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The flexibility of departure times for work trips
0191-2607/64 $3.00 + .oo ~ergamon Press Ltd.
THE FLEXIBILITY OF DEPARTURE FOR WORK TRIPS
TIMES
CHRIS HENDRICKSON Department of Civil Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A.
EDWARDPLANK PRC Voorhees, McLean, VA (Received
15 November 1982; in revisedform
28 May 1983)
examine the flexibility of departure times for the journey to work making use of data gathered in Pittsburgh, Pennsylvania. Measured travel time peaking is pronounced for trips into the Abstract-We
Pittsburgh Central Business District, although the variation in travel time is low for a particular route, mode and departure time. Estimation of a logit model of simultaneous mode and departure time interval choice is reported. Departure time decisions are found to be much more flexible (elastic) than are mode choices. Some implications for dynamic or time dependent transportation system management strategies arc considered.
1. INTRODUCXION
ations in travel impedance are presented in Section 2 below. The exclusion of time of day variation in travel characteristics is not valid simply because an analyst is only interested in mode choice. Time of day variation may often affect the characteristics of different modes to quite different degrees. Travel time, wait time, fares, and service reliability are all characteristics of transit service which may reasonably be expected to vary over the course of the peak period. Similarly, travel time and perhaps parking charges or tolls may be time dependent variables for auto users. For a mode choice analysis to be complete, the time of day variation of these modal parameters should be included. Several dynamic tradeoffs are of particular interest in analyzing departure time decisions and mode choice for travel to work. To illustrate, suppose that individuals have a particular work start time. As outlined by Hendrickson et al. (1981b), four major influences may cause a traveler to plan to arrive earlier or later than this start time: (i) Congestion avoidance: by avoiding peak congestion periods, an individual’s travel time might be considerably lower. (ii) Schedule delay: early or late arrivals at work may be dictated by the schedule of shared ride vehicles such as transit or carpools. (iii) Service reliability: since travel times may vary from day to day, workers may plan to arrive earlier than their work start (on the average), to avoid a late arrival when travel times are longer than normal on a particular day. (iv) Peak/off-peak tolls and parking availability: monetary charges for parking, transit fares, or roadway facilities may vary by time of day, thereby inducing changes in planned arrival times. Parking availability may be restricted for late arrivals as parking lots fill up.
Management policies for urban transportation systems often involve direct or indirect influences on users’ departure time decisions. Capacity expansions to roadway facilities may result in additional bunching or peaking of departure times, so that the resulting reduction in congestion is less than would otherwise occur. Staggered work hours or peak period transit fares attempt to directly influence departure time decisions. A better understanding of the factors which influence departure time decisions and their relative.importance should greatly aid the transportation system management and planning process. This is particularly the case for transit services, in which the problem of service peaking and off-peak under-utilization has long been recognized (see, for example, Meyer, 1965 or Oram, 1979). Transit vehicles and vehicle operators which provide service during peak periods are often under-utilized during the remainder of the day. The need to reduce both operating and capital costs has renewed interest in policies which will spread demand for transit service more evenly across the morning and afternoon periods. This would allow more efficient use of existing vehicles and operators and @ossibly) a reduction in the numbers of each required. In much of the research on work trip decision making, no consideration of departure time or the dynamic nature of transportation system performance during the peak period is included. The “peak” period of travel is typically described by a set of uniform travel characteristics, representing an unrealistic but analytically convenient compromise. (In addition, individual travel characteristics are often represented by zonal averages, e.g. travel time, transit wait time, etc., further reducing the validity of the results.) Some data on actual time of day vari25
26
C. HENDRICKSON and
In each of these cases, time dependent variations in travel characteristics may affect mode and departure time choices. The flexibility of departure time decisions can be seen during temporary disruptions of transportation facilities. During transit strikes, it is common to read reports of individuals departing for work much earlier than normal. For example, 65% of CBD commuters reported earlier departure times during a transit strike in 1976 in Pittsburgh, PA (Blumstein, 1982). As another example, work trip departure times were 19min earlier during the reconstruction of a major roadway in Pittsburgh; this data is derived from a survey of 1800 travelers through the construction zone (Hendrickson, 1982). Clearly, individuals do possess the opportunity to change departure times. Recently, the realization of the importance of considering the time dependent nature of transportation level of service has led to increased empirical research in this area. Several researchers have isolated the departure time decision for separate attention, much as was done for the mode choice decision (Cosslett, 1977; Small, 1982; McCafferty and Hall, 1982). In this research, trip timing decisions are usually modelled using multinomal logit models with utility functions representing linear functions of time dependent variables. Preliminary estimation of simultaneous mode choice/departure time models has also been performed by Abkowitz (1980). Most of these past studies (Cosslett, 1977; Small, 1982; Abkowitz, 1980) used a travel dataset developed for the San Francisco Bay Area. Since little reliability or time related impedance information was contained in the data set, the researchers constructed the necessary data based upon relationships reported in the literature or suggested by past work. Several variables which might be important to the trip timing decision, including travel time variance, as well as wait time and wait time variability over the peak, were not included in the dataset. In addition, the validity of these past results is questionable, especially since they were often based on data consisting of several observations for one day rather than the same set of observations across several days. Observations on the same day may be correlated, so that accurate estimates of day to day variability are impossible. Although convenient to the analysis, this approach is unsatisfactory. As Abkowitz (1980) states, “Another major problem encountered in developing the analysis methodology was the lack of objective reliability data. . . . The collection of a sound ‘reliability’ data set. . . would be extremely useful and should be treated as a high research priority.” In this paper, we shall use a set of data gathered in Pittsburgh, PA for the express purpose of analyzing dynamic level of service variations and departure time decisions. Collecting this dataset involved independent measurement of travel times and transit wait times for travei to the Pittsburgh Central Business District (CBD) as well as survey of 1800 workers in
E. PLANK
the CBD. This survey was conducted among twelve large employers and included a small number of workers with flexible working hours. A detailed discussion of the dataset appears in Plank (1982). The next section summarizes data on travel characteristics over the peak period of travel. Section 3 summarizes information on work starts and modal choice. Following this, a disaggregate departure time and mode choice model is reported. Section 5 summarizes the elasticities of this choice model and several simulations of policies affecting departure time decisions. 2. VARIATIONS IN TRIP LEVEL OF SERVICE FOR MORNING COMMUTES IN PITTSBURGH, PA
The Pittsburgh, PA CBD offers a useful laboratory to study time dependent travel variations. Approximately 80,000 workers commute to this triangular area of roughly 0.75* miles. Surrounded by rivers or hills, the major access roads to the CBD generally have bridges or tunnels which act as bottlenecks and cause queues (Fig. 1). Thus, route choices are limited, and congestion is concentrated at a limited number of major bottlenecks. To measure travel times into the CBD, at least eight vehicle trips were made from each of four suburban areas during the morning peak period of travel (Fig. 2). On the five separate routes, the average travel time during the most congested travel period ranged between one quarter and one half more than the average for the base, free flow travel time. The pattern of travel time peaking was quite regular in each area, with the maximum travel time occurring at about the same time on each day of observation. The increase in congestion to the maximum travel time and subsequent decline can be represented by a quadratic function in which extra or congested travel time was a function of departure time from the suburb (Fig. 2). Despite the scatter of measurements shown in Fig. 2, the variability in travel times for a given departure time was relatively low. The average ratio of the standard deviation to average travel time (i.e. the coefficient of variation) was 0.13 over all routes and departure times. This suggests that, with experience, commuters can fairly accurately predict the amount of time required to travel to work on any given day with a particular departure time. In effect, travel time peaking occurs in a fairly regular pattern from one day to the next. The pattern of expected wait times for transit and the variance of wait times was crucially dependent upon local operating policies. For example, in an area with unscheduled service (Bethel Park streetcar service), the average wait time was relatively short and constant throughout the peak period of travel. The variance of wait time was approximately equal to the average wait time for this service, suggesting an essentially random or Poisson arrival process of transit vehicles. In contrast, scheduled transit services exhibited irregular variations in average wait times and variances of wait times over the course of the
21
The flexibility of departure times for work trips
Fig. 1. Study areas in the Pittsburgh, PA region.
.. . . . .. .
100
120 /7:03
140 am.)
.
.
.
.
.
160
100 (FL00
200
220
%n.)
Fig. 2. Travel times at different departure times from Greentree to the Pittsburgh CBD.
C. HENDRICKSON and
28
E.
PLANK
12.0
f
r 8.0 Y
. .
z I-
i
*
-1
3
t
*i
;
.
