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1 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos VALUING CROWDING IN PUBLIC TRANSPORT SYSTEMS USING MIXED STATED/REVEALED PREFERENCES DATA: THE CASE OF SANTIAGO Marco Batarce Industrial Engineering School, Universidad Diego Portales, Chile; [email protected] Juan Carlos Muñoz Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile [email protected] Juan de Dios Ortúzar Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile [email protected] Sebastián Raveau Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile [email protected] Carlos Mojica Department of Infrastructure and Environment Inter-American Development Bank; [email protected] Ramiro Alberto Ríos Department of Infrastructure and Environment Inter-American Development Bank; [email protected] Word count:, words text + tables/figures x 0 words (each) =, words

2 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos 0 ABSTRACT This paper presents the valuation of comfort in public transportation using mixed Stated Preferences (SP) and Revealed Preferences (RP) data. In this case, comfort is measured mainly as the level of crowding in the vehicles (bus or train) using the in-vehicle passenger density (pax/m ). To value comfort we use a stated preference survey where crowding levels are presented by means of figures, and revealed preference data on route choice inside the subway network of Santiago, Chile. The data collected in the surveys are used to estimate discrete choice models and obtain subjective valuation of passenger density through the parameters of the utility function. We assume that disutility for traveling in crowding conditions is proportional to the travel time; therefore, the longer the trip, the higher the utility loss. The results indicate that passenger density has a significant effect on utility of public transportation modes. In fact, marginal disutility of travel time in a crowded vehicle ( passenger/m ) is two times the marginal disutility in a vehicle with low level of crowding ( passenger/m ). Keywords: Crowding, Comfort, Public transportation, Discrete choice, Stated preference

3 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos INTRODUCTION In transport planning literature, it is widely recognized that one of the best solutions, or perhaps the best one, in facing traffic congestion and air pollution derived from urban transport activity is the promotion of high quality mass public transit. In doing so, many cities have already implemented high-capacity transit systems (BRT, tramway or subway). However, quite often the engineering and operational design of these systems does not consider adequately the effect of comfort on the travel demand. This overlooking leads to use a design standard of six or more passengers/m, which can even be exceeded at peak times in some corridors. In addition, crowdedness is usually left aside in most public transport demand models used for planning. Thus, it urges the need for more detailed understanding of crowding in mass transit systems and its impact on travel decisions. The mode-choice process is complex as it considers many more variables than those usually included in traditional demand models: fare, in-vehicle travel time and waiting time (). In particular, it has been empirically demonstrated that the level of comfort of different alternatives may be a significant factor in explaining travel behavior (,, ). Crowding, which is obviously associated with comfort, can also imply a perceived lack of control, stimulus overload, amongst other stressors. Thus, travel decisions involving comfort and crowding are complex mental process involving attitudes, psychological states, preferences and socioeconomic constraints. For that reason, the question of how to measure crowding is relevant for transport policy and planning. The general objective of this study is to analyze crowding and comfort attributes using mixed stated preference and revealed preference data. The study is being carried out in Santiago, Chile. The focus is on estimation of comfort valuation in terms of travel time. Almost all works addressing valuation of comfort in public transport systems use stated preferences (SP) methods (see ), and most of them use choice-based SP. But some SP studies have also applied contingent valuation to find the willingness to pay for reducing overcrowding (e.g., and ). () reviewed public transport crowding valuation research, focusing on studies conducted in the UK, USA, Australia and Israel. Most of these studies use logit models with choice-based SP data covering commuters, and focused mainly on invehicle congestion costs. () estimated crowding costs at the platform (related to waiting time) and in the access-way/entrance to train stations (related to walking time). In choice-based SP surveys, the crowding representation is very relevant. () conducted an SP experiment using as a proxy for crowding the seat occupancy rate and the number of standing passengers. These parameters allowed them to calculate the load factor (number of passengers/number of seats) and passenger density (standing passengers/m ), and specified time multipliers according to each level. This means that the effect of crowding in the modal utility is represented as a factor increasing the negative perception of travel time. In addition, (0) suggest that passenger density is a better indicator of congestion, given that a same load factor may have different levels of crowding across different types of trains with varying seat composition.

