nth Iteration to then + Ith lteratlon For mdlcators 18 and 19 we are comparmg matrlces we show the sum of the absolute differences between each cell m the nth and the n + 1 th lteratlon dlvlded by the sum for all ceils UI the nth lteratlon. 232

Transport Modellingr Sensitivity Analysis and Policy Testing

233

restraint relationships which we apply in the Leeds area. The new costs give a different trip distribution and modal split and the new times give different trees from which the first mcrement of the next assignment is calculated. The discontinuity inherent in changing from one set of trees to another in an incremental assignment leads to poor convergence of link flows (see indicators 14, 15 and 19 in Table 23). In consequence the link times in Leeds vary, leading to a relatively poor convergence in the Leeds area (see indicators 1,2,3,5, 16 and compare them with 4,17 and 18). Systemwide outputs, however, show good convergence, no systemwide output value varying by more than 0.04% in MLF. Note the marked stability of the number of trips by private transport starting and terminating in zone 41 (17). This is because this particular zone, Harrogate, is typical of those zones not in that part of the study area to which we apply capacity restraint procedures and so, con~quently, there is no change in the cost matrix for trips in the Harrogate area. Any fluctuations which do occur are due to the indirect effects of redistribution and competition caused by changes in the cost matrix in the Leeds area (10 miles away). We note that some links

TABLE 23b. The convergence process: various indicators ’ The doubled car running cost test Iterations compared Indicator* Mean speed in the Leeds area

: 3

10 11 12 13 14 15 16

17 18 19

Trips by private transport from suburban Leeds to central Leeds Trips by pubhc transport from suburban Leeds to central Leeds Modal split (systemwide) Modal split into Leeds city centre Expendrture on car running costs Expenditure on public transport fares Mean trip cost Mean trip cost for non-caravailable-persons drvided by mean trrp cost for caravailable-persons Mean trip length by pnvate transport Mean trip length by public transport Hansen accessibdity of carava~bIe~ersons to dest~tlons Accessibility advantage of car-available-persons Flows on link 2143 (private network) Flowsonlink313 (private network) Private transport trips from a suburban zone (Zone 9) to Leeds city centre (Zone 1) Private transport intrazonal trips for a freestanding town (Zone 4 1) Matrrx of public transport trips by caravailablepersons Private network flow matrix

1st & 2nd 13.89 4.30 -1.68 0.69 8.13

2nd & 3rd -3.28 -0.66 0.26 -0.10 -1.39

3rd & 4th 1.05

Value of indicator in 4th iteration 23.229 19080

0.06 -0.04

56280 0.406 0.107

0.03 0.28

1.59 -0.646

-0.24 0.107

0.11 -0.027

91216 71152198

-0.115 0.100

0.018 -0.013

-0.0017 0.00025

550.106 1.1106

0.88 -0.155

-0.13 0.0348

0.08

3.9632

-0.0083

3.854

2.218

-0.294

0.035

1357807

0.86

-0.148

0.033

6.078

12.627

26.727

.25.70

-2.256

4.258

-0.044

-0.151 0

-19.66

89.9

6.365

2197

-2.727

642 0

1.48

0.242

0.108

48.371

4.482

2.017

11210

*For indicators l-17 we show the percentage increase in the indicators vahre resulting from the change from the nth iteration to then + lth iteration. For indicators 18 and 19 we are comparing matrices: we show the sum of the absolute differences between each cell in the nth and the n + 1th iteration divided by the sum of all cells in the nth iteration.

234

Progress in Planning

display greater instability of flow than others (compare indicators 14 and 15 in Table 23); but the fact that while, in the MLF, link 2143 is more convergent than link 313 the reverse is true when we double car running costs showing that there is no simple correlation between a link’s position in the network (vis-a-vis competitor lmks) and its stability of flow. We also find that there is no clear correlation between volume of flow and stability ln that volume. We do find however that changes in link times are normally greater when links are close to their limiting capacity. Figure 40 compares the progress of convergence of some of the outputs shown in Table 23. While the MLF outputs (solid lines) do not appear to be achieving better convergence from one iteration to the next the double car running cost outputs (dashed lines) show a consistent trend towards a better convergence. Indeed it appears that the dashed lines will end up below their solid counterparts implying that, had the double car running cost run been taken to the tenth iteration as was the MLF run, a better convergence would have been achieved than for MLF. It is thought that p&or convergence, where it occurs, is caused by route switching and that it will therefore be associated with large changes of link times (due to capacity restraint) in proportion to other route costs.

