VALUING CROWDING IN PUBLIC TRANSPORT SYSTEMS USING

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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: [email protected]
Juan Carlos Muñoz
Department of Transport Engineering and Logistics,
Pontificia Universidad Católica de Chile Email: [email protected]
Juan de Dios Ortúzar
Department of Transport Engineering and Logistics,
Pontificia Universidad Católica de Chile Email: [email protected]
Sebastián Raveau
Department of Transport Engineering and Logistics,
Pontificia Universidad Católica de Chile Email: [email protected]
Carlos Mojica
Department of Infrastructure and Environment
Inter-American Development Bank; Email: [email protected]
Ramiro Alberto Ríos
Department of Infrastructure and Environment
Inter-American Development Bank; Email: [email protected]
Word count: 4,614 words text + 4 tables/figures x 250 words (each) = 5,614 words
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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/m2). 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 (6
passenger/m2) is two times the marginal disutility in a vehicle with low level of crowding (1
passenger/m2).
Keywords: Crowding, Comfort, Public transportation, Discrete choice, Stated preference
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1. 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/m2, 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 (1). In
particular, it has been empirically demonstrated that the level of comfort of different
alternatives may be a significant factor in explaining travel behavior (2, 3, 4). 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 5), 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., 6 and 7). (5) 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. (8) 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. (9) 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/m2), 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,
(10) 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.
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Besides the time multiplier approach, crowding cost can be obtained directly as a monetary
value. (11) conducted an SP experiment for train users in Greater Manchester in 2005, 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 30 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 9.5 million trips occur on a daily basis. Public transportation
represents about 60% 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 2.3 million
passengers daily. The average travel time for a trip in public transportation is 28.5 minutes (invehicle) and the average travel distance is 12 km. The average speed of bus-based trips is 17
km/h while the subway average speed is 33.4 km/h.
Section 2 presents the data used for estimation. Section 3 discusses the modeling approach,
based on discrete choice modeling, and presents the results of estimation. Section 4 presents
some final comments and policy implications.
2. 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 (12), using the software Ngene
(http://choice-metrics.com/). All choice scenarios include an answer “I would not travel in any
alternative”, as recommended in the literature (1). (13) 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
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of the reference trip. Travel cost level depended on the transport mode. If the mode was bus or
train, travel cost levels were $590 CLP (US$1.00) or $650 (US$1.20) CLP (Chilean pesos). In
turn, if the alternative was car, travel cost levels are 100% or 110% 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, 5 or 10 minutes for bus, and 3 or 5 for train. Waiting time variability is
measured with the coefficient of variation, which was zero for car, and 0, 0.5, 0.7, 1.0 and 1.5
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 1).
Each figure was associated to a level of crowding starting in 1 until 6 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 15 to 20
minutes. Figure 1 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 (4). 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 2008. Information was gathered on the trips of 92,800 individuals (about
12% of all users). Only those whose origin-destination pairs could have been taken by more
than one route are included in our analysis, leaving 28,961 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).
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TABLE 1 Passenger density and figures used to represent level of crowding
Level of crowding
Bus
Train
(passenger/m2)
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Attribute
Mode
Cost
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.
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Alternative A
Alternative B
Bus
$ 590
Metro
$ 650
25 minutes
15 minutes
10 minutes
5 minutes
Between 0 and 29 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
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□ Alternative B
□ I would not travel
FIGURE 1 Example of SP choice scenario presented
3. MODELING AND ESTIMATION
3.1 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.
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
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(xm, zi, emi), where the vector xm with m mode attributes (
travel time, cost, etc.), zi is a vector with characteristics of individual i (income, driver license,
etc.), and emi 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(xm, zi, emi) ≥ V(xk, zi, eki) 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(xm, zi, emi) ≥ V(xk, zi, eki), 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 Vi = ai +
bCi + cTi + ei, where Ci is travel cost and Ti 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 (5). Thus, the marginal utility of travel time is specified multiplying
passenger density (7). 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 (1):
eVim
Prob  i chooses m   Pim 
(1)
 eVik
k
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and the utility functions are given by expressions (2) and (3):
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SP Data:
Vm   m   Cm   j  j D jmTm   WTm
(2)
2
RP Data:
Vm   m   j  j D jmTm   WTm  Wm   TRm
(3)
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where Cm is the cost of mode m, Tm is travel time, Djm is a dummy variable for passenger
density j, WTm is waiting time, Wm is walking time and TRm 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: 1 passenger/m2.
The parameter  in equation (1) 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 (14).
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.
3.2 Estimation results
The estimation sample is composed of 3,380 choice situations corresponding to 580
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 28,961 choices.
Table 2 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.
