Travelers who use public transport

Transcription

1 IA LogitModel of Public Transport Route Choice BY JOHN DOUGLAS HUNT Travelers who use public transport must select a path through the network of available routes. A better understanding of what influences travelers in making this decision would contribute to the design of public transport services in at least two ways. Algorithms that allocate flows of public transport passengers to routes must include some representation of the factors that influence this route selection process. Typically, these algorithms are based on the idea that people seek to minimize some form of generalized cost expression that incorporates representation of the influences of various factors (preferably weighted in order to indicate relative strengths of influence) on the attractiveness of routes. A better understanding of these influences will improve efforts at specifying what should be included in such expressions. Public transport routes and the networks comprising these routes must be designed. Knowledge of what influences the attractiveness travelers associate with routes can be used to design a service that will be more attractive and therefore have a greater patronage. This paper describes research considering travelers behavior in selecting Conversion Factors To convert from to multiply by m K 3.28 mls ftls 3.28 from among available public transport routes. It focuses on the estimation of a Iogit model of this public transport route choice behavior using disaggregate revealed preference observations of the behavior of individuals traveling to work at locations in the central business district (CBD) of Edmonton, Canada. The resulting model includes explicit representation of the influence of various factors on travelers selection of a route. As such, it provides insights into the nature of public transport route choice behavior that contribute to the design of public transport services in the ways indicated earlier. ModeI Formulation The Iogit model formulation can be developed using the random utility theory of individual choice behavior. ] This development is outlined briefly here. Each individual in a set of individuals must choose one alternative out of a set of discrete alternatives. Each of these individuals is assumed to associate a utility (which is a numeric measure of attractiveness) with each alternative and then choose the alternative with the highest utility. This utility is influenced by the attributes of the alternative. An approximate representation of these influences is provided by a linear-in-coefficients utility function with numeric representations of the attributes of the alternatives as independent variables and a utility value as the dependent variable. It is acknowledged that this utility function will only approximate the exact nature of these influences; thus, a randomly varying term is added to the utility function. In mathematical terms, the result is as followsz : T(i) = u(i) + E(i) = ; z(k) X(i,k) + E(i) [ 1 i= index representing alternative, k= index representing attribute, K= set of all attributes considered, T(i) = true utility for alternative i, U(i) = utility value for alternative i as determined by utility function, E(i) = randomly varying term, X(i, k) = numeric representation of attribute k of alternative i, and Z(k) = utility function coefficient associated with attribute k. If it is assumed that the E(i) terms are independently and identically distributed according to a Weibull distribution, then the resulting analytic expression for the probability that T(i*), for a particular alternative i*, will have the largest value is as followsz 3:.[l(,.> P(i*) = ~ ~ls 1</ 1 = set of all available alternatives, and 26. ITEJOURNAL. DECEMBER 1990

2 P(i*) = probability that t(i ) will have the largest value; that is, the probability that alternative i will be selected. This is the logit model formulation. * It has an analytic form that is relatively simple and convenient to work with when estimating the utility function coefficients (which are the weights discussed earlier) using empirical data. Computer programs that perform this estimation are readily available, and the statistical properties of the resulting estimates are well behaved. Consequently, this formulation is a very attractive one for use in modeling choice behavior, and it enjoys widespread use. Data Collection Preparation and In June 1983, 1702 individuals employed by 80 different employers located in the CBD of Edmonton, Canada, were interviewed concerning various aspects of their morning trip to work. A total of 834 of these individuals indicated they regularly used public transport for their trip to work. These 834 were then asked to indicate the specific route they used, including where they boarded, where they transferred (if at all), and where they alighted. The term route in this case does not refer to the various numbered routes individual public transport buses or trains follow in providing services, such as Route 45. Rather, it refers to any path along the network of services that may include transfers from one vehicle to another or a segment of the network where several numbered