A transportation-sensitive model of a regional economy

Transpn Rrs. Vol. 8. pp. 4562.

Pergamon Press 1974.

Printed in Great Brwin

A TRANSPORTATION-SENSITIVE MODEL REGIONAL ECONOMY*

OF A

M. S. BRONZM~?,J. H. HERENDEEN, JR.~, J. H. MILLERand N. K. WOMER$ Pennsylvania Transportation

and Traffic Safety Center. The Pennsylvania State University

(Receitied 20 Nouemher 1972; iu revised_form 20 June 1973) Abstract-An integrated model system for analyzing alternative regional multimodal freight transportation infrastructures is developed. An econometric model uses transportation price information to determine the origin-destination flows of commodities throughout a region. These flows are input to a freight modal split model, which apportions them among the various modes on the bases of relative transport service variables. A network simulation model assigns the commodity flows by mode to specific routes and calculates flow-dependent origin-destination impedance values. Equilibrium values of model outputs are attained by means of a multi-feedback iteration process. The nature of model system interactions is explored by applying the model to a hypothetical region.

I. INTRODDCTION The Pennsylvania Transportation and Traffic Safety Center, in conjunction with the Transportation Research Institute of Carnegie-Mellon University, has developed a methodological framework for comprehensive transportation planning for the Commonwealth of Pennsylvania (Transportation Research Institute, 1968).This methodology is the first step toward a comprehensive regional transportation planning tool for Pennsylvania, that is, a tool capable of incorporating planning decisions and forecasting their impact on the Commonwealth. The Methodological Framework itself does not contain a series of forecasting models, but rather provides a set of guidelines for model development. This study constituted a logical extension of that research effort. Its purpose was to develop a transportation-sensitive model of a regional economy based upon the guidelines proposed in the Methodological Framework, and to apply this model to an example in order to ascertain the nature of model interactions and model system equilibrium. It should be noted at the outset that the scope of this paper is limited specifically to that intent which has just been stated. No attempt is made to survey the literature, as such information is readily available elsewhere. References are given in most cases solely to sup* This research was supported by The Pennsylvania State University. t Present address: Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A. $ Present address:’ Gannett Fleming Corddry and Carpenter, Inc., Harrisburg, Pennsylvania 17105. U.S.A. §Present address: Air Force Institute of Technology, Wright Patterson AFB. Ohio 45433, U.S.A.

port assumptions and to provide certain results which

cannot be derived within the confines of the paper. Although heavy reliance for supplying analytical details is placed on previous publications emanating from the research program of which this study was but one part, the paper is reasonably self-contained, in that prior reading of those documents is not necessary for following the development and main results presented below. One part of the Methodological Framework concerns itself with the “Forecasting Model System” that forms the analytical nucleus of the comprehensive planning tool. While the guidelines presented in that report form the basis of the model developed in this paper, there are several significant differences beween the two efforts. The Forecasting Model System provides a means by which alternative planning decisions may be evaluated. The model developed for this project, on the other hand, predicts equilibrium solutions to a set of initial conditions. It is concerned only with short-run responses to changes in prices (which may be caused by changes in the transportation network) and does not consider changes in variables covered by a ceteris paribus assumption, namely, the state of technology, population, and public policy. Unlike the Forecasting Model System the model presented herein was designed for application to any closed region, not necessarily the Commonwealth of Pennsylvania. The example discussed in Section 6 is not necessarily representative of any particular geographic region, but is intended to represent several of the important complexities of a regional economy. The transportation network analysis, however, has been somewhat limited in that only commodity flows 45

M. S. BRONZINI, J. H. HERENDEEN,JR.. J. H. MILLER and N. K. WOMER

46

lowing manner: Sections 2, 3 and 4 are devoted, respectively, to the econometric model, the freight modal split model and the network simulation model. Section 5 details integration of the model system, and Section 6 describes the example problem used to test the model. 2. THE ECONOMETRIC

Fmght _

ImdalsPllt

___

model

Fig. 1. Regional transportation planning model system.

are presently considered. Development of a companion passenger demand model has been left for future research efforts. The omission of passenger flows in the network analyses merely has the effect of forcing passenger flows to be constant in the short run. A flow diagram of the model system developed for this study is shown in Fig. 1. This system of models forms a subset of the Forecasting Model System, with the distinctions noted above. The econometric model uses transportation cost information to determine the flow of commodities throughout the study region. The freight modal split model determines how much of each commodity is shipped by each mode and the cost of transporting each commodity between each origin and destination. The network simulation model assigns the commodity flows by mode to specific routes and determines the travel time between each origin and destination by each mode. The remainder of this paper is organized in the foll This assumption is made merely for expository purposes and can be easily relaxed. To do so requires an additional model which explains the interaction between the regional economy and the rest of the world. t The nth industry is the household sector. irs output being the services of labor. ; Final demand is the quantity of each of the (II - I)UI commodities demanded by the household sector.

MODEL

The econometric model is the result of an attempt to give body to a general and somewhat imprecise set of recommendations found in Chapter VII of the Methodological Framework. Consider a closed geographic region* consisting of m production nodes (locations) and n-1 industries? each producing some of a well defined commodity group. Commodities, the members of a commodity group, are further characterized by location. (Commodities within the same group may differ in other respects as well, as will be discussed shortly.) Thus there are (n - 1)m commodities and the model predicts their flows among the m production nodes of the region for any set of transportation costs. The production ofeach of the (n - 1)m commodities is assumed to be described by a function which is linearly homogeneous. This allows the total output of each of the commodities for a given set of prices and a given level of final demand$ to be found with the use of the Leontief input-output model. In matrix notation: x = (I - Q-1 D

(L)

where Y. is the vector of outputs of length (n - I)m, I is the identity matrix, R is the matrix of technological coefficients, and D is the vector of final demand. Changes in transportation costs influence the production and distribution of commodities throughout the region by causing changes in the elements of the R and D matrices in (1). That is, changes in transportation costs are assumed to cause changes in delivered prices which induce producers and consumers to reallocate their expenditures on commodities, substituting the relatively cheaper commodities for the more expensive ones. This behavior is revealed by using production and demand functions of a form that reflects the ideas presented by Lancaster (1966). In the case of production. a function is used which specifies industry behavior of first allocating expenditures between inputs of dissimilar characteristics and then between elements of a group of similar inputs. The following notation is used to describe the econometric model in more detail: Xigjh = the quantity of commodity i produced in node 9. shipped to industry j located in node h p,,

= the price of good i produced in node g

A transportation-sensitive

the cost of transporting good i produced in node g to node h Pig + Tish = the delivered price of good i produced in node (I and shipped to node h Riah = the technological coefficient of industry .j located in node /7 associated with input i produced in node 61 C, = the total expenditure of industry j located in node I7 on all inputs Ci,,, = the expenditure of industry j located in node I? on inputs of type i. The symbol (.) is used throughout to indicate the operation of summation. e.g.

j= ,

It=

I

Ajhfi f i= 1

g=

1

;.,A%,r

(Zij,, 1

XijShY1””

(2)

where A. LY,/?, and ;’ are parameters of the function. It is important to notice that the theory is intended to recognize the realities of data collection. All of the variables are therefore aggregates over some classification scheme in the same sense that the outputs of some two-digit standard industrial classification industry are aggregates of the outputs of industries and firms making up that classification. Therefore. Xi, is not the same input as Xi,, a member of the same commodity classification produced at a different node. The theory specifies only that they are in some sense more similar than two inputs from two different commodity classifications. This somewhat novel definition of “commodity” or “industry”*, recognizing as it does the economic importance of regional spatial relationships. is a major source of the transportation sensitivity of the model. The data collection considerations mentioned above also necessitate such a definition, since aggregation of shipment data will result in large variations in the actual composition of shipments of a given commodity class originating at different nodes. It is assumed that the production function (2) is linear and homogeneous. That is. given the relative prices of inputs the expansion path of the industry is * These two terms are used interchangeably For the most part. Conceptually, “commodities” are associated with the rows of an input-output table. and are the outputs of “industries.” which form the columns. t The necessary and sufficient conditions for a minimum require ;I,,,, > 0. z,cJH > 0 and fi ,.,,, c 1. The assumption of linear homogeneity requires ;‘.,,,, = 1. T.R. R’I-D

47

a ray through the origin. The production function is a combination of a Cobb-Douglas production function and one of the Constant Elasticity of Substitution (C.E.S.) variety. Each industry is assumed to minimize its cost of production. Therefore. using Lagrange’s method. the industry’s demand function for input XIGJH is found to be (Bronzini c’tul., 1972; Womer. 1970: Transportation Research Institute. 1968):t

X IGJH=

(3)

1

The production function for industry j located at node It is assumed to be:

xj, =

model

Dividing this by XJH., yields one element of the technological coefficient matrix R. It is readily seen that the technological coefficients, Riej,,, are functions of prices. including transportation costs. Hence these R’s may be revised when prices change if the coefficients of the production function are known. Procedures for estimating the parameters of (3) have been developed by Womer (1970). The ;‘,JH are estimated from time series observations on expenditures of the industry. The prJH and the normalized l,gJH are estimated from time series observations on inputs and prices. Substituting the estimates for the parameters of equation (3) yields a set of relations predicting the changes in quantity demanded of any commodity (or labor) due to changes in total expenditure and delivered prices for a decision unit. There are 77777 sets of these relations, one for each of the (77 - 1)~ industries of the region, and one for each of the 177 household groups supplying labor to them. The resulting set of equations, describing the demand for the IGth input to the JHth industry. is:

I=1 “J z

, _, ’ ;,

; ,

H =

. . ., I7 . . ., 777

(4)

, . , . . 77

1.2....777

Likewise, R,cIB, the JHth element of the IGth row of the estimated R matrix, is found as:

The elements of the final demand vector, 0, are obtained from those equations of (4) that apply to the

M. S. BRONZINI. J. H. HERENDEEN.JR.. J. H. MILLER and N. K. WO.WR

48

vity model. To see this let

m household groups. That is,

TGH

=

l’lGJH.

plGH

CJH

=

OH =

c

bIJH

=

D

In YIJH.

Two problems remain in the attempt to predict shipments of commodities from transportation costs. They concern the effect of changes in transport costs on prices and expenditures of the industry. These may be overcome, however, by assuming the region operates in accordance with pure competition. This assumption requires that for each industry a “normal” rate of profit obtains. In addition, this “normal” rate of profit is assumed to be equal for all industries. The existence of this “normal” rate of profit allows equilibrium home prices, P,, to be computed. That is, given some initial allocation of commodities and given the transportation costs consistent with that allocation there exists a unique set of equilibrium relative prices in the economy. These prices are found as the solutions to the following set of simultaneous equations:

$ CXigJHtPig + Tighll = tpJH - n, XJH.. J = 1, 2, . . .) n

blJ.=iil

-

G= 1

XIGJH.PIGH

G uIGJH

PIGH fPIGH)

PIJH/bIJH

-

=

1 =

e6H fteGH),

Then (3) may be expressed as TGH

where

=

(10)

AH”HDGfteGH)

An =[;D,f(e,,)l-i.

Here trips of type IJ, flows of commodity group I to industry J, are measured in dollars; OH the total number of such trips has the same units; DG is a parameter of the model to be estimated: PrGH is a measure

(7)

23= 1, 2, . ., m. In the equation (7) the transportation costs, Tigb are determined as will be described below; l7,the normal rate of profit, and Xigjhr the initial allocation of commodities, are given. Also, from (7) total expenditures of the industry are found to be: CJh = (PM - WXJff

is)

.

The profits are returned as income to the household sector of the node in which they originate, node h. Substituting from (8) and (3) into (5) yields the final form of the relation which describes a representative element of the R matrix:

I

Find

Find prices and wsts

shipments X w,n

c,, )

(9,.

I Find technological coeffmmts and fmol demxd (R,,.O,,

YIJH(PJH - II)

RIGJH

flm,‘-@rJH

( > @)2L” UIGJH

PIGH =

f

x,n.=

x;n.

1 I

SOlVe

’

(9)

It can be shown that SRIGJH/aPIGH varies between - x, and 0 as flIJH varies between 1 and - zo. Thus positive values of filJH that are close to I imply that the coefficients of R are very sensitive to price changes while large negative values for flIJH limit the effect of price changes on the quantity of XrG used to produce a unit of XJH. The effect of relation (3) may be easily seen to be analogous to that of the single competition term gra-

Fig. 2. Econometric

model

A

transportation-sensitive model

of impedance between points G and H; and the functional form offis given with one parameter to be estimated. Clearly. the analogy between (3) and the gravity model is very close and their effects are similar. The complete econometric model is described with the help of Fig. 2. Given time series observations on Xinj,,. Taj,,, and Pi,. estimates of Yigj,,,&,,. and zisih are obtained. These estimates, together with Xigjh. the quantities of all commodities shipped to all points in the region for some initial time period. and l7, the normal rate of profit. are the initial data to the econometric model. The initial Xisjh are used by the freight modal split and network simulation models to calculate transportation costs. The transport costs, commodity flows, and normal rate of profit are used to find equilibrium prices in (7) and expenditures of each decision unit in (8). The R matrix and the vector D are then calculated using equations (5) and (6), respectively. Estimates of the total output of each industry. X’j,., , are then obtained by solving (I - R)-’ D. These estimates are then compared to the initial total outputs of each industry. If the difference between these two elements are less than some convergence criterion, the run ends; if not. new shipments and commodity flows are found as Risjh Xjh,, and the process is repeated. Normally, convergence has been obtained in a small number of iterations for the following criterion:

Ix;,. -

x,b.j<

xjb..

=

0.10

’

3. FREIGHT MODAL SPLIT MODEL

The output of the econometric model is the amount in tons of commodity i that will be shipped from node g to industry j in node 11,Xisjb. The network simulation procedure requires that these noderto-node flows of commodities provided by the freight demand model be allocated to various modes of transportation. These modal allocations are the responsibility of the freight modal split model. Considering the nature of the shipper decision process. and the data constraints, multiple regression analysis provides an advantageous technique for developing a freight modal split model. The model is formulated as follows:

(11) with the constraint

49

in which P&Xi,,-,) = Percentage of Xeigjbthat will be shipped by mode XRk = Reliability of mode I( = Percentage of deliveries made on schedule C, = Relative cost by mode k lowest rate by all available modes = rate by mode k Tk = Relative transit time by mode k lowest time by all available modes =---time by mode k F, = Relative frequency of service frequency of service by mode k = best frequency of service t(1,2,3,4= Coefficients to be estimated and r0 can be computed by substituting (11) into (12). This formulation follows closely the abstract mode model proposed by Quandt and Baumol (1966). Further details regarding the development of this model are provided by Herendeen (1969). Discussiorz of thcfreigltt

modal split model

The premise upon which the model is based is that shippers make rational mode choice decisions on the basis of those factors which influence logistic costs Notice that there is no attempt in the model to minimize the total logistic costs. Calibration of the model on historical data determines how ‘important each of these considerations is with respect to the rest of the independent variables. One of the most important variables to the modal split decision is the cost of the transportation service to the shipper. or the price the shipper is required to pay for the movement service. There is little doubt that present patterns of freight movements are influenced in most cases by the rates charged by the carriers. Also of importance is that the cost differential between modes affects the modal split decision in varying degrees depending upon the commodity type. For any given commodity. the transportation cost will be directly influenced by the size of shipment and the distance between origin and destination. The effect of distance on rates is attributable to the variable costs ofcarriers, e.g. fuel costs, which increase with distance. The size of shipment affects costs because of economies experienced by the carriers in terminal costs with larger shipments. A modal split model proposed by Church (1967) uses distance and size of shipment to help allocate shipments among modes. The proposed method of applying the model uses these variables to determine transportation cost. Based upon this consideration,

50

M. S. BRONZINI. J. H. HERENDEEN.JR..J. H. MILLERand N. K. WOMER

transportation cost can be used in the regression analysis in place of the distance and the size of shipment. It should also be pointed out that transportation cost is more compatible with this effort than the size and distance variables. The econometric model is transportation cost sensitive. i.e. commodity shipment predictions are based to some extent on transportation costs. Transit time has been used in several of the models examined as a consideration for carrier selection. The importance of time to shipments of perishable commodities and to “rush order” shipments is quite apparent. Transit times are important to other commodities as well because long transit times may necessitate large inventory levels at destination points. Related to the transit time is the carrier’s reliability regarding delivery schedules. or the variation which occurs with respect to transit time. The probable reliability of a carrier regarding delivery time variations affects the level of safety stock held by receivers. Some shippers are willing to use a slower mode of transportation in order to obtain more reliable service, and thus reduce the chance of having a “stock out ” situation while holding lower levels of safety stock. Reliability or variability in delivery time is the most difficult variable to describe quantitatively. Further, previous research efforts have indicated the difficulty of obtaining delivery time information (Roberts rt al., 1966). Most shippers appear to have only an impression of service reliability at destinations since little detailed information is recorded. These two factors together make reliability easier to deal with in the regression equation than would be the case if another formulation were used. A possible definition of this variable is the percentage of deliveries made on schedule. An alternative approach to this problem is to use two dummy variables in conjunction with a rating or classification scheme (poor, good, excellent). As noted in the discussion above. transit time and service reliability are important to the shipper because they affect the total cost of using a particular mode. The levels of such costs, as reflected through warehousing or inventory costs are very important for some commodities. A further measure of service quality that intluences the modal split decision is the frequency of service. This variable has been included in the equation because of the effects of service frequency on handling and inventory costs and on the convenience to the shipper. Also, its use in the equation is quite compatible with the transit time and reliability variables. The basic advantage of the model involves

the method ofdescribing different modes of transport. An) means of shipping that ditTers from other modes with respect

to cost. travel time, freyuencq

of service

01

reliability of service can be described as a separate mode. Thus, regular rail and piggyback could be described as separate modes. even though they are both “rail” modes. The procedure is particularly advantageous if a new transport mode is to be considered in some future time period. The modal split prediction can be made if the cost, travel time, reliability and frequency of service can be estimated. It is this characteristic of the model which Quandt and Baumol (1966) were referring to when they described their model as the abstract mode model. Freight rate sub-model

Of great significance in an aggregate modal split decision model is the relative cost of transportation by the various modes. For the purposes of the freight modal split model. the cost of each mode of transportation relative to the cheapest mode of transportation is needed. In the Methodological Framework jbr Comprehensice Transportation Planning. it is suggested that this rate information be contained in a table listing the rates for the various commodities between the node pairs in the model. These rates would be determined by actually looking up existing rates for the various modes considered and entering them in the table. Initially, it must be realized that what is needed is not a rate which would describe the cost of transportation of a given movement of a specified commodity between two points, but rather a general representation of the rate level and structure which exists at a given time. The larger model considers at most 80 commodity groups following the guidelines of the Standard Industrial Commodity classification. Using this scheme of classification, all foods or primary metals, for example, would be aggregated. At this level of aggregation. the desired rate could not. and should not, represent the rate of a specific movement of a commodity. Given these requirements, it was determined that a table of rates would be impractical and almost impossible to construct. In order to construct a rate table, rates for specific commodities within the general commodity group would have to be aggregated by weighting the particular rate by the significance of that commodity’s movement between each pair of nodes. In order to do this with any degree of accuracy. a listing of product movements between nodes would be required. These datu are not currently available. nor can it be expected that they will be available in the future. Another disadvantage of the table-look-up approach to rate determination is a practical consideration of computer storage requirements.

A transportation-scnsltive

A more reasonable alternative was determined to be a list of equations. one for each mode and commodity. These equations would determine a rate as a function ofcommodity. mode, distance, and shipment size. The general form of this relationship would be: RighA= F(D*S)

(13)

where

Righl = rate for commodity i moving between nodes g and 11by mode li = Distance between nodes g and 11 D = Shipment size s Data suggest that the form of. this relationship is non-linear. Lates per mile generally decrease with increasing distances since terminal costs become a smaller percentage of total cost. It is also true that costs decrease with increasing shipment size due to efficiencies in operations. These considerations would suggest the following log-linear relationship:

where x1, x2, x3 are parameters to be estimated by least squares regression. The above formula implies a continuous functional relationship. This however, is not entirely accurate. Rates are quoted based on vehicle and less than vehicle loads. The functional relationship is discontinuous at the vehicle load break. This relationship is shown

A

TonsA = Carload minimum

relght

Fig. 3. Cost per ton for commodities shipped by class rates. * “Cost” and “time“ are used interchangeably in this section. The actual impedance units are determind by the model user. 7 The flow units used can be tons, cwt. vehicles, or any other unit which the system programmer finds convenient. Cost functions must then be specified in terms of the units selected.

model

51

graphicall! in Fig. 3. A revised relationship including this consideration would use dummy variables to indicate vehicle and less than vehicle loads. as follows:

where X 1 and _Y? are dummy variables to indicate vehicle and less than vehicle loads. Using this relationship. an estimate of the rate can be calculated for each combination of commodity type. shipment size, and distance once the equation has been calibrated. 4. NETWORK SIMULATION MODEL

The purpose of the network simulation model is to assign the origin-destination (O-D)commodity flows by mode to the various links of the transportation network serving a region. and to determine the internodal impedances associated with these flow volumes. Comparisons of link volumes and capacities, as well as examination of impedances, may then be used to test the adequacy of existing or proposed transportation networks and to evaluate the effects of improving the transportation system. The overall model system also requires the feedback of impedance information to the freight modal split model. The network simulation model accepts as input Xij,, the number of tons of goods per day moving between each pair of nodes by each mode. Using a description of the network serving each mode. it determines the specific routes utilized between each pair of nodes, together with the impedances incurred on these routes. The model then provides as output the volumes using each link. the final link costs* associated with these volumes, and the average travel costs between each pair of nodes. The techniques used for the above calculations are those of classic traffic assignment. A network consisting of nodal centroids, arcs and vertices is delineated for each mode. Minimum path trees are determined for each origin node, and flow units? are assigned to these minimum paths. Based upon these assigned flows, new arc costs are calculated. using a capacity restraint function. The procedure is repeated until some convergence criterion is satisfied. The actual assignment program used is a modification of one developed at the Pennsylvania Transportation and Traffic Safety Center (Davinroy. Bronzini and Herendeen, 1969). At this point it might well be asked why traffic assignment techniques should be used for simulating all portions of the transportation system of a region. For some modes, such as inland waterway, there may be no choice of routes between origin and destination. For

52

M. S. BRONZINI.J. H. HERENDEEN,JR., J. H. MILLER and N. K. WOMER

others such as rail, route selection may not be solely a function of link travel times. Terminal and transfer times may be the critical determinants of journey time for some modes, such as air and rail. Thus, it may appear that classical traffic assignment techniques are appropriate for use only with highway networks. There are several compelling reasons for using traffic assignment techniques for non-highway modes which appear to override the preceding arguments. First, the abstract networks defined for such modes to not have to include links representing every physically existing facility. It is sufficient to merely define spider networks composed of major travel corridors. Links representing terminal facilities may also be included in such a network. The formal analysis of the traffic assignment process then gives the transportation planner a powerful tool for determining the effects of major increases in corridor traffic, selected terminal facility improvements. the opening of entirely new corridors, etc. The effort required to define a non-highway network is relatively minimal. Also, the use of a single network analysis tool is computationally efficient, particularly since the non-highway networks will usually be very small.

cessive increments of flow units are loaded on the network. The network simulation model uses the hyperbolic cost function proposed by Mosher (1963). which may be expressed as follows: w=w

A

_m

’

where

= link volume (Row units/time unit) = link impedance at flow rate Q (cost/flow unit) w” = impedance when traversing the link at mean free speed = horizontal impedance asymptote of the funcwA tion C = link capacity; the maximum flow rate possible on the link. This function is illustrated in Fig. 5. The characteristics of the hyperbolic function make it virtually ideal for use with multimodal networks. The shape of the function is controlled by C and WA. Thus, a large number of smooth, monotonically increasing curves passing through the points (0.17) and (C, + x) may be represented adequately by the function. In addition. the cost curves for those links on Q

A.ssigi7mrntprocrdtlir The network simulation model utilizes an incremental loading technique. Thus, the steps of the traffic assignment to each network are carried out in the following order: 1. Link costs at zero-flow are calculated. 2. The minimum path tree from node 1 is determined. 3. The first increment of flow units from node 1 to all other nodes is loaded on these minimum paths. 4. Steps 2 and 3 are repeated for each of the remaining nodes. 5. New link costs. corresponding to the flow volumes determined in steps 2-4. are calculated. 6. Steps 2-5 are repeated for as many loading increments as specified. Figure 4 presents a Row diagram of this procedure. Note that How units are assigned to the network in equal increments. The number of increments may be as few as one, and the maximum number of increments is limited only by computer storage capacity and run time considerations. Four or five increments are usually sufficient to produce acceptable results.

-WA Cl’, < W, Q < C (15)

Q-C

start

“r‘

N = NO.of IXXIIW M.ND.Of nodes

Incmmmts

K*O All link flows (~7)=O

I 8ulld m,",mum path tree frcm nodeI

Cos~Jirr7ctiorl As indicated above. the incremental loading approach requires the use of a capacity restraint or Fig. 4. Assignment cost function to update link impedance values as SLIC-

procedure for model.

network

simulation

A tracsportation-sensitive I

/I / /

--w-0

w fi Flow (0)

Fig. 5.

-

C

Hyperbolic cost function.

which the impedance is judged to be insensitive to flow volume may be represented by allowing WA = m, which implies that W = WA = w. For this model, all impedance values are expressed as cost per unit length. This allows various link classifications to be defined, so that only a limited number of cost curves must be developed. Dummy (non-physical) links are given a length of 1.0 units to allow the impedance values of such links to be expressed directly as cost units. The three parameters of the cost function, m, WA and C. must be estimated. Standard statistical estimation procedures should be used for this task. This requires that a series of observations of impedance vs flow volume be obtained for each link or class of links. One possible drawback in using the hyperbolic function is that it is not defined for Q 1 C. It is quite possible that at some point during the network simulation process, some link or links will be assigned a volume exceeding the stated capacity. This is particularly true when many elements of a network are operating at or near capacity, as is rapidly becoming the case in many parts of the United States, The network simulation model overcomes this difficulty by defining a new function for Q 2 V, where V = 0.9OC. This new function is obtained by rotating the hyperbolic function 180 about an ordinate through V and 180” about a horizontal line through W( I/). Information conversion

Input to the network simulation model from the other portions of the model system consists of the amount of goods moving between each pair of nodes by each mode. Normally, the quantity of goods will be expressed as tons/year. but the network simulation will

model

53

be most conveniently carried out in units of vehicles/ day. This implies that the yearly flow of goods must be factored to an average day. and that tons must be converted to equivalent vehicles. Nothing in the network simulation model. however. requires that these be the information conversion procedures utilized. Any unit system which is convenient for the particular problem undergoing analysis may be used. Thus. for example, flows may be expressed as tons/day. and the hyperbolic cost function parameters may be defined in terms of these same units. The primary output from the network simulator to the model system consists of the average internodal impedances by each mode. It is necessary that these impedances be expressed in the same units, since the freight modal split model calculates impedance ratios. This implies that either all networks are analyzed using the same impedance units or impedance conversion factors are applied. The network simulator employs the latter alternative. 5. DYNAMIC

OPERATION

OF THE MODEL

SYSTEM

The manner in which the individual component models interact to produce an equilibrium solution for the given input conditions is now described. The flow diagram in Fig. 1 provides a basis for this discussion. The econometric model requires socioeconomic data for the entire study area. as well as for all external nodes considered. This information is a representation of the distribution of economic activity among the nodes and the flow of commodities between these nodes. Transportation system variables are included in the form of estimated costs of freight transportation between each O-D pair. Freight flows predicted by the econometric model are used as part of the input for the freight modal split model. Here, the transportation system characteristics required are the cost. time, and relative convenience of each mode being considered. The values of the time (and in some cases, cost) variables used at this point are preliminary, pending the loading of the transportation network by the network simulation model. Freight flows by mode for each @D pair are predicted on the basis of these estimates. The function of the network simulation model is to allocate the flows of goods to the individual components of the transportation network. The outputs of the model include the volumes of traffic flow for the various components and revised values of network performance characteristics to the extent that they are affected by loading. In general, the time and cost of travel on the networks must be calculated based on the predicted

M. S. BRONZINI. .I. H.

54

HERENDEEN. JR.. J. H. MILLER and N. K. WOXEK

flows for each mode and link since heavy loadings suggest congestion. These revised estimates of travel time and cost are fed back to the freight modal split model, which uses these measures as explanatory variables. The revised flows by mode which are then estimated by this model are input once again to the network simulation model to produce another estimate of network characteristics. This iterative process is continued until the changes in traffic volumes and/or impedances (travel times or costs) are small. The equilibrium values of the network parameters are then utilized by the freight modal split model to obtain a revised estimate of the cost of freight transportation services. These costs are then returned to the econometric model. If they cause significant changes in commodity flows between zones, the entire process is repeated. The process is continued until equilibrium is established in the commodity flows from one iteration to the next. Several items deserve reemphasis before proceeding to an example. Notice that in each part of the forecasting model system, predictions are a function of transportation characteristics. The econometric model predicts the distribution of commodities and economic activity based, in part, on the costs of transporting goods. The freight modal split model uses the travel time. cost, and convenience of the individual freight modes to predict the volume of goods that will use each mode. The network simulation model allocates traffic to the transportation network’s various routes on the basis of those routes’ times (or costs). It also adjusts times (and costs, if desired) to reflect high utilization of network components. leading to the iterative process described above. The transport-sensitivity and dynamic features of the regional model system are achieved because each iteration of the process provides more accurate estimates of the equilibrium values of network characteristics and traffic flows. 6. APPLYING

THE MODEL

SYSTEYvl

The purpose of this section is to graphically demonstrate the procedures involved in applying the model system to an economic region. Because data concerning a real geographic region are presently unavailable in enough detail to allow application of the model system. it was necessary to design a hypothetical economy. In order to demonstrate the model’s capabilities, a hypothetical region should contain alternate transport modes, several production nodes. and a sufficient number of commodity types to show interaction of the productive processes. For computational ease. it was decided to make the problem as simple as possible g&n the above constraints.

The design region was composed of four production nodes. Four nodes provided for a relatively complex interaction with 12 possible 0-D pairs. Nine commodity types were chosen for examination in the hypothetical region. This number was used because it allowed for the inter-industry interaction that is analyzed by the econometric model. The nine commodities coupled with the 12 O-D pairs allowed for 972 internodal commodity flows and 324 intranoda1 transactions. Two modes of transportation were considered in the hypothetical region. One mode was designed to resemble the railroad mode while the other resembled the trucking industry. Two modes allowed for a modal split calculation but again did not introduce unnecessary complexity. Each mode was provided with a network to accommodate the Rows of goods. The highway network contained 244 separate links, and the rail network had 60 links, 38 of which were used to represent non-line haul system elements (e.g. classification yards). These networks were sufficiently complex to allow alternate routings between O-D pairs so that the assignment procedure could perform its functions. The hypothetical region. while completely artificial, involved many of the elements of a real economy. The data used by the model system are not valid for any particular region; however, they were derived from existing data and. therefore, describe an economy that could exist. The transportation network used was based upon a network that does exist. The rates charged for freight service were based upon a representative sample ofexisting rates. Modal split information was taken from national average data. Commodity flow information was hypothesized based upon inputoutput information for Standard Metropolitan Statistical Areas. While the region studied did not consider all the complexities of a reai economy, enough detail was included to show that the model system could be applied to a much more complex economy. Data sources utilized and the resulting model parameter estimates are given by Bronzini et ~11. (1972). Testing was performed on the transportation system described above (termed the “base network”) and upon two alternative networks-one incorporating a new interstate highway (“Alternative A”) and one incorporating the new highway and a high speed rail line (“‘Alternative B”). The results obtained for each network are discussed and compared below. To begin the operation of the model system. it was necessary to obtain a set of commodity Hews. One of

A transportation-sensitive

55

model

Table 1. Input travel times and resulting modal split for base network O-D pair

Daily shipments (tons) Rail Truck

Travel time (hr) Rail Truck

l-1 l-2 1-3 1-4

0.0 8.94 163.18 882.9 1

0.0 141.94 2334.05 12356.30

0.0 47.81 49.19 34.95

0.0 6GCI 6.75 4.82

2-l 2-2 2-3 2-4

10.944.90 0.0 2075.15 258 1.67

4088 0.0 1121.02 13200

58.84 DO 40.48 51.91

5.95 00 2.47 7.99

Fl 3-2 3-3 F4

468.13 339.74 0.0 326.89

724.62 73619 0.0 653.94

52.71 39.85 0.0 56.16

6.24 2.42 0.0 10.03

4-l 4-2 4-3 4-4

534.99 120.01 732.11 0.0

5867.27 141.91 752.21 0.0

34.83 46.78 55.97 0.0

3.30 7.20 9.27 0.0

the sets of observations used to estimate demand function parameters served this purpose. These initial commodity flows in conjunction with an assumed set of internodal travel times produced the modal split shown in Table 1. Note that a modal split was performed for each commodity group, and that the information presented in the table represents an aggregation over all

* The convergence criterion used was that all internodal travel times must be within 10 per cent of those for the previous iteration.

commodity groups. Four iterations between the freight modal split model and the network simulator (as de-

scribed in section 5) were required to obtain convergence of internodal travel times.* The resultant equilibrium modal split and travel times are shown in Table 2. Note that the total flows between O-D pairs remained constant throughout this iteration process. At this point new internodal transportation costs by commodity group were calculated and returned to the econometric model. These new transportation costs were used by the econometric model to calculate a revised set of prices.

Table 2. Travel times and modal split after first complete iteration-base O-D pair

Daily shipments (tons) Rail Truck

l-l l-2 l-3 l-4

0.0 11.85 21144 2061.45

2-l 2-2 2-3 2-4

19939.20 0.0 2257+rO 2587.35

network

Travel time (hr) Rail Truck

0.0 139.03 228580 11,177.77

0.0 40.25 41.45 27.74

0.0 7.95 9xKl 1584

4658 0.0 939.17 126.32

82.98 0.0 2958 71.58

684 0.0 2.79 1670

3-l 3-2 3-3 3-4

483.73 426.68 0.0 383.11

709.02 649.25 0.0 597.72

56.12 28.65 @O 55.20

746 2.60 0.0 2@01

4-1 4-2 4-3 4-4

932.86 147.02 96530 0.0

5469.39 114.89 5 I 9.02 0.0

27.51 4078 44.61 0.0

6.41 1018 13.42 00

M. S. BRONZINI, J. H. HERENDEEN, JR., J. H. MILLER and N. K. WOMER

56

Table 3. Equilibrium

O-D pair

travel times and modal

Daily shipments Rail

(tons) Truck

split for base network Travel time (hr) Rail Truck

l-1 1-2 1-3 l-4

0.0 7623 379.19 71 I.59

0.0 628.21 2017.77 5494.73

0.0 4040 41.73 26.94

0.0 9.61 11.34 7.58

2-1 2-2 2-3 2-4

1983.21 0.0 884.40 700.09

192.87 0.0 1960.38 433.33

42.76 @O 2900 41.63

7.77 0.0 3.23 11.35

3-l 3-2 3-3 34

273.12 770.94 0.0 541.86

975.97 1745-61 0.0 2461.87

42.73 28.82 0.0 44.60

8.74 3.08 0.0 14.91

4-l 4-2 4-3 4-4

66544 713.60 1615.36 0.0

2575.95 844.35 3187.04 0.0

2698 42.40 4603 0.0

5.96 1221 16.33 0.0

were used to find a new set of outputs of each industry and the allocation of those outputs throughout the region. The initial set of outputs together with the revised set are shown respectively in columns 1 and 2 of Table 6 in the Appendix. Obviously, further iterations were required to produce convergence of outputs; hence the new set of commodity flows was sent to the freight modal split model and the process begun again. Five iterations between the econometric model and the remainder of the model system were required for production to converge to equilibrium values. The production calculated which

Table 4. Equilibrium

O-D pair

during each iteration is shown in Table 6. The resultant aggregated shipments and internodal travel times are shown in Table 3. An examination of Table 6 leads one to the conclusion that the production of the region is sensitive to changes in transportation cost. Tables 1 and 2 show that changes in travel times had the expected effect on freight modal split. That is, an increase in travel time by one mode coupled with a decrease in travel time by the other mode caused more to be shipped by the latter mode and less to be shipped by the first mode.

travel times and modal split for alternative

Daily shipments Rail

(tons) Truck

A

Travel time (hr) Rail Truck

- 0.0

0.0

4O.a 41.73 26.84

8.19 9.73 7.29

206.05 0.0 191 I.24 34344

42.8 1 0.0 29.05 41.53

7.05 0.0 3.45 11GO

268.30 786.07 0.0 529.62

981.26 173 1.89 0.0 ‘475.85

42.78 28.53 0.0 44.50

8.13 3.25 0.0 I-1.01

645.16 704.67 1556.92 0.0

‘596.95 853’95 3247.87 0.0

26.97 42.37 46.03 0.0

l-l l-2 1-3 l-3

0.0 64.98 349.38 696.40

‘-1 2-2 2-3 2-4

1970.79 0.0 935.01 69087

31 32 3-3 34 4-l c2 J-3 -14

0.0 639.79 ‘048.6 I 55 12.67

5.39

1I.15 l-t.35 0.0

57

A transportation-sensitive model Alternative network A This alternative consisted of the base highway network with the addition of a new interstate highway, connecting node 2 to nodes I and 4. At this point. the rail network was left unchanged. The entire model system was run again, the new highway being the only change in the input data. Table 4 contains the resultant travel times and modal split for equilibrium conditions. Notice that travel times by highway decreased compared with the equilibrium travel times for the base network, even though in all cases but one the shipments by truck increased. The increase in truck shipments noted above did not only result from a change in the modal split favoring truck, but also from an increase in the production of the economy, as shown in Table 7 (in the Appendix). This increase in production was caused by decreases in transportation costs. Decreases in transportation costs occurred because the modal split shifted to favor the highway mode, which had lower rates than rail for the particular shipments involved. Decreases in transportation costs caused increases in production because, in the hypothetical economy under study. the transportation sector was not included as a producer or consumer. This situation had the effect of releasing funds to the household sector that were previously paid for transportation services. Consequently, final demand increased, effecting an increase in production. If the transportation sector were included. the value of output of the economy would remain unchanged. Increases in demand by some sec-

tors would be offset by decreases in demand by the transportation industry. Alternative network B As a further test of transportation sensitivity, a rail network improvement_ consisting of a high-speed rail line connecting nodes 1 and 3. was added to the transportation system. Operating characteristics of this new facility included a constant (i.e. flow-independent) linehaul speed of 90 m.p.h.. a constant collection-distribution time of 6 hr, and the by-passing of intermediate classification yards. The highway network for Alternative A was retained. The equilibrium modal split and travel times are shown in Table 5. Notice that rail travel times were lower than those for Alternative A (Table 4) and that rail shipments were higher in every case but one. The increases in rail shipments noted above occurred in spite of a decrease in the economy’s production (Table 7). This production decrease resulted from increases in transportation costs and the fact that the transportation sector was not included in the economy. The increases in transportation costs are a result of the assumption that shippers are willing to pay more for faster service. However, the logical basis for this assumption, i.e. a theory of inventories, is not included in the model system. 7. CONCJAJSIONS

The primary achievement of this study was the development of a transportation sensitive model of a regional economy. Further, the model was shown to

Table 5. Equilibrium travel times and modal split for alternative B O-D pair

Daily shipments (tons) Rail Truck

Travel time (in) Rail Truck

l-l 1-2 l-3 l-4

@O 87.71 595.27 724.13

0.0 615.75 1797.83 5477.06

0.0 29.36 15.33 24.85

00 8.04 9.14 7.21

2-l 2-2 2-3 2-4

201260 00 101260 699.36

161.61 0.0 1828.13 432.96

30.24 0.0 26.77 4088

6.93 0.0 3.49 11.14

3-l 3-2 3-3 3-4

35235 804.45 0.0 631.08

894.48 1709.39 0.0 2369.14

15.33 2664 00 28.18

8.01 3.24 0.0 13.73

4-l 4-2 4-3 4-4

644.91 707.36 1744.88 0.0

2593.89 849.17 3051.02 0.0

25.01 W76 28.35 O-0

502 11.11 13.93 60

58

M. S. BRONZINI,J. H. HERENDEEN.JR.. J. H. MILLER and N. K. WOMER

yield results consistent with the initial assumptions upon which it was based. The fact that equilibrium solutions were obtained without any conscious effort or data manipulation indicates that the multifeedback, iterative modeling strategy employed is a valuable transportation planning technique. The study did reveal several areas where future research is required to insure successful implementation of the model system. The econometric model in its present state is still incomplete. Two necessary additions to the model are the mechanisms to analyze the flows of goods and services between the transportation sector and the rest of the economy, and a method to account for the relationship between changes in inventories and changes in transportation services. The area of parameter estimation also requires more research. Finally, the assumption of pure competition, required to calculate the effects of changes in transportation costs on prices, is unduly restrictive. Alternative methods of calculating these effects should therefore be investigated. Some advances along the lines suggested have been reported by Sauerlender (197 I) and Hoe1 and Sauerlender (I 972). Further research on methods of determining average transportation costs is also needed. Rate information is presently available in an abundance of detail. The problem here is in ag’gregating rates over a commodity classification to determine an average rate for that classificatidn. In conjunction with this. the effect on rates of considering all the shipments from a production node to originate at a common point should be investigated. There is also a significant amount of work to be accomplished in the area of delineation of modes. A mode in the abstract sense is any transportation service that differs in service characteristics from all other transportation services. Clearly, two modes do not adequately describe the variety of transportation services available, either now or in the future. The relevant question is how many modes are necessary to adequately describe the transportation system. Existing network simulation techniques that use cost functions were developed to examine traffic flows that occur over a small interval of time, such as the Ihr peak flow on an urban street network. Further research is required to convert these techniques into techniques that are appropriate for analyzing average flows over a somewhat longer period of time. The application of traffic assignment techniques to non-highway networks must also be more thoroughly investigated. Particular attention should be given to network delineation and to route selection principles. Also, methods for analyzing interdependent networks must be developed. The procedures required will bc directly

related to the research in mode delineation discussed above. The necessity of including a passenger demand model in the model system is almost obvious. The time and cost impedances associated with various links in the regional transportation network play important roles in the model system’s dynamics. These impedances are. in general, functions of the torn/ traffic volume, which consists of both passenger and freight flows for many system elements. Hence both types of flow must be considered if the network simulator is to achieve acceptable levels of accuracy. With regard to a passenger demand model. it should be noted that estimates of population, personal income and employment (by industry), as well as other indicators of the regional distribution of economic activity, can be derived from the output of the econometric model. This type of information is usually included in the input of a passenger demand model. A great deal of work (none of which can be reviewed here) on the modeling of regional, multimodal passenger transportation has been accomplished quite recently, and the results of that research should be of immense benefit in formulating an operational passenger model for use in the present context. The general form of a suggested model is also set forth in the Methodological Framework. The model system is designed to produce an equilibrium solution to a set of initial conditions consistent with known and specified constraints. Because this equilibrium state is reached through an iterative process. various convergence criteria must be specified. Research is needed to identify those output variables upon which convergence should be tested, and to determine the allowable errors in the equilibrium values of these variables. From a practical point of view, the model’s extensive data requirements. particularly those of the econometric model. clearI! cannot be met from present sources. And, although the requisite data coultl be collected, it was estimated (Transportation Research Institute. 1968) that this task would require 2 yr and se\cral millions of dollars for the Commonwealth of Pennsylvania alone. Hence it might prove to be more attractive to develop some newer, approximate forms of the models which utilize existing data. Finally. a note on the applicability of the model [in its present form] to actual planning problems is in order. Inasmuch as the model system has yet to be tested in actual usage. it would be premature to base policy decisions strictly on the output of the model. It will be necessary to establish that the equilibrium values for flows and costs predicted by the model are representative of r?::;ll world conditions. and are re-

A

transportation-sensitive

sponsivr to actual changes in the infrastructure and in transportation policy variables. before the model system can be used with confidence as an aid to decisionmaking. In the interim. the model may well be usable for the analysis of broad planning issues. but even then its results must be interpreted with caution and supported by ancillary findings of an independent nature. As a concluding observation. it is noteworthy that the results of this study confirm the general findings reported by Manheim PI al. (1968) regarding a prototype transportation systems analysis conducted at M.I.T. That study considered passenger flows among five nodes in an integrated multimodal (three modes) network abstracted from the Northeast Corridor and used a set of models completely independent of those described in this paper. Despite the differences in the two modeling contexts. both studies affirm the feasibility of the iterative approach to predicting equilibrium flows in transportation networks.

AckrlorvI~~dar,llertrs-The helpful suggestions and criticisms of T. D. Larson. R. D. Pashek. 0: H. Sauerlender, J. J. Coyle. T. B. Davinroy and J. L. Carroll. all of The Pennsylvania State University, are greatly appreciated.

REFERENCES

Bronzini M. S., Herendeen J. H., Jr., Miller J. H. and Womer N. K. (1972) A regional transportation systems analysis model. Pennsylvania Transportation and Traffic Safety Center Report TTSC 7204, University Park. Church D. E. (1967) Impact of size and distance on intercity highway share of transportation of industrial products. Hi
model

59

Davinroy T. B.. Bronzini hl. S. and Herendeen J. H.. Jr. (1969) Transportation network analysis utilizing selective left turn penalties. Pennsylvania Transportation and Traffic Safety Center Report TTSC 6912. University Park. Herendeen J. H.. Jr. (1969) Theoretical development and preliminary testing of a mathematical model for predicting freight modal split. M. S. thesis. The Pennsylvania State University, University Park. Published as Pennsylvania Transportation and Traffic Safety Center Report TTSC 6908. University Park. Hoe1 L. A. and Sauerlender 0. H. (1972) Statewide comprehensive transportation planning. HigkwaJ. Res. Rec. 401,

l&20. Lancaster K. J. (1966) A new approach to consumer theory. J. pd. Ecou.14, 132-l 57. Manheim M. L.. Ruiter E. R. and Bhatt K. U. (1968) Search and choice in transport systems planning: summary report, Res. Rept. R68-40. Dept. of Civ. Eng., Mass. Inst. of Technology, Cambridge. Mosher W. E.. Jr. (1963) A capacity restraint algorithm for assigning flow to a transportation network. Highway Res. Rec. 6,258-289. Quandt R. E. and Baumol W. J. (1966) The demand for abstract transport modes: theory and measurement. J. Reg. Sci. 6, 1>26. Roberts M. J. et al. (1966) Inrermodal Freight Transportation Coordinafion: Problems and Potential. Graduate School of Business, University of Pittsburgh. Sauerlender 0. H. (1971) A variable coefficient input output model for transportation analysis. Fifth international Conference on Input-Output Techniques, Geneva. Switzerland. Transportation Research Institute, Carnegie-Mellon Universitv. and Pennsvlvania Transportation and Traffic Safet; Center, The Pennsylvania State University (1968) Methodological Framework for Comprehensive Transportation Planning. Transportation Research Institute,

The Carnegie-Mellon University, Schenley Park, Pennsylvania. Womer, N. K. (1970) Estimating the relations of an inputoutput model with variable coefficients. Ph.D. dissertation, The Pennsylvania State University, University Park.

M. S. BRONZINI, J. H. HERENDEEN, JR., J. H. MILLER and N. K. WOMER

60

APPENDIX-PRODUCI’ION

Table 6. Successive

estimates

BY COMMODITY

of production

obtained

AND ZONE

from the base network

Yearly production Commodity type 1

Location of industry

Estimate 1

Estimate 2

Estimate 3

Estimate 4

1 2 3

8741468 123080 1083167 2857278

3665468 578266 2953388 5369262

3451871 581259 2811558 5059170

3316777 571960 2716526 4862883

3212429 558734 2637410 4710671

153069 549217 778070 25563 1

168393 203103 815301 248254

113816 244749 975659 207161

95358 253200 1009010 190413

88024 251400 1001592 181655

155100 22963 48258 512035

96008 117782 134215 89519

97630 112629 135736 90213

96371 108991 133801 88786

94232 105877 130786 86727

1 2 3 4

18761 4085 21603 62838

34860 9169 36830 17507

34043 9290 36884 17347

33154 9155 36215 16972

32268 8946 35343 16543

1 2 3 4

1114552 88103 227464 368445

346453 344527 459453 425587

271922 342562 470464 411407

244648 336011 465777 399838

231904 327894 455965 389037

1 2 3

566649 5026 1175194 973279

533623 613476 719925 515669

489539 593144 748862 508601

467167 576476 744993 497556

451725 560777 730482 485206

4

2

1 2 3 4

4

Labor

1 2 3 4

Equilibrium condition

3617 5994 17463 0

2480 6341 19505 0

2093 6342 19800 0

1938 6229 19538 0

128046 42992 151706 208953

13474 171214 184738 186733

11861 177077 191530 194770

11140 175662 190160 193696

10711 172025 18628 1 189835

683314 5374221 39434 123681

153937 2153577 168770 209463

144725 2075 130 160870 ‘04465

139004 2012537 155370 199128

134617 1956016 150788 193813

104621 149895 725980 395064

96550 148496 729781 381704

92315 145408 717822 370441

13135 8729 14729 0

9

(tons)

185114 127655 461226 443148

124949 146204 67225 1 413368

A transportation-sensitive

model

161

Table 7. Production equilibrium conditions for the three test networks Yearly production (tons) Commodity type

Location of industry

2

3 A 2

1 2 4

3

1 2 4

4

1 2

4 1 2

4

Labor

1

2 3 4

Base network

Alternative “A”

Alternative “B”

3212429 558734 2637410 4710671

3213700 558988 2638539 4712388

3209340 558113 2634424 4706152

88024 251400 1001592 181655

88056 251571 1002155 181716

87947 251432 1000666 181502

94232 105877 130786 86727

94279 105929 130846 86768

94118 105742 130624 86624

32268 8946 35343 16543

32286 8950 35361 16551

32228 8934 35299 16523

231904 327894 455965 389037

232000 328100 456180 389198

231646 327499 455463 388625

451725 560777 730482 485206

452101 561228 731161 485802

450259 559011 728224 483674

1938 6229 19538 0

1939 6232 19546 0

1936 6223 19519 0

10711 172025 186281 189835

10715 172093 186354 189906

10696 171841 186082 189640

134617 1956016 150788 193813

134684 1957180 150867 193886

134494 1951713 150620 193618

92315 145408 717822 370441

92359 145488 718163 370610

92210 145173 717002 370056

R&arm&Un modtle inttgre destine a analyser des infrastructures rtgionales alternatives pour le transport de marchandises en plusieurs modes est Clabort. Un modele economttrique utilise les informations concernant les coCts de transport pour determiner les flux origine-destination de marchandises sur I’ensemble de la region. Ces flux constituent les donntes d’entree dun modele de choix modal qui repartit Ies marchandises entre les differents modes, sur la base de paramttres de qualitts de service relatives. Un modble de simulation affecte les flux de marchandises par mode aux itintraires propres a chaque mode et calcule les fonctions de resistance origine-destination dependant des flux. Les valeurs d’tquilibre des don&es de sortie du modble sont obtenues au moyen d’un processus d’ittrations multiples. La nature des interactions du modtle est etudiee au moyen dun cas d’application du modile a une region hypothetique.

62

M. S. BRONZINI. J.

H. HERENDEEN. JR..

J. H. MILLERand N. K. WOMER

Zusammenfassung-Die Abhandlung beschreibt ein integriertes Modellsystem zur Analyse alternativer multimodaler Gilterverkehrsinfrastrukturen in einer Region. Ein iikonomisches Model1 verwendet Informationen liber Transportkosten, urn die Quelle-Ziel-Strome einzelner Gilterarten innerhalb des Untersuchungsgebietes zu bestimmen: Diese Strijme sind wiederum Eingabegrolken fur ein Modal-Split-Modell, das sie aufder Grundlage relativer Bedienungsvariablen auf die einzelnen Verkehrsmittel verteilt. Ein NetrSimulations-Model1 schlieljlich legt die verkehrsmittelspezifischen Giiterstrome auf bestimmte Routen urn und berechnet belastungsabhlngige Quelle-Ziel-Widerstlnde. Die Abgleichung der Modellergebnisse erfolgt mittels Iteration mit vielfacher Riickkoppelung. Die Art der Wechselbeziehungen innerhalb des Modellsystems wird durch dessert Anwendung auf eine hypothetische Region untersucht.