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TABLE 2 Model Estimation for Santiago with mixed data
SP Data
RP Data
Parameter
Estimate
t-test
Estimate
t-test
Monetary Cost
-0.001
-3.67
2
Travel Time at 1-2 pax/m
-0.042
-6.41
-0.117
-51.17
2
Travel Time at 3-4 pax/m
-0.054
-8.41
-0.132
-56.65
2
Travel Time at 5-6 pax/m
-0.091
-11.71
-0.194
-43.99
Waiting Time
-0.098
-9.69
-0.183
-8.24
Walking Time
-0.257
-13.00
Transfers
-0.698
-10.26
Bus Constant
0.000
Metro Constant
0.017
0.21
Car Constant
1.64
2.39
SP Scale Factor Design 1
1.000
SP Scale Factor Design 2
0.692
3.62
SP Scale Factor Design 3
1.150
9.35
SP Scale Factor Design 4
0.519
4.05
RP Scale Factor
1.000
Sample Size
3,380
28,961
Log-Likelihood
-1,870
-13,480
2
0.567
0.382
Corrected 
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SP/RP Data
Estimate
t-test
-0.0008
-4.37
-0.035
-9.24
-0.045
-8.87
-0.078
-8.63
-0.079
-13.18
-0.076
-7.65
-0.241
-5.13
0.000
0.031
0.44
1.93
8.37
1.000
0.692
3.62
1.150
9.35
0.519
4.05
3.821
8.84
32,341
-15,609
0.403
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 2). These levels may be
associated with three travel conditions. In the crowding level of 1-2 passenger/m2 there is a
clear chance to get a seat. In the level of 3-4 passenger/m2, users have to travel standing, but
with some space. In the level 5-6 passenger/m2, 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 29% when passenger density increases from 1-2 passenger/m2 to 3-4
passenger/m2, and 73% when passenger density increases from 3-4 to 5-6 passenger/m2. A
minute of traveling in the higher density condition (5-6 passenger/m2) produce a discomfort
2.3 times greater than that produced in the lower density condition (1-2 passenger/m2). For
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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 3 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 $2,626 CLP/hr (US$4.60) to $5,894 CLP/hr
(US$10.40) depending on the crowdedness levels. Valuations for waiting time and walking
time are higher. Individuals are willing to pay $250 CLP (US$0.44) to avoid a transfer.
TABLE 3 SP/RP Marginal Rates of Substitution for Santiago
Parameter
Valuation
2
Travel Time at 1-2 pax/m
2,626 CLP/hr
Travel Time at 3-4 pax/m2
3,389 CLP/hr
2
Travel Time at 5-6 pax/m
5,894 CLP/hr
Waiting Time
4,903 CLP/hr
Walking Time
4,642 CLP/hr
Transfers
250 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 6 minutes of in-vehicle travel time; i.e. $263 CLP
(US$0.46).
4. 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 6
passenger/m2 is twice as the marginal disutility in a vehicle with 1 passenger/m2.
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
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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
1.
2.
3.
4.
5.
Ortúzar, J.de.D. & Willumsen, L. (2011). Modelling Transport. John Wiley and Sons.
Chichester.
Ben-Akiva, M., Walker, J., Bernardino, A. T., Gopinath, D. A., Morikawa, T., &
Polydoropoulou, A. (2002). Integration of choice and latent variable models.
Perpetual motion: Travel behaviour research opportunities and application
challenges, 431-470.
Cherchi, E., & J. de D. Ortúzar, J. (2002). Mixed RP/SP models incorporating
interaction effects. Transportation, 29(4), 371-395.
Raveau, S., Muñoz, J. C., & De Grange, L. (2011). A topological route choice model
for metro. Transportation Research Part A: Policy and Practice, 45(2), 138-147.
Li, Z., & Hensher, D. A. (2011). Crowding and public transport: A review of
willingness to pay evidence and its relevance in project appraisal. Transport Policy,
18(6), 880-887.
Batarce, Muñoz, Ortúzar, Raveau, Mojica, Ríos
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
6.
7.
8.
9.
10.
11.
12.
13.
14.
13
Guerra, G. & Bocarejo J. (2013). Congestion cost in mass transit systems; pricing and
investment policy implications – case study: Bogotá’s BRT system. Paper presented at
the 13th World Conference on Transportation Research, Rio de Janeiro, July 2013.
Haywood, L., & Koning, M. (2013). Estimating crowding costs in public transport
(No. 1293). Discussion Papers, DIW, Berlin.
Douglas, N., & Karpouzis, G. (2005). Estimating the passenger cost of station
crowding. In Proceedings of the 28th Australasian Transport Research Forum,
Sydney.
Whelan, G., & Crockett, J. (2009). An investigation of the willingness to pay to reduce
rail overcrowding. In Proceeding of the First International Conference on Choice
Modelling, Harrogate, England.
Wardman, M., & Whelan, G. (2011). Twenty years of rail crowding valuation studies:
evidence and lessons from British experience. Transport Reviews, 31(3), 379-398.
Lu, H., Fowkes, T., & Wardman, M. (2008). Amending the Incentive for Strategic Bias
in Stated Preference Studies: Case Study in Users' Valuation of Rolling Stock.
Transportation Research Record: Journal of the Transportation Research Board,
2049(1), 128-135.
Rose and Bliemer, (2009). Constructing efficient stated choice experimental designs.
Transport Reviews, 29(5), 587-617.
Batarce, M., Muñoz, J.C. & Ortúzar, J. de D. (2014) Valuing Crowding in Public
Transport Systems: The Case of Santiago. Paper presented at the 13th Pan-American
Conference on Transportation, Traffic and Logistics, Santander, Sapin June 2014.
Ben-Akiva, M., & Morikawa, T. (1990). Estimation of travel demand models from
multiple data sources. In International Symposium on Transportation and Traffic
Theory, 11th, 1990, Yokohama, Japan.