4 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos Besides the time multiplier approach, crowding cost can be obtained directly as a monetary value. () conducted an SP experiment for train users in Greater Manchester in 00, and estimated values for crowding costs which were more than twice as high as the value of invehicle time in a non-congested scenario. In their survey, crowding was represented as the combination of a probability of occurrence and length of time (for instance, two out of five times someone stands for the whole journey of 0 min). Our study uses disaggregated, mixed SP/RP data. In the choice-based SP surveys, one attribute of the alternatives is related to crowding. The level of crowding is supported by pictures depicting passenger densities on board of vehicles. The revealed preferences (RP) data are observed route choices in the subway network of Santiago and collected by means of a survey. Therefore, the mixed data not only comprise observed and hypothetical choice, but also choices of transport mode and route. Santiago is a city where. million trips occur on a daily basis. Public transportation represents about 0% of all trips. The number of people using the bus system is very similar in magnitude to the people who use the subway. Each mode transports about. million passengers daily. The average travel time for a trip in public transportation is. minutes (invehicle) and the average travel distance is km. The average speed of bus-based trips is km/h while the subway average speed is. km/h. Section presents the data used for estimation. Section discusses the modeling approach, based on discrete choice modeling, and presents the results of estimation. Section presents some final comments and policy implications.. DATA SP data were collected with an experiment that considers six choice scenarios with two alternatives each one. Each alternative is described by six attributes: i) transport mode; ii) travel time; iii) travel cost; iv) average waiting time; v) waiting time variability (by means of the coefficient of variation), and; vi) crowding level in the vehicle (bus or train). Transport modes were presented to individuals according to the real availability in the reported trip. If the respondent reports to use public transportation, the choice scenarios only include bus and train as alternatives. If the respondent declared to use car, s/he was asked whether s/he is able to use public transportation to travel. In this case, if respondent can use only bus, the choice scenario includes car and bus; otherwise the choice scenarios include car versus bus or train. If the respondent cannot use public transportation, the choice scenarios are completely hypothetic by including only public transportation alternatives. Depending on mode availability, four optimal designs were built (), using the software Ngene ( All choice scenarios include an answer I would not travel in any alternative, as recommended in the literature (). () reports a detailed description of the PD survey. The level of attributes is determined according to the actual level reported by the respondent in a reference trip. Levels of travel time were pivoted on the actual travel time of the longest leg

5 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos of the reference trip. Travel cost level depended on the transport mode. If the mode was bus or train, travel cost levels were $0 CLP (US$.00) or $0 (US$.0) CLP (Chilean pesos). In turn, if the alternative was car, travel cost levels are 00% or 0% of the actual travel cost computed on basis of travel time, average speed and average fuel consumption. If the respondent paid for parking or urban highway toll in the reference trip, they were added to the car travel cost, only in the final survey design. Average and variability of waiting time levels were different for every mode. Average waiting time was zero for car, or 0 minutes for bus, and or for train. Waiting time variability is measured with the coefficient of variation, which was zero for car, and 0, 0., 0.,.0 and. for public transportation. This attribute was presented in the survey as a range of time within which the next bus or train arrives with uniform probability. Crowding levels for bus and train were presented in six levels by means of figures (Table ). Each figure was associated to a level of crowding starting in until passengers by square meter. The survey was developed in a computer and applied in person by a surveyor. The survey was carried out in the workplace of the respondents because the interview took to 0 minutes. Figure shows a choice scenario presented to the respondents. The survey form also includes questions to get information on respondent s characteristics, and a reference trip to work. The former type of information is gender, age, car ownership, income. The information on a trip of reference is travel time, frequency, legs of the trip, and for every leg, mode, in-vehicle travel time, waiting time, comfort level (sit, standing with room around, standing with little room, standing in a quite crowding vehicle), and parking and toll cost if necessary. This information is used for pivoting the attributes presented in the choice scenarios. Revealed preferences data comes from real (i.e. observed) choices made by travelers inside the Santiago Metro network (). In this case, the alternatives are the potential routes to be taken between the travelers origin and destination, which differ in terms of in-vehicle travel time, waiting time, walking time (when transferring), number of transfers, and crowding level inside the trains. This data was obtained from an origin-destination survey conducted at metro stations in October 00. Information was gathered on the trips of,00 individuals (about % of all users). Only those whose origin-destination pairs could have been taken by more than one route are included in our analysis, leaving, individual choices to be used for estimating the models. This data was complemented with detailed information regarding the levels-of-service of the system, obtaining values for all the explanatory variables. In particular, crowding levels for the RP database were obtained from observed load profiles in the different Metro lines. It is important to notice that in this RP database the fare is not included as an explanatory variable, as monetary cost is the same inside the metro network regardless of route length or transfers (and thus has no effect on route choice).

6 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos TABLE Passenger density and figures used to represent level of crowding Level of crowding Bus Train (passenger/m )

7 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos Attribute Alternative A Alternative B Mode Bus Metro Cost $ 0 $ 0 In-vehicle Travel Time Average Waiting Time Waiting Time Range It is possible for the bus or metro to pass at any moment in this time range. minutes minutes 0 minutes minutes Between 0 and minutes Waiting time is fixed Occupancy The figure represents how crowded the bus or metro will be when it arrives at the stop/station. Which alternative would you choose for your trip? Alternative A Alternative B I would not travel 0 0 FIGURE Example of SP choice scenario presented. MODELING AND ESTIMATION. Model specification The framework for model specification is the random utility theory. In the context of the choice of transport mode, the random utility theory can be summarized in the following assumptions about the individual s behavior: There is a (finite) set of transportation alternatives, mutually exclusive, for the individual s trip. Individual preferences on alternatives can be represented by a utility function that depends on attributes of the alternatives and individual s characteristics. Individual chooses the mode that generates the highest utility among all available alternative in the choice set. In the individual s utility function, there are variables that are only s/he observes. This way, two individuals with the same choice set and the same observable characteristics may choose different transportation mode.

8 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos It is assumed that the unobservable individual utility components are random and independently distributed in the population. The utility random component comes from different sources. For example, any nonobservable or unmeasurable attribute of the alternatives, or unobserved individuals taste variation. In practical terms, the theory of random utility involves defining a utility function for each mode, which has as variables modal attributes, individual characteristics and a random component that distributes over the population. Analytically, the random utility of alternative m for individual i is written as V(x m, z i, e mi ), where the vector x m with m mode attributes ( travel time, cost, etc.), z i is a vector with characteristics of individual i (income, driver license, etc.), and e mi is the random component. This utility is also a random variable. Since it is assumed that individuals choose the alternative that maximizes their utility, then the mode m is chosen if V(x m, z i, e mi ) V(x k, z i, e ki ) for all k mode in the set of available modes of individual. Since the utility is a random variable, the probability that individual i chooses alternative m is Prob(i chooses m) = Prob (V(x m, z i, e mi ) V(x k, z i, e ki ), for all k). According to the assumptions made about the functional form of the utility and the probability distribution of the random component, different models are obtained. In particular, the logit model is obtained assuming that the additive random component is separable in the utility function and distributes Gumbel. Moreover, the logit models generally assume that the observable part of the utility function is linear in mode attributes. Thus, if the utility function includes time and cost, the parameters associated with them represent the marginal utility of such variables. For example, if V i = a i + bc i + ct i + e i, where C i is travel cost and T i is travel time, then b is the marginal utility of income and c is the marginal utility of time (in simplified terms). The marginal rate of substitution between money and time corresponds to the subjective value of time (SVT). Therefore, this value can be calculated as the ratio between the parameters of time and cost of the linear utility function. This study assumes that the marginal utility of travel time depends on the level of crowding in the vehicle. This approach is consistent with time multipliers approach (). Thus, the marginal utility of travel time is specified multiplying passenger density (). This specification captures the increasing discomfort for traveling in crowding conditions, and also implies that total discomfort is proportional to travel time. Summarizing, the discrete choice models are logit models with linear utility functions and time multiplier to capture crowding effects. Therefore, the choice probability is given by expression (): Vim e Prob i chooses m Pim () Vik e k and the utility functions are given by expressions () and ():

9 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos SP Data: Vm m Cm j jdjmtm WTm () RP Data: Vm m jdjmtm WTm Wm TRm () j where C m is the cost of mode m, T m is travel time, D jm is a dummy variable for passenger density j, WT m is waiting time, W m is walking time and TR m is transfers in the subway network. Note that crowding effect is modeled with dummy variables; therefore it is possible to capture a nonlinear effect. Note also that RP utility function does not includes the cost of the alternative, because data correspond to individuals making route choices inside the subway network without having to pay extra for changing between the lines. Thus, all alternatives have the same cost. Socio-economic variables (in particular, the respondent s gender) were interacted with the explanatory variables, but were found to be non-significant. One important assumption of our specification is that crowding level on car is equal to the lowest crowding level on public transport: passenger/m. The parameter in equation () is the scale factor and measures the variance of the error term in the utility function. Usually, this factor is not identifiable with a unique sample of individuals, thus it is normalized to one. However, when estimation data come from different samples, it is possible identify the scale factors for every sample except one. Difference between samples depends on the nature of the data. For instance, data coming from stated preferences and revealed preferences, or data from responses of stated preferences surveys with different experimental designs have different nature and, thus, choice probabilities with different scale factor (). The SP survey is comprised of four different experimental designs, which are differentiated by specific scale factors. The RP survey also possesses a specific scale factor, to differentiate it from the SP survey.. Estimation results The estimation sample is composed of,0 choice situations corresponding to 0 individuals. This sample comprises the individuals surveyed using four final experimental designs. These differences in the designs imply that model estimation should consider different scale factors into the logit model. For identification one scale factor is normalized to one. The RP database consists of, choices. Table below summarizes the estimation results for three proposed models: (i) SP data, (ii) RP data, and (iii) joint SP/RP data. The parameter associated to waiting time uncertainty is not shown, although this variable was presented in the SP survey and estimated its effect in the utility function, because this work focuses on the direct effect of crowding on time valuation. To prevent the bias on other parameters of the utility because of misspecification of waiting time uncertainty, its effect was modeled with dummy variables.

10 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos TABLE Model Estimation for Santiago with mixed data SP Data RP Data SP/RP Data Parameter Estimate t-test Estimate t-test Estimate t-test Monetary Cost Travel Time at - pax/m Travel Time at - pax/m Travel Time at - pax/m Waiting Time Walking Time Transfers Bus Constant Metro Constant Car Constant SP Scale Factor Design SP Scale Factor Design SP Scale Factor Design SP Scale Factor Design RP Scale Factor Sample Size,0,, Log-Likelihood -,0 -,0 -,0 Corrected All explanatory variables are significant on the three estimated models, using different data. Only the metro constant is not statistically different from the bus constant. Marginal disutility of in-vehicle travel time increases as the crowdedness levels increase. Waiting and walking times present a higher disutility than the in-vehicle time (due to uncertainty and physical effort, respectively). The utility specification considers a nonlinear effect of crowding into travel time by means of using dummy variables for representing the levels. Preliminary estimations considered specific parameters for each level of crowding; however some of them are statistically equal each other. Thus, crowding effect is aggregated into three levels (Table ). These levels may be associated with three travel conditions. In the crowding level of - passenger/m there is a clear chance to get a seat. In the level of - passenger/m, users have to travel standing, but with some space. In the level - passenger/m, users travel standing and overcrowding. The nonlinearity in the utility function indicates the great discomfort of travelling under overcrowding conditions with respect to travelling seating or standing with few passengers in the vehicle. The results indicate that crowding produce significant increase in travel disutility. Marginal disutility increase % when passenger density increases from - passenger/m to - passenger/m, and % when passenger density increases from - to - passenger/m. A minute of traveling in the higher density condition (- passenger/m ) produce a discomfort. times greater than that produced in the lower density condition (- passenger/m ). For

11 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos policy design, to decrease crowding form the third level to the second may produce significant impact on demand and users welfare. To further analyze the individuals perceptions, Table presents the marginal rates of substitution between variables (most notably, the values of time) for the joint full-data SP/RP model. Value of in-vehicle travel time varies from $, CLP/hr (US$.0) to $, CLP/hr (US$0.0) depending on the crowdedness levels. Valuations for waiting time and walking time are higher. Individuals are willing to pay $0 CLP (US$0.) to avoid a transfer. TABLE SP/RP Marginal Rates of Substitution for Santiago Parameter Valuation Travel Time at - pax/m, CLP/hr Travel Time at - pax/m, CLP/hr Travel Time at - pax/m, CLP/hr Waiting Time,0 CLP/hr Walking Time, CLP/hr Transfers 0 CLP/transfer Other travel conditions are also significant in the modal utility. Waiting time is valued as high as the travel time in very crowded conditions. The same is true for the walking time in transfers. This result implies that comfort improvements may also focus on reduction of walking time in transfers. On top of that, the need of transfer to reach the destination produces significant disutility. In fact, one transfer, without considering the needed for walking and waiting time, is valued in money as minutes of in-vehicle travel time; i.e. $ CLP (US$0.).. FINAL COMMENTS This paper valued the effect of crowding in public transportation using mixed SP/RP data. SP data was collected in a survey based on mode choice, including both public transport and car. RP data was collected in a survey applied to subway users choosing routes inside the metro network. In the SP survey, the level of crowding was measured as in-vehicle passenger density and presented to respondents by means of images. In the RP survey, routes are different in travel time, number of transfer, crowding level, walking time in transfer and waiting time. Thus, it is assumed that users choose taking in consideration these trip variables. Discrete choice models were used to value crowding and specify modal utility function where the passenger density increases the effect of travel time on the utility. In other words, this supposed an interaction between passenger density and travel time. The results of the parameter estimation show that crowding has a significant and non-linear effect on the marginal utility of travel time. Indeed, marginal disutility of travel time in a vehicle with passenger/m is twice as the marginal disutility in a vehicle with passenger/m. Methodologically, the paper is innovative by mixing data on modal choice with data on route choice. This joint SP/RP model not only benefits from the advantages of both preference

12 Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos approaches, but also allows us to value more attributes related to comfort, which were not shown in the SP experiment in order to prevent a cognitive burden when respondents filled the survey. A policy implication of this study is that the effect of crowding is perceived for transit passengers in a similar way as road congestion is perceived by motorists. The improvement of travel time of a bus line increases the demand for that service. In turn, this new demand increases crowding, and consequently the generalized travel cost (travel disutility). These two effects counterbalance, which may raise additional challenges to effectively implement transport policies oriented to increase operation speed of public transport without increasing capacity to avoid crowding. Two examples of this effect are the BRT system in Bogota and the Metro system in Santiago. Both cities reduced the generalized travel cost either through travel time or fare (Bogota reduced travel time by implementing TransMilenio and Santiago reduces the Metro fare by an integrated fare scheme with the bus system). As a result, invehicle passenger density in both systems is higher than the design density. This high crowding might prevent car users from being attracted to public transportation. Our results can be used to include cost of crowding (or congestion) in public transportation during the planning and appraisal stages of public transport projects. Cost-benefit analyses could benefit from better estimating the technical and economic feasibility of transit investments. Moreover, planners and policy makers might be able to prepare adequate finance provisions for additional vehicle capacity to control negative effects of crowding. Finally, if the level of crowding is considered by users when choosing the line or route of public transport, final demand of each line is the result of an equilibrium state. This equilibrium is similar to that in a road network with traffic congestion. This implies that it is necessary to develop transit network assignment models that consider a similar effect to road congestion on bus routes. This should be a topic for future research. REFERENCES. Ortúzar, J.de.D. & Willumsen, L. (0). Modelling Transport. John Wiley and Sons. Chichester.. Ben-Akiva, M., Walker, J., Bernardino, A. T., Gopinath, D. A., Morikawa, T., & Polydoropoulou, A. (00). Integration of choice and latent variable models. Perpetual motion: Travel behaviour research opportunities and application challenges, -0.. Cherchi, E., & J. de D. Ortúzar, J. (00). Mixed RP/SP models incorporating interaction effects. Transportation, (), -.. Raveau, S., Muñoz, J. C., & De Grange, L. (0). A topological route choice model for metro. Transportation Research Part A: Policy and Practice, (), -.. Li, Z., & Hensher, D. A. (0). Crowding and public transport: A review of willingness to pay evidence and its relevance in project appraisal. Transport Policy, (), 0-.

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