4.0
I 7:oo
,m
Fig. 3. Average wait time vs arrival time at a transit stop in Greentree.
peak period, reflecting the fact that scheduled transit service in Pittsburgh does not use headways of fixed length throughout the peak period. An example of such variability is shown in Fig. 3, in which each point represents the average wait time for different arrival times at a transit stop in Greentree, as measured over eight days. The variance of wait times with scheduled service depended crucially upon the frequency of service. With scheduled transit departures quite frequent, the variance of wait times was relatively low. One phenomenon illustrated in Fig. 3 deserves mention. Note that the average waiting time for a bus increases for patron arrivals slightly before the scheduled services at 7:02 and 7:20 a.m. This occurs because buses occasionally run early on the route, and patrons arriving near the scheduled departure time missed the bus and had to wait for the next. Accordingly, patrons wishing to minimize their waiting time should arrive at the stop a few minutes before the scheduled departure time. As noted above, though, greater control of vehicle operations would reduce this problem. By and large, the frequency of transit service varied in proportion to the level of demand in the areas of scheduled transit service. That is, extra vehicles were scheduled during the peak departure time periods. The equilibrium effect of this scheduling practice is to concentrate transit demand even more in the peak departure time period, since this period has the shortest average wait and the lowest variancein wait time. 3. WORK ARRIVALS, START TIMES MODAL CHOICES
AND
The cumulative proportions of arrival times at work and official work start times is shown in Fig. 4
for a sample of 1800 workers in the CBD. In this figure, there is a significant jump in the cumulative distribution of work start times at 8:00 a.m., with 42% of all workers reporting an 8:00 a.m. work start time. The cumulative distribution of arrival times is shown to the left of the work start time curve, suggesting that most downtown workers arrive early. Indeed, the mean departure time is 7:00 a.m., the mean arrival at 7:40 a.m., and the average work start occurs at 8:OOa.m. As shown in Fig. 4, the median work start time is slightly before 8:00 a.m. Also shown in Fig. 4 is the cumulative distribution of “desired” work start times. This function indicates a generally flatter and earlier distribution of desired work starts compared to existing arrangements, although there is a minority of workers who would like a work start time of 9:00 a.m. or later. “Desired” work start times were self-reported by respondents to our survey. Concerning the various modes of travel, shared ride modes (carpools, vanpools, etc.) exhibit the greatest amount of travel time peaking, with 77% of all the workers sharing rides arriving in the hour from 7:15 to 8:15 a.m. (Table 1). Workers driving alone had the lowest degree of arrival time peaking, with transit services at an intermediate level between shared ride and drive alone modes. Thus, promotion of shared rides probably will disproportionally draw from transit travelers at the peak period of travel, thereby reducing the need for capacity increases in transit or roadways. The modal choice of those surveyed reflected the availability of direct transit service to the CBD. Public transportation was used by 55.5%, while 15.9% drove alone, 24.2% shared a ride in a private vehicle, and the remainder scattered among bicycles and walking.
The flexibility
Fig. 4. Cumulative
Table
Arrival
work starts,
1. Distribution
Time
arrivals
times for work
and desired
of arrival
time at
starts
29
trips
in the Pittsburgh,
PA CBD.
work by mode of travel
Shared Ride With Family Member
Drove AkJlle
Transtt
Before
7 15
17
16
16
19
16
7 15-7
45
35
30
30
42
34
745-a
15
32
31
43
35
33
10
14
6
2
10
5
11
3
2
6
B 15-645 After
Source
4.
of departure
645
Survey
of
1600
CBD
workers
conducted
DEPARTURE TIME AND MODE CHOICE DEMAND MODEL
To further analyze traveler decisions, a logit model of departure times and mode choice was estimated. Logit choice models are described in Ben Akiva (1977) and Hensher (1981). Estimation is performed by the technique of maximum likelihood for these models. The logit model form was selected to take advantage of the disaggregate data gathered and to adequately represent the irregular nature of variations in factors such as transit wait time. The base model included up to twenty-eight alternatives, representing combinations of four modes (drive alone auto, shared ride, transit with walk access and transit with auto access) and seven different departure time intervals of 10 min each. In our analysis, mode and departure time choices are treated as a simultaneous interactive decision based upon maximization of individual traveler’s utility or satisfaction with each alternative mode and
by the authors.
departure time combination. The probability of an individual selecting each mode/departure time alternative (PU,) is assumed to be of the logit form: (1) where individual i has mode j and departure time I available among the mode choice set k and the departure time choice set n, respectively. For each mode choice/departure time alternative, the satisfaction or “utility”, Vi,, is specified to be: Vi, = a, + a,FFTTV + u,CONG,
+ n,(COST/ Y),
+ n,ACC, + a,WAITV, + u,LATEV, + u,(LATEgJ2 + u,EARLY,, +u,(EARLY,,,)~
(2)
plus a random component, where the variables are defined as follows for individual i:
30
C. HENDRICKSON and E. PLANK
1. FFTT,-free flow in-vehicle travel time for mode j. The inclusion of this variable provides a mode dependent variable representing free flow travel time. Since increasing travel time for any mode would discourage its selection, a negative coefficient is expected. 2. CONG,i,-portion of total travel time on mode j due to congestion associated with travel at departure time t. The inclusion of this variable provides a mode and departure time dependent indication of congested travel time and, since increases in congestion time would result in decreased alternative usage, a negative coefficient is expected. Also, congestion time might be expected to be more onerous than free flow travel time. 3. (COST/Y),i,-monetary cost for mode j and departure time t divided by the household income index of individual i. The cost term is generally felt to be mode dependent, however, the time subscript indicates the possible inclusion of departure time dependent cost considerations (e.g. peak hour tolls and fares or parking surcharges). The division by household income provides an income effect on travel cost (i.e. a $10 parking charge may have different mode or departure time impacts for an individual earning $10,000 per year as opposed to an individual earning $40,000 per year?). 4. ACC,-walking time on the home end of a transit trip associated with departure time t. This variable provides a measure of the accessibility of transit service to the traveler, and is only included for the transit with walk access mode. The time subscript allows for variation in access time associated with different departure times from home, and might be important in situations where individuals have more than one transit route available to provide express service to the CBD (which was the case in the Monroeville study area). A negative coefficient was expected. tIncome was measured on a scale of 1 to 6; 1 representing annual household income of less than S10,ooO; 2 representing $10,000 to %20,000,3 is %20,000to $3O,ooO;4 is $30,000 to $40,000, 5 is $40,000 to $50,000; and 6 is over $50,000.
5. WAIT,wait time associated with mode j and departure time t. This variable allows an objective measure of transit level of service and its variability during the peak period. Since longer wait times would discourage transit usage, a negative coefficient was anticipated. 6. LATEe,-minutes of late arrival at work associated with mode j and departure time t. LATE, provides a linear component of the schedule delay impacts on the mode/trip timing decision. Mode and departure time subscripts are included because schedule delays depend upon both mode of travel and time of departure. A negative coefficient was expected. Workers on flextime had LATE set to zero. 7. (LATE,)*-as for LATE, above, this quadratic term is proposed to more accurately represent individual perceptions of late arrival at work. 8. EARLYU,--minutes of early arrival time at work associated with the use of mode j and departure time t. This value, similar to LATE,,, provides a linear component of schedule delay implications for mode and departure time selection. Since the variable value is mode and departure time dependent, mode and time subscripts are included. A negative coefficient was expected, but of smaller magnitude than that of LATE; this is because late arrival at work is felt to be more onerous than early arrival. Workers on flextime had EARLY set to zero. 9. (EARLY,)‘-as with (LATE,,)* above. A negative sign is anticipated to reflect the increasing disutility associated with earlier and earlier arrivals at the work place. Modal constants were also included in the model to represent the effects of unspecified mode dependent characteristics. The base mode for these constants is transit with walk access. Estimated coefficients for the model appear in Table 2. For this model estimation, the observations included 363 residents of four suburban areas who took part in the downtown survey. The high statistical significance of most of the estimated coefficients is encouraging. The significance of free flow in-vehicle travel time and congested travel time are the only two in question; the low t-statistics indicate the estimated
Table 2. Estimated model coefficients Estimated
Variable drove
alone
constant
Coefficient
-1.47
t-statistic 3.5
shared
rode constant
-2 09
66
tran*,t
auto constant
-126
63
free
flow
I” vehicle
congeston
trne
travel
time
-0 006
0.3
-0021
0.7
cosl/lncome
-0699
2.0
(early
-0 00042
53 64
trne?
late time
-0
llate tImeI
+.0014
2.3
access
-0095
50
-0066
32
wait
tome
time
146
The flexibility of departure times for work trips
31
implicit value of $2.52 was placed upon arrival five minutes late, while a value of $4.79 was placed upon being ten minutes late. This suggests that individuals would be willing to pay about $2.52 to avoid five minutes late, on average, and $4.79 to avoid being ten minutes late. Generally, late time is regarded much more onerously than is early time. The complete arrival time “cost” relationship, including both early and late arrival time, projected by these final model coefficients, is graphed in Fig. 5. This graph indicates the relative disutility of different arrival times at work. The shape of the late time disutility curve is surprising. A negative coefficient on both the linear and quadratic LATE terms was anticipated; this would indicate increased disutility associated with later and later arrival after the official work start. What was found, however, contradicts this. Based on the estimated model coefficients, the
coefficient may not be significantly different from zero. This result is likely due ta the similarity of in-vehicle travel times for the different modes in our dataset. The implied values of time based upon the coefficient values in Table 2 are summarized in Table 3 for the average income in the sample. The dollar amounts presented by this table appear reasonable both in terms of their magnitude and relationships. The high cost associated with access to transit may be explained by the fact that in four of the five study areas, access was predominantly along unpaved roadway shoulders with no sidewalks. This should indicate to transit operators the apparent extreme disutility associated with suburban walking access to transit routes. In addition, the high late time cost represents the significant penalty which individuals perceive to be associated with late arrival at work. An
Table 3. Values of time based upon estimated model coefficients Average Based Upon
Time Variable free
flow
travel
congestlo” access
,,me
of Time Coeffaaents
51 71/hr2
tme
time
Value Model
54 502
Iwalktng)
520 3Whr
Walt time
S17.14lhr
late time3
S2.52 54.79
early
5004 for SO. 15 for
twne3
for for
betng 5 min late bang 10 man. late being being
5 min early 10 min. early
’ These conversions were performed using the coefficient of the costllncome term 1699). where costs were in dollars and the average #“come was surveyed to be 2.5 units, or approxamately S20.000 per year ’ The low Statistical signtflcance of these time values
of
the estomated
coefficients
reduces
3 These values depend upon the amount of late and early time because times enter as quadratac functons in the utility express~ns
Eerly
Ar,lv.l
Work
St.,,
Th.
L.1.
the dependablllty
early
Arrlr.1
Fig. 5. Relative disutility of different arrival times at work.
and late
C. HENDRICKWN and E. PLONK
32
Table 4. Effects of additional variables on estimated model coefficients Model
1
Model 2 lnzludes Walt twne
Model 3 luxludes seat avalab!lQl
VXlXlCd
drove
alone
shared
ride
transit
auto constant
free
constant constant
flow
IV77
con9estlo”
t,me
-
-2 0918 81
-2.0918
- 1 3316 31 - 0031 ll
008l3l
-021(7l
-021171
- 03211 01
030( 651
-.698(2 3)
- 1481641
wait
twne
wait
time
01
-.00042(5
-.6912 31
-. 146(6.41
01
+ 001412.31
+0014(221
- 09515 01
-.09915.1
-.08813
-.08312
-0811261
2)
61
41
- 14616 3)
+.001412.3l
vanance
- 67312.0)
- 00044(5
- 09515.01
(late tImeI time
- 1 2316 ll
- 1.2616 31
- 69912 01
end walk
-1.41(341 -2 20(9 51
-.00813l
- 0004215
home
-2 031301 -2 6414 51
- 1 26(6 31
OPTCllncome
late trne
51 81
- 008l3)
(early
time?
14813
- 1 47(3 51
Model 4 Iincludes departure tnmet
- 00046(4
II
- 143f5.71 +0013(23l
I
-. 10215 01 - 06813
11
- 0019131 -.OOl
seat availability
II1 Ol
departure
time
+ 006041221
(departure
tImeI
- 0000265(
Value of Ilkellhood
the logfunction
NOTE
t-statistics
-1021
appear
5
-10214
-10209
271
-10180
in parentheses
disutility associated with these later arrivals increases only slightly. The positive coefficient on the quadratic term (LATE,)* signifies that once an individual is quite late (approximately 1 hr) in arrival, additional late time has little effect. Table 4 reports estimated coefficients for models which included several variables in addition to those in Table 2. These additional variables included the variance of transit wait time, an index of the availability of seats on transit, and the absolute clock time of departure. In each case, the variables were not statistically significant and were excluded in the final mode!. For seat availability, this lack of significance may be due to lack of variation in the sample of observations, since the Pittsburgh transit agency scheduled vehicles to arrive at capacity during the peak period. However, in contrast to the other models reported, inclusion of seat availability did result in changes in other estimated coefficients. Exploration of the effect of seat availability on choice would be of considerable interest in future work. 5. IMPLIEDELAWICITlES AND CHOICEFLEXIBILITY The model described in the previous section may be used to forecast the demand effects of a variety of policies on both modal split and travel peaking patterns. In this section, we explore the effects of a variety of such changes. Our intent is to indicate the relative sensitivity of mode choice and departure time decisions as well as to estimate the effects of policies, such as tolls, which might vary over the course of the peak period. One consideration in performing this analysis is the equilibrium effects of demand shifts either over time
or between modes. If policies substantially affect demand patterns, then the pattern of travel time peaking and, subsequently, the demand pattern will also change. Here, changes in demand patterns without considering such equilibrium effects are discussed. The results represent approximate estimates of impacts, with the amount of error from the approximation depending upon the extent of the change. For many policies examined, the effects are sufficiently small so that equilibrium effects are likely to be of minor importance. Equilibrium effects in an abstract setting are discussed in Hendrickson et al. (198 la and 198lb). Since the logit demand model is based on individual choices, elasticity value estimates from the model represent the choice sensitivity of individuals. Table 5 reports the choice characteristics of two individuals which we use for illustration of such elasticities. These individuals were chosen to be representative of residents traveling to a CBD workplace from two suburbs. Individual A has a high likelihood of transit use (80%), while individual B has only a 53% probability of using transit. These high transit probabilities reflect the relative attractiveness of transit service to the CBD. For both individuals, there is slightly more than a 20% probability that they will choose to depart in a particular ten minute interval. For both individuals, auto travel to a park-and-ride lot to access transit service results in slightly longer in-vehicle travel times than for transit with walk access. Table 6 reports elasticity estimates for these two individuals for various changes. The first group of these estimates represent elasticities of transit choice over all departure time intervals and both transit access modes. These elasticities are calculated for
The flexibility
of departure
times for work
33
trips
Table 5. Individual trip characteristics for elasticity
calculations
lndwdual A Free Flow In Vehticle Travel time lmin) TransltIWalk Access Transit/Auto Access AUKI Average Income
Congested
In Vehicle
Travel
Time
lmlnl’
lndcator’
Work
Start
Home
End Transit
Note:
Access
taken
IWalk)
Twne (mini
over
all departure
time
to an annual household
variable
Times
750
600
2 Corresponding 3 Includes
244
auto
are given
operating in minutes
of
Choice
59 64
64 5.5
parking
1
2
Chotca/Peak Probabnllty2
Period
Departure
lndwidual A
tndwiduai 6
-0 63 -0.060 -0.009 -0015 0.15
-06 -0 16 -0 26 -0 095 051
Peak Period Peak Period
Transit Transit
Fare’ Wait Time
-26 -033 -0031 0 030
-16 -0 11 -0.20 0073
Time
Travel Time Travel Cost
Elasticities on choice probabilities calculated numerically from variable values shown on Table 5. Transit choce probabll!tles transit use wth walk and auto access Elastlctty cost for
calculated from a 1% fare change, auto access to transit service.
Vol. 18. No. 14
with
constant
Peak periods correspond with a departure tnme of lndwtd@ A and 630 to e40 AM for individual 6.
changes in transit fares, transit wait times, walk time to transit, congestion delays on transit, and auto travel costs. For each of these changes, choice sensitivity is inelastic, so that a 1% change in the level of service characteristic results in a less than 1% change in transit choice probabilities. The direction of change is as expected in each case. The second group of elasticities reported in Table 6 represents the sensitivity of transit use in the most likely departure time interval to changes in transit fare, wait time, travel time, and auto cost. Each of TR-A
elasticities
Probablllty
Peak Period Transit Congested Auto Peak Period Out-of-Pocket
NOTE.
525.000
charges.
thereof.
Transit Fare’ Transit Walt Time Transit Walk Time Transit Congested Travel Time Auto Out-of-Pocket Travel Cost Transit Choice
AM
43
approximately
and average
or fractions
600
0.66
intervals
income
costs
AM
Table 6. Estimated choice probability
Transit
075 1.13 3 13 096
050 050 1.94 0.6 1
Transit Wait T&me Imini Trawl/Walk Access Transit/Auto Access
are
37 07 3722 35 36
Idollarsl
Time
’ Averages
655 9.00 8.51
25
Out-of-Pocket Travel Cost TransltlWalk Access Transit/Auto Access Auto/Drive Alone3 Auto/Shared R,de3
Average
lndwidual 9
7.20
1% changes in the are the sum Of
out-of-pocket
to 730
AM
travel
for
these elasticities was calculated for changes only in the peak interval, representing, for example, the imposition of a fare surcharge during the peak period. These peak interval transit demand elasticities generally show a much greater sensitivity to changes than do the previous transit service elasticities. These greater sensitivities reflect the possibility that individuals could alter their departure time yet still choose to use transit. In effect, such changes imply a change in the overall distribution of transit service demand during the peak period. Most dramaticaIly, the elas-
33
C. HENDRICKSON and E. PLANK Table 7. Effects of policy changes on travel from Greentree No No
Base case
$1.00 auto toll
Peak period auto toll
10 12 16 62
8 11 17 64
8 IO 17 65
10 II 16 62
12 13 16 16 15 15 13
Mode share (percentage)’ Drive alone Shared ride Transit/auto Transit/walk
Auto departure time (a.m.) (percentage)’ 6:40 10 10 650 13 13 7:00 15 I5 7:lO 16 17 7:20 17 17 7:30 17 17 7:40 13 13 Transit departure time (a.m.) (percentage)’ 6:40 8 8 650 12 12 7:00 17 17 7:lO 14 14 7:20 19 19 7:30 18 18 7:40 11 11 Average change in consumer surplusf - 0.03
No congestion
transit congestion
transit or shared ride congestion
Double frequency
10 II
10
16 63
16 63
9 9 17 65
9 12 14 16 16 17 15
10
13 15 17 17 17 13
9 12 14 16 17 17 14
9 12 15 16 17 17 13
8 12 17 14 19 18 II
7 11 15 14 19 21 13
7 II 15 14 19 20 13
7 I1 15 14 19 20 13
9 12 I5 15 18 18 13
-0.04
0.06
0.05
0.06
0.16
II
tCalculated as the average of choice probabilities for each individual in the sample. :Calculated as the average change in consumer surplus for each individual in the sample. ticities suggest the sensitivity
of departure times to transit fares. For individual A, a 1% increase in the peak beriod fare results in a 2.6% reduction in the probability of transit use during the peak period. In addition to calculation of choice elasticities for small changes in explanatory factors, the logit demand model can be used to indicate the effect of new policies such as tolls, exclusive bus lanes, or changes in congestion. Table 7 reports the effects of various policy changes on travel from Greentree. This Pittsburgh suburb has a moderate degree of travel time peaking and is served by bus routes without an exclusive right of way. In the base or current situation (Column 1 of Table 7), the transit mode share is quite large, with 78% of commuting trips on transit with either walk (62%) or auto (16%) access. Departure times are spread throughout the peak period, but with the highest proportions of departures occurring between 7:15 and 7:35. For auto travel, 34% of all departures occur in these two intervals. In the same periods, 37% of all transit users depart, representing the greater amount of departure time peaking on transit. This peak departure time period of 7:15 to 7:35 is not surprising since it corresponds with workplace arrivals shortly before 8:00 a.m., which is the most common work start time. The final row in Table 7 reports the estimated average change in consumer
tSee Williams (1977) or Daganzo (1979) for a discussion of this measure. It is calculated as the change in the logarithm of the denominator of the logit choice function.
surplus from the base case which is due to policy changes. Thus, this figure indicates the relative levels of changes in individuals’ net travel benefits.7 The various policies considered and their effects are described below. These policies generally represent extreme outcomes since they neglect equilibrium effects. However, they are useful in indicating the range of potential demand effects. $1.00 Auto roll. This policy imposes a flat $1.00 toll on all automobile trips. This toll might be collected at the Fort Pitt Bridge (the route bottleneck) or as a parking tax surcharge. The result of the toll is a shift towards transit ridership (with an increase in mode share of 3x), but little shift in departure times. In terms of modal volumes, this represents a 14% decline in auto usage and a 4% increase in transit patronage. For shared rides, we assume that the toll payment is divided by the average number of riders; with a smaller individual payment, the shift from shared ride is correspondingly lower. Peak period auto toN. This hypothetical toll policy represents a $2.00 charge in the period 7:30 to 8:00 a.m. and a $1.00 charge in the periods 7:00 to 7:30 a.m. and 8:00 to 8:30 a.m. The object of such a toll might be to reduce peak period travel. The toll is assumed to be paid at the Fort Pitt Bridge and, as before, the toll is divided among riders in carpools. With the higher toll in the time period 7:30 to 8:00, a larger diversion from auto modes occurs than in the flat $1.00 toll case (Column 2). The increase in transit mode share is 4%, representing an 18% decline in auto volumes and a 5% increase in transit volume.
The flexibility of departure times for work trips The time differential in the toll structure does affect the departure time distribution, with substantially less peaking for auto travel. In effect, auto travelers both switch to transit and alter their departure times. Their is no significant net change in the distribution of transit departure times. No congestion. The effect of roadway capacity increases which would result in no roadway con-
gestion is simulated in this case. Peak period travel times are equal in this scenario. The removal of congestion does not result in significant mode shifts in Greentree. Departure times do have a significant shift, however. The proportion of transit user departures in the peak period of 7:15 to 7:35 a.m. increases from 37% (in the base case) to 40% with no congestion. Thus, there is shift towards later departures and periods with lower wait times. No transit congestion. This scenario models the effect of an exclusive right of way for transit vehicles. There is an increase in the transit mode split, of 1% in this case. In addition, the transit user departure time distribution becomes even more peaked than in the base case, as both current and new transit users shift towards the peak departure times. No transit or shared ride congestion. This scenario represents the effect of a high occupancy vehicle (HOV) lane. The reduction in transit congestion time includes a shift towards transit, even from shared ride services. That is, while both transit and shared ride service become more desirable compared to the base case, transit improvement is disproportionally larger. The net modal shift is relatively small, however. Again, the transit users’ departure time distribution becomes
more peaked.
Double transit frequency. This scenario represents a substantial improvement in transit service by, in essence, halving transit wait times. The result is an increase in the transit mode share of 4%. This shift represents an 18% decline in auto riders and a 5% increase in transit service. These modal shifts are comparable to those found with a peak period auto toll of $1.00 or $2.00 (Column 3). The distribution of transit users’ departure times is slightly less peaked than in the base case, but this effect is relatively small. These policy scenarios indicate relatively minor effects on actual travel choices. It is fairly difficult to increase the transit mode share in the highly transitoriented market of work commuting from Greentree to the CBD. Somewhat larger shifts occur in the distribution of departure times, with many transit improvements resulting in a greater degree of departure time peaking. An exception to this increased peaking is an increase in service frequency. Similar results were obtained for other residence areas in Pittsburgh. The calculation of average changes in consumer surplus allows some comparison of the relative benefits of the different policies. The most notable result in this comparison is the desirability of wait time decreases: the increase in average consumer surplus is three times higher for halving transit wait
35
times (Column 7) than for eliminating in-vehicle congestion time on transit (0.16 vs 0.05, as shown in Table 6). The decline in average consumer surph~s with auto toils (Columns 2 and 3) is expected. Against these reductions in net user benefits, revenues of $0.13 per traveler will be collected with the $1 .OO toll (Column 2) and $0.21 per traveler with the peak period toll (Column 3). In addition, some benefits will be derived from reduced travel times due to less congestion.
6. CONCLUSIONS
Observations of traveler responses to disruptions, demand theory and the empirical demand models reported here all suggest that individuals can exhibit flexibility in the choice of departure time for work. Indeed, the departure time decision seems to be more elastic than the choice of mode. This flexibility in departure time choice has some important implications for transportation planning. First, congestion relief due to capacity increases or transit service improvements is likely to be overestimated since reduction in congestion will induce shifts into travel during the most congested period. Second, time dependent tolls tire likely to be useful tools in transportation system management, particularly if the tolls are more greatly differentiated than a simple peak/offpeak differential. Fourth, departure time flexibility offers a “latent” capacity in transportation facilities which may be exceedingly useful during short run disruptions such as transit strikes or reconstruction of heavily used facilities. Finally, shared ride modal travel exhibits more peaking of demand than do either transit or drive alone modes, suggesting that increased ride sharing would reduce the peak demand on transit. The research reported here should be regarded as exploratory in nature for the subject of dynamic adjustments. Several interesting research issues exist, including investigation of attributes such as seat availability on transit service, parking availability, the variety of possible flex-time working arrangements, and preference variations among different types of workers. From a methodological standpoint, hierarchical logit or probit models might be useful analysis approaches to investigate. Acknow[edgemenrs-This paper benefitted from comments from several anonymous reviewers. Sue McNeil aided in the computation of elasticities and percentage shifts. Financial SUPPOrt was provided by the Urban Mass Transportation Administration’s Program of University Research and Training under contract No. PA-I I-0024; views expressed are not necessarily those of UMTA. REFERENCES
Abkowitz, M. D. (1980) The Impact of Service Reliability Ph.D. thesis, Massachusetts Institute of Technology. Ben Akiva M. and Atherton T. (1977) Methodology for short-range travel demand predictions. J. Trans. Econ. on Work Travel Behacior.
and Policy, 224-261.
36
C. HENDRICKSON and E. PLANK
Blurnstein A. and Miller H. D. (1982) Making do: The effects of a mass transit strike on travel behavior. Transpn (to be published). Cosslett S. (1977) The trip timing decision for travel to work by automobile. The Urban TraTel Demand Forecasting Project V. Daganzo Carlos (1979) Economic Theory, Econometrics, and Mathematical Economics. Multinomial Probit: The Theorv and Its Application to Demand Forecasting. Academic Press, New-York. Hendrickson C. and Kocur G. (1981) Schedule delay and departure time decisions in- a deterministic model. Transpn Sci. 15(l), 62-77. Hendrickson C., Nagin D. and Plank E. (1981) Characteristics of travel time and dynamic user equilibrium for travel to work. Proc. 8th Int. Conf. Trans. Trafic Theory, 245-258. Hendrickson C., Dubyak T., Carrier R. and Anderson R. (1982) Traveler responses to reconstruction of the parkway east (l-376) in Pittsburgh, PA. Transpn Rex Rec. 890, 3339.
Hensher D. and Johnson L. (1981) Applied Discrete Choice Modelling. Wiley, New York. McCafferty D. and Hall F. L. (1982). The use of multinomial logit analysis to model the choice of time to travel. Econ. Geography S(3). Meyer J. R., Kain J. F. and Wohl M. (1965) The Urban Transportation Problem. Harvard University Press. Oram L. (1979) Peak period supplements: The contemporary economics of public transport. Progress in Planning XII Part 2. Plank E. (1982) An investigation of peak period mode choice and departure time travel behavior. Master’s thesis. Carnegie-Mellon University. Small K. A. 11982) The scheduling of consumer activities: Work trips: Amer. Economic Rk. 72(3), 467479. Williams H. (1977) On the formation of travel demand models and economic evaluation measures of user benefits. Emiron. Plan. A(9), 285-344.
THE FLEXIBILITY OF DEPARTURE FOR WORK TRIPS
TIMES
CHRIS HENDRICKSON Department of Civil Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A.
EDWARDPLANK PRC Voorhees, McLean, VA (Received
15 November 1982; in revisedform
28 May 1983)
examine the flexibility of departure times for the journey to work making use of data gathered in Pittsburgh, Pennsylvania. Measured travel time peaking is pronounced for trips into the Abstract-We
Pittsburgh Central Business District, although the variation in travel time is low for a particular route, mode and departure time. Estimation of a logit model of simultaneous mode and departure time interval choice is reported. Departure time decisions are found to be much more flexible (elastic) than are mode choices. Some implications for dynamic or time dependent transportation system management strategies arc considered.
1. INTRODUCXION
ations in travel impedance are presented in Section 2 below. The exclusion of time of day variation in travel characteristics is not valid simply because an analyst is only interested in mode choice. Time of day variation may often affect the characteristics of different modes to quite different degrees. Travel time, wait time, fares, and service reliability are all characteristics of transit service which may reasonably be expected to vary over the course of the peak period. Similarly, travel time and perhaps parking charges or tolls may be time dependent variables for auto users. For a mode choice analysis to be complete, the time of day variation of these modal parameters should be included. Several dynamic tradeoffs are of particular interest in analyzing departure time decisions and mode choice for travel to work. To illustrate, suppose that individuals have a particular work start time. As outlined by Hendrickson et al. (1981b), four major influences may cause a traveler to plan to arrive earlier or later than this start time: (i) Congestion avoidance: by avoiding peak congestion periods, an individual’s travel time might be considerably lower. (ii) Schedule delay: early or late arrivals at work may be dictated by the schedule of shared ride vehicles such as transit or carpools. (iii) Service reliability: since travel times may vary from day to day, workers may plan to arrive earlier than their work start (on the average), to avoid a late arrival when travel times are longer than normal on a particular day. (iv) Peak/off-peak tolls and parking availability: monetary charges for parking, transit fares, or roadway facilities may vary by time of day, thereby inducing changes in planned arrival times. Parking availability may be restricted for late arrivals as parking lots fill up.
Management policies for urban transportation systems often involve direct or indirect influences on users’ departure time decisions. Capacity expansions to roadway facilities may result in additional bunching or peaking of departure times, so that the resulting reduction in congestion is less than would otherwise occur. Staggered work hours or peak period transit fares attempt to directly influence departure time decisions. A better understanding of the factors which influence departure time decisions and their relative.importance should greatly aid the transportation system management and planning process. This is particularly the case for transit services, in which the problem of service peaking and off-peak under-utilization has long been recognized (see, for example, Meyer, 1965 or Oram, 1979). Transit vehicles and vehicle operators which provide service during peak periods are often under-utilized during the remainder of the day. The need to reduce both operating and capital costs has renewed interest in policies which will spread demand for transit service more evenly across the morning and afternoon periods. This would allow more efficient use of existing vehicles and operators and @ossibly) a reduction in the numbers of each required. In much of the research on work trip decision making, no consideration of departure time or the dynamic nature of transportation system performance during the peak period is included. The “peak” period of travel is typically described by a set of uniform travel characteristics, representing an unrealistic but analytically convenient compromise. (In addition, individual travel characteristics are often represented by zonal averages, e.g. travel time, transit wait time, etc., further reducing the validity of the results.) Some data on actual time of day vari25
26
C. HENDRICKSON and
In each of these cases, time dependent variations in travel characteristics may affect mode and departure time choices. The flexibility of departure time decisions can be seen during temporary disruptions of transportation facilities. During transit strikes, it is common to read reports of individuals departing for work much earlier than normal. For example, 65% of CBD commuters reported earlier departure times during a transit strike in 1976 in Pittsburgh, PA (Blumstein, 1982). As another example, work trip departure times were 19min earlier during the reconstruction of a major roadway in Pittsburgh; this data is derived from a survey of 1800 travelers through the construction zone (Hendrickson, 1982). Clearly, individuals do possess the opportunity to change departure times. Recently, the realization of the importance of considering the time dependent nature of transportation level of service has led to increased empirical research in this area. Several researchers have isolated the departure time decision for separate attention, much as was done for the mode choice decision (Cosslett, 1977; Small, 1982; McCafferty and Hall, 1982). In this research, trip timing decisions are usually modelled using multinomal logit models with utility functions representing linear functions of time dependent variables. Preliminary estimation of simultaneous mode choice/departure time models has also been performed by Abkowitz (1980). Most of these past studies (Cosslett, 1977; Small, 1982; Abkowitz, 1980) used a travel dataset developed for the San Francisco Bay Area. Since little reliability or time related impedance information was contained in the data set, the researchers constructed the necessary data based upon relationships reported in the literature or suggested by past work. Several variables which might be important to the trip timing decision, including travel time variance, as well as wait time and wait time variability over the peak, were not included in the dataset. In addition, the validity of these past results is questionable, especially since they were often based on data consisting of several observations for one day rather than the same set of observations across several days. Observations on the same day may be correlated, so that accurate estimates of day to day variability are impossible. Although convenient to the analysis, this approach is unsatisfactory. As Abkowitz (1980) states, “Another major problem encountered in developing the analysis methodology was the lack of objective reliability data. . . . The collection of a sound ‘reliability’ data set. . . would be extremely useful and should be treated as a high research priority.” In this paper, we shall use a set of data gathered in Pittsburgh, PA for the express purpose of analyzing dynamic level of service variations and departure time decisions. Collecting this dataset involved independent measurement of travel times and transit wait times for travei to the Pittsburgh Central Business District (CBD) as well as survey of 1800 workers in
E. PLANK
the CBD. This survey was conducted among twelve large employers and included a small number of workers with flexible working hours. A detailed discussion of the dataset appears in Plank (1982). The next section summarizes data on travel characteristics over the peak period of travel. Section 3 summarizes information on work starts and modal choice. Following this, a disaggregate departure time and mode choice model is reported. Section 5 summarizes the elasticities of this choice model and several simulations of policies affecting departure time decisions. 2. VARIATIONS IN TRIP LEVEL OF SERVICE FOR MORNING COMMUTES IN PITTSBURGH, PA
The Pittsburgh, PA CBD offers a useful laboratory to study time dependent travel variations. Approximately 80,000 workers commute to this triangular area of roughly 0.75* miles. Surrounded by rivers or hills, the major access roads to the CBD generally have bridges or tunnels which act as bottlenecks and cause queues (Fig. 1). Thus, route choices are limited, and congestion is concentrated at a limited number of major bottlenecks. To measure travel times into the CBD, at least eight vehicle trips were made from each of four suburban areas during the morning peak period of travel (Fig. 2). On the five separate routes, the average travel time during the most congested travel period ranged between one quarter and one half more than the average for the base, free flow travel time. The pattern of travel time peaking was quite regular in each area, with the maximum travel time occurring at about the same time on each day of observation. The increase in congestion to the maximum travel time and subsequent decline can be represented by a quadratic function in which extra or congested travel time was a function of departure time from the suburb (Fig. 2). Despite the scatter of measurements shown in Fig. 2, the variability in travel times for a given departure time was relatively low. The average ratio of the standard deviation to average travel time (i.e. the coefficient of variation) was 0.13 over all routes and departure times. This suggests that, with experience, commuters can fairly accurately predict the amount of time required to travel to work on any given day with a particular departure time. In effect, travel time peaking occurs in a fairly regular pattern from one day to the next. The pattern of expected wait times for transit and the variance of wait times was crucially dependent upon local operating policies. For example, in an area with unscheduled service (Bethel Park streetcar service), the average wait time was relatively short and constant throughout the peak period of travel. The variance of wait time was approximately equal to the average wait time for this service, suggesting an essentially random or Poisson arrival process of transit vehicles. In contrast, scheduled transit services exhibited irregular variations in average wait times and variances of wait times over the course of the
21
The flexibility of departure times for work trips
Fig. 1. Study areas in the Pittsburgh, PA region.
.. . . . .. .
100
120 /7:03
140 am.)
.
.
.
.
.
160
100 (FL00
200
220
%n.)
Fig. 2. Travel times at different departure times from Greentree to the Pittsburgh CBD.
C. HENDRICKSON and
28
E.
PLANK
12.0
f
r 8.0 Y
. .
z I-
i
*
-1
3
t
*i
;
.
4.0
I 7:oo
,m
Fig. 3. Average wait time vs arrival time at a transit stop in Greentree.
peak period, reflecting the fact that scheduled transit service in Pittsburgh does not use headways of fixed length throughout the peak period. An example of such variability is shown in Fig. 3, in which each point represents the average wait time for different arrival times at a transit stop in Greentree, as measured over eight days. The variance of wait times with scheduled service depended crucially upon the frequency of service. With scheduled transit departures quite frequent, the variance of wait times was relatively low. One phenomenon illustrated in Fig. 3 deserves mention. Note that the average waiting time for a bus increases for patron arrivals slightly before the scheduled services at 7:02 and 7:20 a.m. This occurs because buses occasionally run early on the route, and patrons arriving near the scheduled departure time missed the bus and had to wait for the next. Accordingly, patrons wishing to minimize their waiting time should arrive at the stop a few minutes before the scheduled departure time. As noted above, though, greater control of vehicle operations would reduce this problem. By and large, the frequency of transit service varied in proportion to the level of demand in the areas of scheduled transit service. That is, extra vehicles were scheduled during the peak departure time periods. The equilibrium effect of this scheduling practice is to concentrate transit demand even more in the peak departure time period, since this period has the shortest average wait and the lowest variancein wait time. 3. WORK ARRIVALS, START TIMES MODAL CHOICES
AND
The cumulative proportions of arrival times at work and official work start times is shown in Fig. 4
for a sample of 1800 workers in the CBD. In this figure, there is a significant jump in the cumulative distribution of work start times at 8:00 a.m., with 42% of all workers reporting an 8:00 a.m. work start time. The cumulative distribution of arrival times is shown to the left of the work start time curve, suggesting that most downtown workers arrive early. Indeed, the mean departure time is 7:00 a.m., the mean arrival at 7:40 a.m., and the average work start occurs at 8:OOa.m. As shown in Fig. 4, the median work start time is slightly before 8:00 a.m. Also shown in Fig. 4 is the cumulative distribution of “desired” work start times. This function indicates a generally flatter and earlier distribution of desired work starts compared to existing arrangements, although there is a minority of workers who would like a work start time of 9:00 a.m. or later. “Desired” work start times were self-reported by respondents to our survey. Concerning the various modes of travel, shared ride modes (carpools, vanpools, etc.) exhibit the greatest amount of travel time peaking, with 77% of all the workers sharing rides arriving in the hour from 7:15 to 8:15 a.m. (Table 1). Workers driving alone had the lowest degree of arrival time peaking, with transit services at an intermediate level between shared ride and drive alone modes. Thus, promotion of shared rides probably will disproportionally draw from transit travelers at the peak period of travel, thereby reducing the need for capacity increases in transit or roadways. The modal choice of those surveyed reflected the availability of direct transit service to the CBD. Public transportation was used by 55.5%, while 15.9% drove alone, 24.2% shared a ride in a private vehicle, and the remainder scattered among bicycles and walking.
The flexibility
Fig. 4. Cumulative
Table
Arrival
work starts,
1. Distribution
Time
arrivals
times for work
and desired
of arrival
time at
starts
29
trips
in the Pittsburgh,
PA CBD.
work by mode of travel
Shared Ride With Family Member
Drove AkJlle
Transtt
Before
7 15
17
16
16
19
16
7 15-7
45
35
30
30
42
34
745-a
15
32
31
43
35
33
10
14
6
2
10
5
11
3
2
6
B 15-645 After
Source
4.
of departure
645
Survey
of
1600
CBD
workers
conducted
DEPARTURE TIME AND MODE CHOICE DEMAND MODEL
To further analyze traveler decisions, a logit model of departure times and mode choice was estimated. Logit choice models are described in Ben Akiva (1977) and Hensher (1981). Estimation is performed by the technique of maximum likelihood for these models. The logit model form was selected to take advantage of the disaggregate data gathered and to adequately represent the irregular nature of variations in factors such as transit wait time. The base model included up to twenty-eight alternatives, representing combinations of four modes (drive alone auto, shared ride, transit with walk access and transit with auto access) and seven different departure time intervals of 10 min each. In our analysis, mode and departure time choices are treated as a simultaneous interactive decision based upon maximization of individual traveler’s utility or satisfaction with each alternative mode and
by the authors.
departure time combination. The probability of an individual selecting each mode/departure time alternative (PU,) is assumed to be of the logit form: (1) where individual i has mode j and departure time I available among the mode choice set k and the departure time choice set n, respectively. For each mode choice/departure time alternative, the satisfaction or “utility”, Vi,, is specified to be: Vi, = a, + a,FFTTV + u,CONG,
+ n,(COST/ Y),
+ n,ACC, + a,WAITV, + u,LATEV, + u,(LATEgJ2 + u,EARLY,, +u,(EARLY,,,)~
(2)
plus a random component, where the variables are defined as follows for individual i:
30
C. HENDRICKSON and E. PLANK
1. FFTT,-free flow in-vehicle travel time for mode j. The inclusion of this variable provides a mode dependent variable representing free flow travel time. Since increasing travel time for any mode would discourage its selection, a negative coefficient is expected. 2. CONG,i,-portion of total travel time on mode j due to congestion associated with travel at departure time t. The inclusion of this variable provides a mode and departure time dependent indication of congested travel time and, since increases in congestion time would result in decreased alternative usage, a negative coefficient is expected. Also, congestion time might be expected to be more onerous than free flow travel time. 3. (COST/Y),i,-monetary cost for mode j and departure time t divided by the household income index of individual i. The cost term is generally felt to be mode dependent, however, the time subscript indicates the possible inclusion of departure time dependent cost considerations (e.g. peak hour tolls and fares or parking surcharges). The division by household income provides an income effect on travel cost (i.e. a $10 parking charge may have different mode or departure time impacts for an individual earning $10,000 per year as opposed to an individual earning $40,000 per year?). 4. ACC,-walking time on the home end of a transit trip associated with departure time t. This variable provides a measure of the accessibility of transit service to the traveler, and is only included for the transit with walk access mode. The time subscript allows for variation in access time associated with different departure times from home, and might be important in situations where individuals have more than one transit route available to provide express service to the CBD (which was the case in the Monroeville study area). A negative coefficient was expected. tIncome was measured on a scale of 1 to 6; 1 representing annual household income of less than S10,ooO; 2 representing $10,000 to %20,000,3 is %20,000to $3O,ooO;4 is $30,000 to $40,000, 5 is $40,000 to $50,000; and 6 is over $50,000.
5. WAIT,wait time associated with mode j and departure time t. This variable allows an objective measure of transit level of service and its variability during the peak period. Since longer wait times would discourage transit usage, a negative coefficient was anticipated. 6. LATEe,-minutes of late arrival at work associated with mode j and departure time t. LATE, provides a linear component of the schedule delay impacts on the mode/trip timing decision. Mode and departure time subscripts are included because schedule delays depend upon both mode of travel and time of departure. A negative coefficient was expected. Workers on flextime had LATE set to zero. 7. (LATE,)*-as for LATE, above, this quadratic term is proposed to more accurately represent individual perceptions of late arrival at work. 8. EARLYU,--minutes of early arrival time at work associated with the use of mode j and departure time t. This value, similar to LATE,,, provides a linear component of schedule delay implications for mode and departure time selection. Since the variable value is mode and departure time dependent, mode and time subscripts are included. A negative coefficient was expected, but of smaller magnitude than that of LATE; this is because late arrival at work is felt to be more onerous than early arrival. Workers on flextime had EARLY set to zero. 9. (EARLY,)‘-as with (LATE,,)* above. A negative sign is anticipated to reflect the increasing disutility associated with earlier and earlier arrivals at the work place. Modal constants were also included in the model to represent the effects of unspecified mode dependent characteristics. The base mode for these constants is transit with walk access. Estimated coefficients for the model appear in Table 2. For this model estimation, the observations included 363 residents of four suburban areas who took part in the downtown survey. The high statistical significance of most of the estimated coefficients is encouraging. The significance of free flow in-vehicle travel time and congested travel time are the only two in question; the low t-statistics indicate the estimated
Table 2. Estimated model coefficients Estimated
Variable drove
alone
constant
Coefficient
-1.47
t-statistic 3.5
shared
rode constant
-2 09
66
tran*,t
auto constant
-126
63
free
flow
I” vehicle
congeston
trne
travel
time
-0 006
0.3
-0021
0.7
cosl/lncome
-0699
2.0
(early
-0 00042
53 64
trne?
late time
-0
llate tImeI
+.0014
2.3
access
-0095
50
-0066
32
wait
tome
time
146
The flexibility of departure times for work trips
31
implicit value of $2.52 was placed upon arrival five minutes late, while a value of $4.79 was placed upon being ten minutes late. This suggests that individuals would be willing to pay about $2.52 to avoid five minutes late, on average, and $4.79 to avoid being ten minutes late. Generally, late time is regarded much more onerously than is early time. The complete arrival time “cost” relationship, including both early and late arrival time, projected by these final model coefficients, is graphed in Fig. 5. This graph indicates the relative disutility of different arrival times at work. The shape of the late time disutility curve is surprising. A negative coefficient on both the linear and quadratic LATE terms was anticipated; this would indicate increased disutility associated with later and later arrival after the official work start. What was found, however, contradicts this. Based on the estimated model coefficients, the
coefficient may not be significantly different from zero. This result is likely due ta the similarity of in-vehicle travel times for the different modes in our dataset. The implied values of time based upon the coefficient values in Table 2 are summarized in Table 3 for the average income in the sample. The dollar amounts presented by this table appear reasonable both in terms of their magnitude and relationships. The high cost associated with access to transit may be explained by the fact that in four of the five study areas, access was predominantly along unpaved roadway shoulders with no sidewalks. This should indicate to transit operators the apparent extreme disutility associated with suburban walking access to transit routes. In addition, the high late time cost represents the significant penalty which individuals perceive to be associated with late arrival at work. An
Table 3. Values of time based upon estimated model coefficients Average Based Upon
Time Variable free
flow
travel
congestlo” access
,,me
of Time Coeffaaents
51 71/hr2
tme
time
Value Model
54 502
Iwalktng)
520 3Whr
Walt time
S17.14lhr
late time3
S2.52 54.79
early
5004 for SO. 15 for
twne3
for for
betng 5 min late bang 10 man. late being being
5 min early 10 min. early
’ These conversions were performed using the coefficient of the costllncome term 1699). where costs were in dollars and the average #“come was surveyed to be 2.5 units, or approxamately S20.000 per year ’ The low Statistical signtflcance of these time values
of
the estomated
coefficients
reduces
3 These values depend upon the amount of late and early time because times enter as quadratac functons in the utility express~ns
Eerly
Ar,lv.l
Work
St.,,
Th.
L.1.
the dependablllty
early
Arrlr.1
Fig. 5. Relative disutility of different arrival times at work.
and late
C. HENDRICKWN and E. PLONK
32
Table 4. Effects of additional variables on estimated model coefficients Model
1
Model 2 lnzludes Walt twne
Model 3 luxludes seat avalab!lQl
VXlXlCd
drove
alone
shared
ride
transit
auto constant
free
constant constant
flow
IV77
con9estlo”
t,me
-
-2 0918 81
-2.0918
- 1 3316 31 - 0031 ll
008l3l
-021(7l
-021171
- 03211 01
030( 651
-.698(2 3)
- 1481641
wait
twne
wait
time
01
-.00042(5
-.6912 31
-. 146(6.41
01
+ 001412.31
+0014(221
- 09515 01
-.09915.1
-.08813
-.08312
-0811261
2)
61
41
- 14616 3)
+.001412.3l
vanance
- 67312.0)
- 00044(5
- 09515.01
(late tImeI time
- 1 2316 ll
- 1.2616 31
- 69912 01
end walk
-1.41(341 -2 20(9 51
-.00813l
- 0004215
home
-2 031301 -2 6414 51
- 1 26(6 31
OPTCllncome
late trne
51 81
- 008l3)
(early
time?
14813
- 1 47(3 51
Model 4 Iincludes departure tnmet
- 00046(4
II
- 143f5.71 +0013(23l
I
-. 10215 01 - 06813
11
- 0019131 -.OOl
seat availability
II1 Ol
departure
time
+ 006041221
(departure
tImeI
- 0000265(
Value of Ilkellhood
the logfunction
NOTE
t-statistics
-1021
appear
5
-10214
-10209
271
-10180
in parentheses
disutility associated with these later arrivals increases only slightly. The positive coefficient on the quadratic term (LATE,)* signifies that once an individual is quite late (approximately 1 hr) in arrival, additional late time has little effect. Table 4 reports estimated coefficients for models which included several variables in addition to those in Table 2. These additional variables included the variance of transit wait time, an index of the availability of seats on transit, and the absolute clock time of departure. In each case, the variables were not statistically significant and were excluded in the final mode!. For seat availability, this lack of significance may be due to lack of variation in the sample of observations, since the Pittsburgh transit agency scheduled vehicles to arrive at capacity during the peak period. However, in contrast to the other models reported, inclusion of seat availability did result in changes in other estimated coefficients. Exploration of the effect of seat availability on choice would be of considerable interest in future work. 5. IMPLIEDELAWICITlES AND CHOICEFLEXIBILITY The model described in the previous section may be used to forecast the demand effects of a variety of policies on both modal split and travel peaking patterns. In this section, we explore the effects of a variety of such changes. Our intent is to indicate the relative sensitivity of mode choice and departure time decisions as well as to estimate the effects of policies, such as tolls, which might vary over the course of the peak period. One consideration in performing this analysis is the equilibrium effects of demand shifts either over time
or between modes. If policies substantially affect demand patterns, then the pattern of travel time peaking and, subsequently, the demand pattern will also change. Here, changes in demand patterns without considering such equilibrium effects are discussed. The results represent approximate estimates of impacts, with the amount of error from the approximation depending upon the extent of the change. For many policies examined, the effects are sufficiently small so that equilibrium effects are likely to be of minor importance. Equilibrium effects in an abstract setting are discussed in Hendrickson et al. (198 la and 198lb). Since the logit demand model is based on individual choices, elasticity value estimates from the model represent the choice sensitivity of individuals. Table 5 reports the choice characteristics of two individuals which we use for illustration of such elasticities. These individuals were chosen to be representative of residents traveling to a CBD workplace from two suburbs. Individual A has a high likelihood of transit use (80%), while individual B has only a 53% probability of using transit. These high transit probabilities reflect the relative attractiveness of transit service to the CBD. For both individuals, there is slightly more than a 20% probability that they will choose to depart in a particular ten minute interval. For both individuals, auto travel to a park-and-ride lot to access transit service results in slightly longer in-vehicle travel times than for transit with walk access. Table 6 reports elasticity estimates for these two individuals for various changes. The first group of these estimates represent elasticities of transit choice over all departure time intervals and both transit access modes. These elasticities are calculated for
The flexibility
of departure
times for work
33
trips
Table 5. Individual trip characteristics for elasticity
calculations
lndwdual A Free Flow In Vehticle Travel time lmin) TransltIWalk Access Transit/Auto Access AUKI Average Income
Congested
In Vehicle
Travel
Time
lmlnl’
lndcator’
Work
Start
Home
End Transit
Note:
Access
taken
IWalk)
Twne (mini
over
all departure
time
to an annual household
variable
Times
750
600
2 Corresponding 3 Includes
244
auto
are given
operating in minutes
of
Choice
59 64
64 5.5
parking
1
2
Chotca/Peak Probabnllty2
Period
Departure
lndwidual A
tndwiduai 6
-0 63 -0.060 -0.009 -0015 0.15
-06 -0 16 -0 26 -0 095 051
Peak Period Peak Period
Transit Transit
Fare’ Wait Time
-26 -033 -0031 0 030
-16 -0 11 -0.20 0073
Time
Travel Time Travel Cost
Elasticities on choice probabilities calculated numerically from variable values shown on Table 5. Transit choce probabll!tles transit use wth walk and auto access Elastlctty cost for
calculated from a 1% fare change, auto access to transit service.
Vol. 18. No. 14
with
constant
Peak periods correspond with a departure tnme of lndwtd@ A and 630 to e40 AM for individual 6.
changes in transit fares, transit wait times, walk time to transit, congestion delays on transit, and auto travel costs. For each of these changes, choice sensitivity is inelastic, so that a 1% change in the level of service characteristic results in a less than 1% change in transit choice probabilities. The direction of change is as expected in each case. The second group of elasticities reported in Table 6 represents the sensitivity of transit use in the most likely departure time interval to changes in transit fare, wait time, travel time, and auto cost. Each of TR-A
elasticities
Probablllty
Peak Period Transit Congested Auto Peak Period Out-of-Pocket
NOTE.
525.000
charges.
thereof.
Transit Fare’ Transit Walt Time Transit Walk Time Transit Congested Travel Time Auto Out-of-Pocket Travel Cost Transit Choice
AM
43
approximately
and average
or fractions
600
0.66
intervals
income
costs
AM
Table 6. Estimated choice probability
Transit
075 1.13 3 13 096
050 050 1.94 0.6 1
Transit Wait T&me Imini Trawl/Walk Access Transit/Auto Access
are
37 07 3722 35 36
Idollarsl
Time
’ Averages
655 9.00 8.51
25
Out-of-Pocket Travel Cost TransltlWalk Access Transit/Auto Access Auto/Drive Alone3 Auto/Shared R,de3
Average
lndwidual 9
7.20
1% changes in the are the sum Of
out-of-pocket
to 730
AM
travel
for
these elasticities was calculated for changes only in the peak interval, representing, for example, the imposition of a fare surcharge during the peak period. These peak interval transit demand elasticities generally show a much greater sensitivity to changes than do the previous transit service elasticities. These greater sensitivities reflect the possibility that individuals could alter their departure time yet still choose to use transit. In effect, such changes imply a change in the overall distribution of transit service demand during the peak period. Most dramaticaIly, the elas-
33
C. HENDRICKSON and E. PLANK Table 7. Effects of policy changes on travel from Greentree No No
Base case
$1.00 auto toll
Peak period auto toll
10 12 16 62
8 11 17 64
8 IO 17 65
10 II 16 62
12 13 16 16 15 15 13
Mode share (percentage)’ Drive alone Shared ride Transit/auto Transit/walk
Auto departure time (a.m.) (percentage)’ 6:40 10 10 650 13 13 7:00 15 I5 7:lO 16 17 7:20 17 17 7:30 17 17 7:40 13 13 Transit departure time (a.m.) (percentage)’ 6:40 8 8 650 12 12 7:00 17 17 7:lO 14 14 7:20 19 19 7:30 18 18 7:40 11 11 Average change in consumer surplusf - 0.03
No congestion
transit congestion
transit or shared ride congestion
Double frequency
10 II
10
16 63
16 63
9 9 17 65
9 12 14 16 16 17 15
10
13 15 17 17 17 13
9 12 14 16 17 17 14
9 12 15 16 17 17 13
8 12 17 14 19 18 II
7 11 15 14 19 21 13
7 II 15 14 19 20 13
7 I1 15 14 19 20 13
9 12 I5 15 18 18 13
-0.04
0.06
0.05
0.06
0.16
II
tCalculated as the average of choice probabilities for each individual in the sample. :Calculated as the average change in consumer surplus for each individual in the sample. ticities suggest the sensitivity
of departure times to transit fares. For individual A, a 1% increase in the peak beriod fare results in a 2.6% reduction in the probability of transit use during the peak period. In addition to calculation of choice elasticities for small changes in explanatory factors, the logit demand model can be used to indicate the effect of new policies such as tolls, exclusive bus lanes, or changes in congestion. Table 7 reports the effects of various policy changes on travel from Greentree. This Pittsburgh suburb has a moderate degree of travel time peaking and is served by bus routes without an exclusive right of way. In the base or current situation (Column 1 of Table 7), the transit mode share is quite large, with 78% of commuting trips on transit with either walk (62%) or auto (16%) access. Departure times are spread throughout the peak period, but with the highest proportions of departures occurring between 7:15 and 7:35. For auto travel, 34% of all departures occur in these two intervals. In the same periods, 37% of all transit users depart, representing the greater amount of departure time peaking on transit. This peak departure time period of 7:15 to 7:35 is not surprising since it corresponds with workplace arrivals shortly before 8:00 a.m., which is the most common work start time. The final row in Table 7 reports the estimated average change in consumer
tSee Williams (1977) or Daganzo (1979) for a discussion of this measure. It is calculated as the change in the logarithm of the denominator of the logit choice function.
surplus from the base case which is due to policy changes. Thus, this figure indicates the relative levels of changes in individuals’ net travel benefits.7 The various policies considered and their effects are described below. These policies generally represent extreme outcomes since they neglect equilibrium effects. However, they are useful in indicating the range of potential demand effects. $1.00 Auto roll. This policy imposes a flat $1.00 toll on all automobile trips. This toll might be collected at the Fort Pitt Bridge (the route bottleneck) or as a parking tax surcharge. The result of the toll is a shift towards transit ridership (with an increase in mode share of 3x), but little shift in departure times. In terms of modal volumes, this represents a 14% decline in auto usage and a 4% increase in transit patronage. For shared rides, we assume that the toll payment is divided by the average number of riders; with a smaller individual payment, the shift from shared ride is correspondingly lower. Peak period auto toN. This hypothetical toll policy represents a $2.00 charge in the period 7:30 to 8:00 a.m. and a $1.00 charge in the periods 7:00 to 7:30 a.m. and 8:00 to 8:30 a.m. The object of such a toll might be to reduce peak period travel. The toll is assumed to be paid at the Fort Pitt Bridge and, as before, the toll is divided among riders in carpools. With the higher toll in the time period 7:30 to 8:00, a larger diversion from auto modes occurs than in the flat $1.00 toll case (Column 2). The increase in transit mode share is 4%, representing an 18% decline in auto volumes and a 5% increase in transit volume.
The flexibility of departure times for work trips The time differential in the toll structure does affect the departure time distribution, with substantially less peaking for auto travel. In effect, auto travelers both switch to transit and alter their departure times. Their is no significant net change in the distribution of transit departure times. No congestion. The effect of roadway capacity increases which would result in no roadway con-
gestion is simulated in this case. Peak period travel times are equal in this scenario. The removal of congestion does not result in significant mode shifts in Greentree. Departure times do have a significant shift, however. The proportion of transit user departures in the peak period of 7:15 to 7:35 a.m. increases from 37% (in the base case) to 40% with no congestion. Thus, there is shift towards later departures and periods with lower wait times. No transit congestion. This scenario models the effect of an exclusive right of way for transit vehicles. There is an increase in the transit mode split, of 1% in this case. In addition, the transit user departure time distribution becomes even more peaked than in the base case, as both current and new transit users shift towards the peak departure times. No transit or shared ride congestion. This scenario represents the effect of a high occupancy vehicle (HOV) lane. The reduction in transit congestion time includes a shift towards transit, even from shared ride services. That is, while both transit and shared ride service become more desirable compared to the base case, transit improvement is disproportionally larger. The net modal shift is relatively small, however. Again, the transit users’ departure time distribution becomes
more peaked.
Double transit frequency. This scenario represents a substantial improvement in transit service by, in essence, halving transit wait times. The result is an increase in the transit mode share of 4%. This shift represents an 18% decline in auto riders and a 5% increase in transit service. These modal shifts are comparable to those found with a peak period auto toll of $1.00 or $2.00 (Column 3). The distribution of transit users’ departure times is slightly less peaked than in the base case, but this effect is relatively small. These policy scenarios indicate relatively minor effects on actual travel choices. It is fairly difficult to increase the transit mode share in the highly transitoriented market of work commuting from Greentree to the CBD. Somewhat larger shifts occur in the distribution of departure times, with many transit improvements resulting in a greater degree of departure time peaking. An exception to this increased peaking is an increase in service frequency. Similar results were obtained for other residence areas in Pittsburgh. The calculation of average changes in consumer surplus allows some comparison of the relative benefits of the different policies. The most notable result in this comparison is the desirability of wait time decreases: the increase in average consumer surplus is three times higher for halving transit wait
35
times (Column 7) than for eliminating in-vehicle congestion time on transit (0.16 vs 0.05, as shown in Table 6). The decline in average consumer surph~s with auto toils (Columns 2 and 3) is expected. Against these reductions in net user benefits, revenues of $0.13 per traveler will be collected with the $1 .OO toll (Column 2) and $0.21 per traveler with the peak period toll (Column 3). In addition, some benefits will be derived from reduced travel times due to less congestion.
6. CONCLUSIONS
Observations of traveler responses to disruptions, demand theory and the empirical demand models reported here all suggest that individuals can exhibit flexibility in the choice of departure time for work. Indeed, the departure time decision seems to be more elastic than the choice of mode. This flexibility in departure time choice has some important implications for transportation planning. First, congestion relief due to capacity increases or transit service improvements is likely to be overestimated since reduction in congestion will induce shifts into travel during the most congested period. Second, time dependent tolls tire likely to be useful tools in transportation system management, particularly if the tolls are more greatly differentiated than a simple peak/offpeak differential. Fourth, departure time flexibility offers a “latent” capacity in transportation facilities which may be exceedingly useful during short run disruptions such as transit strikes or reconstruction of heavily used facilities. Finally, shared ride modal travel exhibits more peaking of demand than do either transit or drive alone modes, suggesting that increased ride sharing would reduce the peak demand on transit. The research reported here should be regarded as exploratory in nature for the subject of dynamic adjustments. Several interesting research issues exist, including investigation of attributes such as seat availability on transit service, parking availability, the variety of possible flex-time working arrangements, and preference variations among different types of workers. From a methodological standpoint, hierarchical logit or probit models might be useful analysis approaches to investigate. Acknow[edgemenrs-This paper benefitted from comments from several anonymous reviewers. Sue McNeil aided in the computation of elasticities and percentage shifts. Financial SUPPOrt was provided by the Urban Mass Transportation Administration’s Program of University Research and Training under contract No. PA-I I-0024; views expressed are not necessarily those of UMTA. REFERENCES
Abkowitz, M. D. (1980) The Impact of Service Reliability Ph.D. thesis, Massachusetts Institute of Technology. Ben Akiva M. and Atherton T. (1977) Methodology for short-range travel demand predictions. J. Trans. Econ. on Work Travel Behacior.
and Policy, 224-261.
36
C. HENDRICKSON and E. PLANK
Blurnstein A. and Miller H. D. (1982) Making do: The effects of a mass transit strike on travel behavior. Transpn (to be published). Cosslett S. (1977) The trip timing decision for travel to work by automobile. The Urban TraTel Demand Forecasting Project V. Daganzo Carlos (1979) Economic Theory, Econometrics, and Mathematical Economics. Multinomial Probit: The Theorv and Its Application to Demand Forecasting. Academic Press, New-York. Hendrickson C. and Kocur G. (1981) Schedule delay and departure time decisions in- a deterministic model. Transpn Sci. 15(l), 62-77. Hendrickson C., Nagin D. and Plank E. (1981) Characteristics of travel time and dynamic user equilibrium for travel to work. Proc. 8th Int. Conf. Trans. Trafic Theory, 245-258. Hendrickson C., Dubyak T., Carrier R. and Anderson R. (1982) Traveler responses to reconstruction of the parkway east (l-376) in Pittsburgh, PA. Transpn Rex Rec. 890, 3339.
Hensher D. and Johnson L. (1981) Applied Discrete Choice Modelling. Wiley, New York. McCafferty D. and Hall F. L. (1982). The use of multinomial logit analysis to model the choice of time to travel. Econ. Geography S(3). Meyer J. R., Kain J. F. and Wohl M. (1965) The Urban Transportation Problem. Harvard University Press. Oram L. (1979) Peak period supplements: The contemporary economics of public transport. Progress in Planning XII Part 2. Plank E. (1982) An investigation of peak period mode choice and departure time travel behavior. Master’s thesis. Carnegie-Mellon University. Small K. A. 11982) The scheduling of consumer activities: Work trips: Amer. Economic Rk. 72(3), 467479. Williams H. (1977) On the formation of travel demand models and economic evaluation measures of user benefits. Emiron. Plan. A(9), 285-344.