routes run together and thereby provide a more frequent service. Detailed route maps and operating schedules were obtained for all the bus services and the light-rail train service in the Edmonton metropolitan region at the time of the survey. A series of 1:5000 scale maps and corresponding aerial photographs displaying the entire region were also obtained. This information was used to develop a set of disaggregate observations of route-choice behavior. Each of these observations concerned one of the travelers interviewed in the survey. It indicated the attributes of the alternatives available to the individual and the selection made by the individual. The following numeric representations of attributes of routes were determined for each alternative included in each observation: OWALK(i) = the walking distance, in meters, along the shortest path from the traveler s home to the stop or station where the first vehicle in alternative i is boarded, called the boarding stop. In general, the stop that provided the smallest value for OWALK(i) was used. However, if the route configuration was such that it was possible for the traveler to walk just a bit farther and reduce in-vehicle travel time by a significant amount, as shown in Figure 1, then the farther stop was used. This was based on the recognition that the traveler will trade off in-vehicle travel time against walking distance in such a situation. RIDE(i) = the total time spent in public transport vehicles for alternative i, in minutes. NTRANS(i) = the number of transfers included in alternative i. WTRANS(i) = the total time spent waiting in making all the transfers included in alternative i, in minutes. WAIT(i) = half the time between successive runs of the first vehicle boarded for alternative i, in minutes. If the times between successive runs varied during the morning, then the average of these times was used. HDWAY(i) = the time between successive opportunities for making the trip using alternative i, in minutes. If there were no transfers, then HDWAY(i) was the time between successive runs of the vehicles traveling the route. If there were transfers, then HDWAY(i) was the time between successive opportunities for the entire trip, including all transfers. DWALK(i) = the walking distance, in meters, along the shortest path from where the last vehicle included in alternative i is alighted, called the alighting stop. In general, the stop that provided the smallest value for DWALK(i) was used, but other stops were used in some cases on the basis of arguments concerning route configuration analogous to those indicated in the discussion of OWALK(i). Lw..ml -j+,0,s,,1. b..,,,.,,,.,. --,0 S.181. w.miw,.th Iirection If travel u In theory, the number of alternative routes available to an individual is very large given all the possibilities for walking to and from different stops and sta- CED II I clm::,io_q 1ori~n of wo;k trip * *6 D! L, awe, public transport route Figure 1. Example of public transport route configuration where it is possible to walk just a bit farther and reduce invehicle travel time by a significant amount. tions and for transferring between vehicles. It was necessary to restrict the number of alternatives included in each observation for practical reasons. An examination of the data obtained in the survey indicated that the selected route always had the following characteristics: A value for OWALK less than 1500; A value for NTRANS less than or equal to 2; and An alighting stop located within an area centered on the CBD. On the basis of this examination, it was judged that alternatives without all these three characteristics are extremely unlikely to be selected and therefore could be excluded from observations in order to keep the number of alternatives down to a manageable size. There is a restriction on the nature of the alternatives that can be included together in an observation. The assump- *The term logit refers to the form of the expression relating /Y(i*) and P(I ) when there are only two alternatives in 1, as follows: U(i*) - U(i ) = In {P (i*)/[l - P(i )]} f/(i ) = utility value for alternative i ; alternative i is the other alternative that together with alternative i* make up the set I. (The right-hand side of this expression is called the Iogit of P(i*).)4 ITEJOURNAL. DECEMBER

3 tion that the randomly varying term, E(i), is independently distributed as indicated in the description of the logit model formulation, along with certain properties of the logit model that arise as a result of this assumption, is most appropriate when no two or more of the alternatives are much more similar to each other than they are to the other alternatives. In order to avoid this in the observations developed here, alternatives that shared the same path through the network of public transport services for anything more than a very small proportion of their total length were not included together in an observation. Only what was judged to be the most attractive of the alternatives was included. The influence of fare could not be considered because the fare structure was such that alternatives with different fares were never included together in an