--

-

MLF ,DDfle car runnmg

Code numbers refer to mdlcators named In table 23

Iteration FIG.

40. “Incremental”

No (Ml

convergence:

comparison

of MLF and double car running costs.

Table 24 shows the degree of convergence of the matrix of public transport trips by people with cars available. These figures are consistent with the hypothesis that lower link loadings give better convergence. Notice that although increasing car occupancy (L) does lead to lower link loadings it also reduces non-time costs to trip makers and so convergence does not improve. It appears from the fact that the dashed lines in Fig. 40 are roughly parallel that the outputs shown approach convergence at the same rate and that in particular the degree of convergence of the matrix of public transport tnps by car-available-people (indicator 18 m Table 23) can be used as a proxy for the degree of convergence of the entire model. If this 1s the case then Table 23 can be used in conjunction with Table 24 to estimate the degree of convergence of any output shown in Table 23 for any of the tests shown in Table 24. In the light of this we feel confident that curves and elasticities produced in this report are, unless otherwise stated, not unduly affected by convergence problems.

Transport Modelling: Sensitivity Analysis and Policy Testing TABLE 24. The convergence of the matrix of pubbc transport trips by persons with car available Test code*

Parameter change

A B C D E

Discrete Discrete Discrete Discrete Discrete

F

Zero NllIliIlg costs 0.5 x MLF costs 2 x MLF costs 3 x MLF costs 4 x MLF costs 10 x MLF costs

1.91 0.62 0.11 0.03 0.01 0.00

G

Zero charge 2 X MLF charge 4 X MLF charge

0.33 0.10 0.10

H

Zero fares 0.75 X MLF fares 2.0 X MLF fares 4.0 X MLF fares

0.14 0.27 0.51 0.65

0.5 X MLF values 1.2 X MLF values 2.0 X MLF values

0.20 0.26 0.35

0.5 X MLF values 0.8 X MLF values 1.2 X MLF values 2.0 X MLF values

0.21 0.28 0.27 0.33

0.5 X MLF value 0.8 X MLF value 1.2 X MLF value 2.0 X MLF value

0.20 0.26 0.25 0.36

L

Car occupancy = 1 car occupancy = 2 Car occupancy = 4

0.30 0.2 1 0.33

M

0.5 0.9 1.1 2.0

0.17 0.30 0.23 0.58

I

J

K

test test test test test

I**

X MLF X MLF X MLF X MLF

value value value value

0.20 0.53 0.95 0.17 0.28

Test code*

Parameter change

t**

N

0.5 X MLF value 0.9 X MLF value 1.1 X MLF value 2 0 x MLF value

0.01 0.30 0.27 1.55

0

0.75 0.87 1.06 1.34

value value value value

0.97 0.44 0.39 1.28

P

0.49 X MLF value 0.8 X MLF value 0.96 X MLF value 1.12 x MLF value 1.25 X MLF value 2.09 X MLF value

0.58 0.29 0.27 0.28 0.26 0.24

Q

0.5 X MLF value 2.0 X MLF value

0.14 0.24

R

0.7 X MLF value 1.3 x MLF value

0.27 0.24

s

0.5 0.9 1.1 2.0

X MLF X MLF X MLF X MLF

value value value value

0.19 0.26 0.34 0.35

T

0.5 0.9 1 .l 2.0

X MLF X MLF x MLF X MLF

value value value value

0.28 0.27 0.27 0.30

U V W X Y Z

Discrete Discrete Discrete Discrete Discrete Discrete

X MLF X MLF X MLF X MLF

test test test test test test

0 36 0.25 0.26 151 1.01 N/A

* Test codes are defined m Table 8. Z ABS (7$ - $1 **r = 100 x where c,,’ is the value of 7;;’ for the penultimate zT(; ’ iteration.

235

References

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237