observation. When this work was finished and incomplete observations were removed, a total of 250 observations, including 869 alternative routes, were left for use in model estimation. Estimation Procedure Estimates of the utility function coefficients were obtained using a computer program that employs the maximum likelihood procedure described by McFadden. This program identifies the values for the coefficients that make the model do the best possible job of reproducing the behavior displayed in the observations. Model goodness-of-fit to what is displayed in the observations was considered using p2(0), which is a measure analogous to the R* statistic for linear regression in that it ranges from Oto 1, with larger values indicating a better fit. The percentage of observations where the model assigns the highest probability of selection to the alternative actually selected, denoted %COR, was not used as a goodness-of-fit measure because it has some undesirable properties. However, its value is presented in the discussion of the results because it is a measure that can be appreciated intuitively. The value for the log-likelihood L(O), which is used to determine P (O), is also indicated to provide points of reference. For complete descriptions of these various measures and their uses, see Horowitz and Tardiff. A variety of alternative utility function specifications, including various combinations of the measures listed above, were considered (by establishing estimates of the coefficients and determining the resulting model s goodnessof-fit), and the one judged best was selected. The correlations among the measures themselves were also considered in order to avoid being unaware that one measure may be acting as a proxy for representing the influence associated with one or more other measures. Results The utility function selected is as shown in Equation 1. All the coefficients have differences from O that are statistically significant at the 95 percent level of confidence. They also all have negative signs, which is consistent with what would be expected in that an increase in any of the measures would reduce the attract iveness of a route. The relative values of the coefficients can be used to establish one factor s equivalent in terms of another factor. For example, the function indicates that a single transfer acts to reduce the attractiveness of an alternative by 2.83 units. An equivalent reduction in attractiveness is accomplished by an increase in riding time of minutes, thus indicating that a transfer is equivalent to minutes of riding time. This provides guidance in designing public transport networks when the intention is to improve the attractiveness of the service provided and thereby encourage use of the system. A change in network structure that eliminates the need to transfer, but does not increase riding times by more than minutes, will increase the attractiveness of the system. This result is independent of the time spent waiting in making the transfer. The fit of the model was better when the influence of transfers was represented using the number of transfers rather than the total time spent waiting in making transfers. This was unexpected. Before these results were obtained, it had been expected that the total time spent waiting would provide a more complete representation of the impact of transferring and thus would provide a better fit. Measurement errors may have contributed to these results. The measurement of transfer wait times is somewhat imprecise, while the number of transfers is measured exactly. The relatively greater error associated with estimates of transfer wait times may have acted to worsen the fit of models that used these times rather than just the number of transfers. Apart from the potential effects of measurement errors, these results suggest that the need to transfer on its own accounts for most of the impact of transfers and that increases in the length of time spent waiting do not have much additional impact once there is a need to transfer. This has an implication regarding the design of public transport networks in Edmonton. The network in Edmonton has been designed using the timed-transfer approach, with one of the major objectives being to minimize transfer wait times even if it means increasing the need to transfer. y It follows from the results suggestion that seeking to minimize transfer wait times, even at the expense of increasing the need to transfer, is somewhat inappropriate. Reducing the number of instances where there is a need to transfer, even if some transfer wait times are lengthened, would appear to be a more appropriate objective because it would act to make the system more attractive overall. However, the use of the timed-transfer approach in Edmonton has made transfer wait times in the Edmonton network very small in most cases and thus not so onerous, which may have made just the need to transfer relatively more influential. Transfer wait times may be less influential only if they remain relatively short. Significant increases in transfer wait times may change travelers perceptions and make them more sensitive to these times. This suggests that just one objective, either reducing transfer wait times or reducing the number of times there is a need to transfer, should not be pursued over the full range of possibilities; rather, the impact of changes on travelers perceptions should also be taken into account and the objective modified accordingly. The coefficients for the walking distances at the origin and destination ends of the alternatives are different. They indicate that travelers are more sensitive to walking distance at the origin end, with 1.00 meters at the origin end equivalent to 1.89 meters at the destination 280 ITEJOURNAL. DECEMBER 1990

4 U(i) = x OWALK(i) 2,83 x NTRANS(i) x RIDE(i) x HDWAY(i) x DWALK(i) (-8.80) (-8.42) (-5.50) (-3.02) (-4.27) Equation 1. (The value in brackets below each coefficient estimate is the t-statistic for the estimate s difference from O. With: L(O) = ; p2(0) = 0.38; and %COR = 72.0.) end. This difference is statistically significant (the t-statistic for it is 3.35), indicating that the common transport modeling practice of adding all walking components together directly (unweighed) in order to establish a single walking distance measure for public transport is inappropriate. This applies for walking times also if it is assumed that the walking speed is the same at both ends of the trip. This result indicates that efforts at increasing the geographic coverage of the public transport network in Edmonton should be focused on areas containing the greatest numbers of origins, if the objective is to make the system more attractive. Given the tidal nature of the morning and evening peak period fiows into and out of the CBD, this suggests that some form of system where there is a dense network in residential areas and a more sparse network in the CBD during the morning peak and the reverse in the evening peak may be the most effective, at least to the extent that such a deployment of services is possible. It is implied that one minute of walking time at the origin end is equivalent to 2.89 minutes riding time (if a walking speed of 1.2 meters per second is assumed). ) This is within the range of such ratios found in studies concerning mode choice behavior, toward the high end of the range. The ratio of 1.00 minutes walking time at the destination end to 1.53 minutes riding time that is implied is also within the range, but toward the low end. WAIT(i) and HDWAY(i) represent slightly different aspects of the impact of only being able to travel when the service is provided. WAIT(i) is the expected wait time at the boarding stop for travelers arriving at a uniform rate. Its use in transport modeling is widespread. The coefficient associated with it is often interpreted as indicative of the relative sensitivity to waiting time. HDWAY(i) is intended to represent the extent to which travelers have to compromise their schedules in order to use alternative i, with a larger value indicating a greater degree of compromise. HDWAY(i) was proposed in this research in response to concerns about problems with WAIT(i). The assumption of a uniform arrival rate for travelers seems unreasonable when the headway is relatively long particularly for regularly made trips where travelers know the public transport arrival pattern from experience, as is the case for the work trips being considered in this research. Work by others has found empirical evidence suggesting that the frequency of passenger arrivals for services with long headways is not uniform, but rather is skewed in a way that suggests planning based on knowledge derived from experience. The use of HDWAY(i) dodges assumptions about travelers arrival plans and resulting arrival patterns and focuses on the magnitude of the overall inconvenience caused by the size of the gap between times when it is possible to make the trip, including the impacts of any adjustments made in scheduling (at both ends of the trip) in order to use the service along with the time spent at the stop. If all connecting services ran with the same headway, then HDWAY(i) would always be twice WAIT(i). The estimations would then establish a coefficient for WAIT(i) with twice the value of the coefficient for HDWAY(i), and there would be no difference between the fit of a model that included WAIT(i) and the fit of a model that included HDWAY(i). However, all connecting services do not run with the same headway; HDWAY(i) is not just twice WAIT(i), but includes representation of the additional factors indicated above that are influenced when connecting services run with different headways. It was found that the fit of the model was better when HDWAY(i) was used. This suggests that the additional factors included in the representation provided by HDWAY(Z) do influence travelers and that HDWAY(i) is a more appropriate measure as a result. Conclusions This research has provided some indications regarding how to design a more attractive public transport service in Edmonton, generally as follows:. The need to transfer should be reduced even at the expense of fairly substantial increases in riding times (of up to 15 minutes and even slightly more). The system-wide tradeoff between transfer wait times and the need to transfer should be restructured in favor of reducing the need to transfer. However, the effect of changes in the duration of transfer wait times on the perception of transferring should be monitored in order to identify possible shifts in perception. The geographic coverage of the network should be more dense where there are greater numbers of origins. A tool for much more specific considerations has also been provided. The utility function presented can be used to consider the impacts of several factors together. The process of network design can be viewed as the task of selecting a mix among the walking distances, numbers of transfers, riding times, and frequencies of service that are involved. The utility function can be used to identify the particular mix for a given set of resources that maximizes the attractiveness of the system as perceived by those traveling to work in Edmonton. The potential exists for similar equations to be established for other travel purposes and for other locations. The sample of observations used here was relatively modest in size and concerned only one type of trip purpose and only one geographical area. However, it is judged that a number of general conclusions can be drawn regarding the specification of generalized cost expressions for public transport routes, as follows: Walking distances or times at the origin and destination ends should not be ITEJOURNAL. DECEMBER

5 IMPACT your traffic count ~ Pro9ram \!.{1 ạ. :...with today s most advanced recordex.. Mkrocounts II Record speed data with 1 sec. and 1 mph precision. Eliminate RADAR spot speed studies.. Speed analysis enables efficient police scheduling. Classify vehicles in 13 FHWA types. Integrate in signal controller cabinets without modi ing,. One-switch fie? d setup; no keyboard entry.. Upload and analyze data in the field using a laptop PC. Reports are presentation quality.. Import data to spreadsheet.. Free utilities. MicroCounts II 3 MODES: Count Classification Speed O-airl JUn!s 11.,ICcwwE8wl LCCAW W8EWT.,11..:; 8 L.C. added unweighed in an attempt to establish a single walking distance or time value for a public transport alternative. Their influences are sufficiently different to warrant separate treatment.. A better model fit may be established using the number of transfers rather than the total time spent waiting in making transfers to represent the influence of transfers.. Half the headway, as an estimate of the initial wait time for using public transport, should not be used to represent the impacts of only being able to travel when the service is provided. Some more complete measure that includes representation of more of the range of effects involved should be considered. Acknowledgments The author would like to thank Stan Teply of the University of Alberta and Martial Echenique of the University of Cambridge for their helpful suggestions. He would also like to thank Dean Cooper of the City of Edmonton Transportation Department for his assistance and the City of Edmonton and the Natural Sciences and Engineering Research Council of Canada for their financial and material support. References 1. Williams, H. C. W. L. On the Formulation of Travel Demand Models and Economic Evaluation Measures of User Benefit. In Environment and Planning A vol. 9, No. 3 (1977): Domencich, T, A., and D. McFadden. Urban Travel Demand: A Behavioral Analysis. Amsterdam, The Netherlands: North Holland/American Elsevier, McFadden, D. Conditional Logit Analysis of Qualitative Choice Behavior. In Frontiers in Econometrics. New York: Academic Press, Van Nostrand Company. The International Dictionary of Applied Ma~hematics. Toronto, Canada: Van Nostrand Company, McFadden, D,, K. Train, and W. B. Tye. An Application of Diagnostic Tests for the Independence from Irrelevant Alternatives Property of the Multinominal Logit Model. In Transportation Research Record 63Z 1977,pp , 6. Hunt, J. D. Description of Morning Commuter Survey. Ph. D. Research Working Paper 7, Unpublished. 7. Horowitz, J. Evaluation of Usefulness of Two Standard Goodness-of-Fit Indicators for Comparing Non-Nested Random Utility Models. In Transportation Research Record 874, 1982, pp Tardiff, T. A Note of Goodness-of-Fit Statistics for Probit and Logit Models. Transportation Vol. 5, No. 4 (1976): Bakker, J. J. Transit Operating Strategies and Levels of Service. In Transporta~ion Research Record 606, 1976 pp. l Richardson, D., et al. Canadian Capaci~y Guide for Signalized Intersections, Edmonton, Canada: ITE District 7 and the University of Alberta, Jolliffe, J. K., and T. P. Hutchinson. A Behavioral Explanation of the Association between Bus and Passenger Arrivals at a Bus Stop. Transportation Science Vol. 9 No. 3 (1975): I John Douglas Hunt is senior engineer with Martial Echenique and Partners, a transport, land use, and economic modeling consulting firm based in Cambridge, England. The work described here was performed while he was an assistant professor in the Department of Civil Engineering at the University of Alberta, Canada. Hunt received his B. Sc. in civil engineering from the University of Alberta and his Ph. D. from Cambridge University. Data Acquisition, Inc Broadway #l 56 Vancouver, WA TEL: