Cats O., Burghout W., Toledo T. and Koutsopoulos H.N. (2010). Evaluation of Real-Time Holding Strategies for Improved Bus Service Reliability. IEEE conference on Intelligent Transportation Systems, Proceedings, ITSC, Portugal, 718-723.

EVALUATION OF REAL-TIME HOLDING STRATEGIES FOR IMPROVED

BUS SERVICE RELIABILITY

Oded Cats1,2

, Wilco Burghout2, Tomer Toledo

1, Haris N. Koutsopoulos

2

1Technion – Israel Institute of Technology, Haifa, Israel 2Royal Institute of Technology (KTH), Stockholm, Sweden

Abstract—Service reliability is one of the main measures of

performance determining transit system level of service.

Holding control strategies are a common transit operations

practice aimed to reduce transit service unreliability by setting

criteria for departure from time point stops. In order to

adequately analyze the sources of uncertainty involved with

transit performance, it is essential to model dynamically the

interactions between traffic conditions, passenger demand and

transit operations. BusMezzo, a transit simulation model has

been developed on a platform of a mesoscopic traffic

simulation model, which enables the representation of large-

scale transit systems. The model implements several real-time

holding strategies. It is used to evaluate the application of these

strategies in a real-world high-demand bus line in the Tel Aviv

metropolitan area, under various scenarios. An analysis of the

results suggests that a holding strategy based on the mean

headway from the preceding bus and the next bus, restricted

by a maximum allowable holding time, is especially efficient.

I. INTRODUCTION

Advanced Public Transport Systems (APTS) designed to

improve operations, management and operations of transit

systems are increasingly integrated into transit systems. The

need to integrate and efficiently operate these systems poses

a challenge to planners and operators. As new technologies

and applications are proposed, tools to assist in their

development and evaluation prior to field implementation

are needed. In the context of general traffic operations,

simulation models have been established as the primary tool

for evaluation at the operational level. Transit simulations

provide a dynamic perspective on transit operations,

enabling comparisons of various scenarios and

representation of complex interactions between the network

components: general traffic, transit vehicles, passengers and

transit operations. A report on simulation models concluded

that their capabilities to effectively simulate APTS

applications in large networks is limited [1]. While they

found that few microscopic models simulate well the local

impacts of APTS, none of the mesoscopic models they

reviewed had any transit simulation component at all. While

most efforts in modeling public transportation and APTS

have focused on microscopic simulations, these models are

inefficient when applied to large-scale networks because of

the unnecessary level of detail and extensive computational

effort they require. In contrast, mesoscopic simulation

models, which represent individual vehicles but avoid

detailed modeling of their second-by-second movement,

may be useful for system-wide evaluation of transit

operations and APTS, as they are for general traffic.

Service reliability is one of the main factors determining

transit system level of service, as unreliable service results

in longer waiting times, uneven passenger loads and missed

transfers. Moreover, service irregularity is associated with

higher operation costs due to fleet assignment

considerations. There are several sources of variability that

contribute to service uncertainty, including variability in the

departure times from the origin terminal, riding time and

dwell time. Holding control strategies are a common transit

operations practice aimed to reduce transit service

unreliability by setting a criteria for departure from time

point stops. Studying the effect of holding strategies

analytically is difficult, even for a single line, because of the

interrelated stochastic processes involved, in particular in

the case of strategies based on real-time information. Many

of the previous studies in this area did not consider the inter-

effect among multiple time points, assumed constant

passenger arrival rates or dwell times and neglected capacity

constraints and trip chaining effects.

This paper reports a simulation-based evaluation of real-

time holding strategies aimed to improve service regularity.

The evaluation is performed using BusMezzo, a transit

mesoscopic simulation model. The model represents

explicitly all of the important sources of uncertainty

associated with transit operations. The rest of the paper is

organized as follows: First, the overall framework and

implementation of the transit simulation model are

presented. Various holding control strategies are discussed

and then applied on a high-demand bus line in the Tel-Aviv

metropolitan area. The case study analyzes the impacts of

holding strategies on bus performance and level of service

and their effectiveness. Finally, a discussion and concluding

remarks are presented.

II. TRANSIT SIMULATION

A. Mezzo

The transit simulation model is built within the platform of

Mezzo, a mesoscopic traffic simulation model. Mezzo is an

object-oriented, event-based simulator, which models

vehicles individually, but does not represent lanes explicitly.

Links in Mezzo are divided into two parts: a running part,

which contains vehicles that are not delayed by the

downstream capacity limit; and a queuing part, which

extends upstream from the end of the link when capacity is

exceeded. The boundaries between the running and queuing

parts are dynamic and depend on the extent of the queue.

Travel time on the running part is defined by a speed-

density function, while the travel time on the queuing part is

determined by queue servers. Separate servers with their

corresponding capacities are used for each turning

movement in order to capture link connectivity and lane

channeling.

B. Transit simulation framework

Mezzo was extended to simulate transit operations with six

transit-oriented classes: Bus Type, Bus Vehicle, Bus Line,

Bus Route, Bus Trip and Bus Stop. As an event-based

simulation model, the time clock of the simulation

progresses from one event to the next according to a

chronological list of events that refers to the relevant objects

that change state. At the start of the simulation, all objects

are initialized and some of them register an event. The

execution of most events triggers the generation of new

subsequent events. On initialization of the simulation run,

the list of the bus lines that are modeled is read and the

corresponding Bus Line, Bus Route and Bus Type objects

are created. At this stage, events are registered in the event

list for the next scheduled departure for each line. When a

scheduled trip departure event is activated the Bus Trip

object is generated and the scheduled Bus Vehicle is

assigned as soon as it is available, representing trip chaining

explicitly. Link travel times are calculated based on traffic

conditions as for all vehicles in Mezzo, while dwell times

are calculated every time a bus vehicle enters a bus stop.

Based on the dwell time and taking into account any control

strategies that may be implemented, the timing for a new

event to exit the bus stop is determined. Finally, when the

bus arrives at the end of its route and the trip ends, Mezzo

progresses the bus according to its vehicle schedule.

The main simulation loop is designed to support the

implementation of control strategies, where each object that

is a potential subject for control strategy is indicated by a

flag. Every time that a transit-related event is executed, the

model checks whether a control strategy is defined for this

type of event, and if so, executing the control logic to

determine the appropriate action. For example, if holding

control is in place, for every bus that enters a stop, the

simulation checks whether the bus stop is listed as a time

point stop for that specific trip and if it is, for how long the

bus should be held according to the applicable holding

strategy (if at all). The result of this check may affect the

time associated with the stop exit event that will be

generated. A detailed description of the transit-related object

framework and simulation progress as well as model

validation is presented in [2].

C. Implemented transit models

The additional transit simulation components were designed

to enable detailed representation of the operations of public

transportation. The main transit simulation sub-models are

passenger arrival and alighting processes, dwell time

functions and trip chaining. These important sources of

uncertainty and their implementation are presented briefly.

Passenger demand is represented at the bus stop level and is

defined by arrival rates at stops of passengers for each line

and the demand to get off the bus at each stop. This level of

representation is detailed enough to support study of the

impacts of demand on service times and on crowding levels,

while avoiding explicit generation of individual passengers.

Thus, the inputs to the model are time-dependent matrices of

passenger arrival rates and alighting fractions for each bus

stop and each bus line. They are used as mean values in

stochastic arrival and alighting processes. We adopt the

commonly used assumption that passenger arrivals follow a

Poisson distribution in the case of high-frequency service.

The passenger alighting process is assumed to follow a

Binomial distribution with the number of draws equal to the

number of passengers on-board.

Dwell times include the time needed for the doors to open,

boarding and alighting of passengers, the closing of the

doors and the bus to get off the stop. Dwell times in the

simulation model are determined as a function of the door

that has the longest passenger service time, as well as the

type of stop (bay or in-lane) and physical space availability.

Passenger service time depends on the distribution of

boarding and alighting passengers between the vehicle doors

and the crowding level on the bus. In addition, the dwell

time calculation incorporates an error term that captures the

variability in dwell time function parameters. The default

dwell time function parameters implemented in the model

are based on those recommended by the Transit Capacity

and Quality of Service Manual [3].

Transit vehicles follow a schedule with a list of trips that are

carried out sequentially. Trip chaining is modeled explicitly.

The actual departure time of a chained trip being calculated

as the latter of the scheduled departure time and the time the

bus vehicle is available to depart after it completed its

previous trip and a minimal recovery time. The explicit

representation of trip chaining allows the simulation to

capture the propagation of delays from one trip to the next

and its effect on the level of service. Furthermore, it allows

taking into account fleet size constraints through the

respective recovery time policy.

III. HOLDING CONTROL STRATEGIES

Holding strategies are a set of transit operation strategies

aimed at improving service reliability by defining a subset

of stops, known as time point stops, where departure times

are subject to strategy constraints [4]. There are three main

decisions involved in implementing holding strategies: the

number of time points, their location along the route and the

holding criteria. Although hypothetically all stops might be

defined as time points, a typical bus line has only a couple

of time point stops (such as main transfer and Central

Business District stations). Several studies [5,6] suggested

that time-point stops should be located at the beginning of a

sequence of high-demand stops. In contrast, [7] found that

there are no significant benefits for defining time points

along bus routes, except the origin terminal. They searched

for the optimum time point location by formulating and

solving a deterministic analytic model, claiming that since

the holding effect is short in nature, the solution for the

deterministic problem is a reasonable approximation.

While holding strategies are aimed at reducing passenger

waiting times they may also introduce longer travel times

for passengers on-board. Several previous studies took into

account the delay caused to passengers on-board due to

holding strategies by incorporating it into the objective

Cats O., Burghout W., Toledo T. and Koutsopoulos H.N. (2010). Evaluation of Real-Time Holding Strategies for Improved Bus Service Reliability. IEEE conference on Intelligent Transportation Systems, Proceedings, ITSC, Portugal, 718-723.

function or by conducting multi-criteria optimization [e.g.

5]. In order to conduct an accurate estimation of this trade-

off and the resulting optimal holding threshold, real-time

Automatic Vehicle Location (AVL) and Automatic

Passenger Count (APC) data is required.

Holding control strategies differ in their criteria for

departure time from a time point stop and the information

that their implementation requires. They are classified

according to whether they are based on a schedule criterion

or a headway criterion. Schedule-based holding enforces

buses that arrive early at a time point stop to wait at the stop

until a pre-defined slack from their scheduled departure

time. The equivalent mathematical definition is:

(1)

Where is the exit (departure) time for line on trip

from stop , is the corresponding scheduled exit

(departure) time and is a non-negative slack size defined

for line at stop . is the actual arrival time and

is the dwell time.

Headway-based holding strategies imply that if the current

headways between the transit vehicle and the preceding

and/or subsequent vehicles do not fulfill a minimal headway

requirement, then the transit vehicle has to wait at the stop

until the requirement is met. In case the headway

requirement takes into account only the headway from the

preceding bus, can be expressed as follows:

(2)

Where

is the planned headway between trips

and on line and is a threshold ratio parameter. This

threshold ratio specifies the minimal allowed headway

relative to the planned headway. Headway-control strategies

are intended for short headways, when maintaining even

headways reduces passenger waiting times. Schedule-

control strategies are more likely to be useful if headways

are longer and passengers tend to follow the timetables [8].

An analytical study on the optimal threshold criteria [6]

concluded that the optimal threshold level is in the range of

0.6 to 0.8 times the planned headway.

Headway-based strategies are not limited to consider only

the headway from the preceding bus. It is possible to also

incorporate the headway to the next bus into the holding

strategy. In order to have even headways on both sides, the

holding criterion is based on the average headway:

( ( ) ( )

) (

)

(3)

Where is the last stop that was visited by bus trip

and is the scheduled riding time between stops

and . The fraction in the first expression is the average

between the known headway from the preceding bus and the

predicted headway from the following one. Applying this

control strategy at origin terminals in a simulation model of

urban rail operations was found promising [9]. AVL systems

allow implementing this strategy also at intermediate stops

along the bus route. Although this holding strategy is

independent of the planned headway, [10] analyzed the

performance of a similar adaptive control strategy based on

bus-to-bus communication and concluded that the deviation

from the schedule and the deviations of the headway are

small and bounded under realistic assumptions.

In addition, it is possible to combine the two headway-based

strategies (2) and (3) in order to restrict the maximum

allowable holding time:

( (

) ) (4)

IV. CASE STUDY

A. Bus line description

The transit simulator is applied to a case study to evaluate

the operations of line 51 in the Tel Aviv metropolitan area in

Israel, under various candidate holding strategies. This high

demand urban line connects a dense satellite residential city

to the CBD. Its 14 kilometer long route follows a heavily

congested urban arterial. The line includes 30 stops on the

inbound direction and 33 on the outbound direction. The

scheduled headway during the peak period is 8 minutes and

the average running time is 49 minutes inbound and 41

minutes outbound. In the case study running times between

stops were assumed to follow lognormal distributions, with

means equal to the scheduled times. At both trip ends,

recovery times were calculated based on the 85th

percentile

of the trip travel times, calculated according to the

lognormal distribution [11]. These recovery times were then

used as minimum requirements in determining the trip

assignment for each bus vehicle, while the layover times are

already integrated into the scheduled times.

B. Experiment

In the case study four holding strategies defined by

expressions (1) to (4) in addition to the base case scenario

with no control strategy were studied. The number and

location of time points, as well as the slack size or threshold

headway ratio, are determined according to common values

and methods in the literature. In order to maintain

comparable settings, the same number and location of time

points were used with all strategies. Applying the rule of

locating time point stops at the beginning of a sequence of

high demand stops on line 51 boarding profiles, three time

point stops (7, 13 and 21) were defined on the inbound route

and two on the outbound route (8 and 20). While

dispatching from the origin terminal is determined by the

schedule and vehicle availability, the second stop on each

direction was defined as a time point stop in order to

regulate the service from the beginning of the trip.

After the number and location of time-points are set, the

holding criteria parameter values have to be defined.

Schedule-based holding is simulated with a slack size of

zero, which implies that the bus does not depart from time

point stop before its scheduled time. In order to examine the

sensitivity of the results to the threshold ratio parameter

value, the holding strategy defined by (2) was simulated

with three levels of threshold ratio: 0.6, 0.7 and 0.8,

following recommended values from previous studies.

In summary, seven scenarios were evaluated, as follows: No

control (strategy 0); Schedule-based control (strategy 1);

Headway-based control based on the preceding bus (strategy

2 with three values of ); Headway-based control based on

the mean of the headway from the preceding and the

expected headway to the next bus (strategy 3); Combination

of strategies 2 and 3 (strategy 4 with ).

The simulations were conducted for the peak period

between 6:30AM and 9:30AM with flat peak hour passenger

demand and headway of 6 minutes for the inbound direction

and 7 minutes for the outbound direction. For each scenario

60 three-hour simulation runs were conducted. This number

of replications results in an allowable error of less than 5%

for the outbound route and less than 10% for the inbound

route for the standard deviation of the headway which is the

outcome of a complex interaction between all random

processes in the system. It should be noted that different

applications or output measures require different number of

replications, depending on the desired level of accuracy. The

total execution time for the 60 runs was about 10 seconds on

a PC with a Pentium 4, 2.26 GHz, 1.85 GB RAM running

windows XP. The reported results are the average of the 60

replications for each scenario.

C. Results

The detailed representation of the bus operations in the

simulation model allows analyzing the system performance

ranging from the level of a single trip or a specific stop to

overall system performance measures.

Figure 1 presents the coefficient of variation of the headway

along the inbound direction for the peak hour (7:30AM-

8:30AM). The time point stops are marked with vertical

dashed lines. As the distance from the origin terminal grows,

the variability accumulates and causes the propagation of

bus service unreliability. This result is consistent with the

findings in empirical studies [12]. It is evident that under

headway-based holding strategies there is an immediate

decrease in the coefficient of variation of the headway after

each time point stop, preventing the continuous propagation

of headway variability. Moreover, mean-headway strategies

(s=3 and s=4) are the most efficient in reducing headway

coefficient of variation. The second time point (stop 7) is

especially useful as it corrects irregular dispatching from the

origin terminal, when the information from the next bus

becomes available. For the preceding-headway strategy

(strategy 2), = 0.7 yields the highest reduction. As the

schedule-based strategy is designed to improve schedule

adherence objectives, it is not surprising that is inefficient

when it comes to regulating headways and is displayed only

for completeness.

Figure 1: Coefficient of variation of the headway

under various control strategies (inbound direction)

Figure 2 presents a time-space diagram showing an example

of trajectories of a sequence of 3 bus vehicles, displaying 2

chained trips (one outbound followed by one inbound trip)

when the mean headway-based strategy (s=3) has been

implemented. In each trajectory, sloped segments represent

running time between stops and vertical segments indicate

dwell times and holding times at time point stops. Recovery

times between trips at both terminals are also apparent in the

figure. This diagram provides a convenient tool for

analyzing operation strategy dynamics. As can be seen

clearly, the applied holding strategy (B) is very effective in

regulating the service by creating even headways at time

point stops. For example, on the first trip, bus 2 is getting

increasingly bunched with bus 1, with time points holding

bus 2 and preventing continuous bunching. When no control

strategy is implemented, the two buses depart closely,

getting bunched and even overtaking each other along the

route. If a schedule-based dispatching is not an operational

constraint (e.g. transfer hub, labor agreements), then fully

headway-based operations can be implemented in order to

reduce the initial headway variability [9].

Figure 2: Time-space diagram of buses on service in line 51

with mean headway-based strategy (B)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

coef

fici

ent o

f va

riat

ion

of h

ead

way

stop

s=0 s=1 s=2, α=0.6 s=2, α=0.7 s=2, α=0.8 s=3 s=4

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 2000 4000 6000 8000 10000 12000 14000

Tim

e [s

econ

ds]

Distance [meters]Bus 1 Bus 2 Bus 3

Cats O., Burghout W., Toledo T. and Koutsopoulos H.N. (2010). Evaluation of Real-Time Holding Strategies for Improved Bus Service Reliability. IEEE conference on Intelligent Transportation Systems, Proceedings, ITSC, Portugal, 718-723.

At the system level, several measures of performance were

calculated for each scenario. Table 1 summarizes these

measures for the inbound direction. While there is no

obvious relationship between schedule adherence and

service headway, the probability to adhere to the planned

headway decreases for shorter headways [12]. The

variability of headways is the main measure for evaluating

transit reliability, in particular for short-headway services,

when bus bunching occurs. Headway coefficient of variation

was calculated for each stop along the route. The reported

statistics are the mean values across all stops in each

direction. Note that the average headway during the entire

simulated peak period is constant as the number of

dispatched buses does not change. Headway-based holding

strategies reduced headway variability, resulting in shorter

passenger waiting times, but they also imply an increase in

total travel time which may impose higher operational costs.

The coefficient of variation decreases up to 20% under the

preceding-headway strategies and more than 45% when the

mean-headway strategy restricted by the planned headway

(s=4) was implemented. The mean-headway strategy (s=3)

results in service regularity gains at the cost of significant

increase in travel time. However, imposing a limit on

holding time for this information demanding mean-headway

strategy (s=4), achieved the highest improvement in service

reliability, with a moderate increase in travel time that is not

higher than the preceding-headway strategy (s=2).

Another important measure of service reliability is on-time

performance. For a scheduled headway of six minutes, a bus

is considered in this study to adhere to schedule in the peak

hour at a specific stop, if it arrives between one minute early

and three minutes late compared to its scheduled arrival [e.g.

13]. Due to the small share of early arrivals, the schedule-

based strategy (s=1) did not improve substantially the share

of on-time arrivals. Headway-based strategies may cause

systematic deviation from the schedule especially with

higher values of the headway ratio parameter ( ).

The evaluation of holding control strategies requires taking

into consideration their effect on several measures. On the

one hand, an effective holding strategy improves service

reliability by reducing headway variability or increasing

schedule adherence which result in shorter passenger

waiting times, more even crowding levels and lower fleet

costs due to layover considerations. On the other hand,

holding strategies may cause delays to passengers on-board

and longer travel times that may require higher fleet costs.

As expected, higher values of headway thresholds result in

both higher probability to trigger holding and longer holding

times. The majority of the buses are not held at stops in all

holding scenarios. The small portion of long holding times

(more than 2 minutes) under mean-headway strategy (s=3)

is eliminated by introducing an upper limit on the holding

time (s=4).Figure 3 summarizes the trade-off between the

decreased waiting time per passenger (y-axis) and the

average increase in in-vehicle time (x-axis) caused by the

implementation of holding control strategies. The dark

square denotes the no control strategy without any delay

caused by holding and the benchmark for waiting time,

assuming that passengers arrive randomly at stops. Such an

analysis can identify dominated alternatives – alternatives

that can be eliminated as they are worse than another

alternative in at least one performance measure and are not

better than it in any other performance measure. In our case,

none of the holding control strategies are dominated by the

no-control scenario. The mean-headway strategy (s=3) is

dominated by its restricted version (s=4) as it results in both

longer average passenger waiting times and riding times.

The schedule-based strategy (s=1) is also dominated by the

preceding-headway strategy with and .

Table 1: Service measures of performance for inbound

direction under various scenarios Scenario Measure of performance

S

CV

(h)

Av

era

ge

wa

itin

g t

ime

per

pa

ss.

(sec

) Av

era

ge

incr

ease

in

tota

l tr

av

el

tim

e (s

ec)

Ea

rly

arr

iva

ls (

%)

La

te

arr

iva

ls (

%)

On

-tim

e

arr

iva

ls (

%)

0 --- 0.34 200.43 0.00 0.44 29.44 70.12

1 --- 0.34 200.29 26.63 0.38 27.58 72.04

2 0.6 0.30 195.37 12.09 0.31 31.07 68.62

0.7 0.28 194.12 25.85 0.23 32.90 66.86

0.8 0.27 192.72 46.82 0.23 40.15 59.62

3 --- 0.23 188.97 79.70 0.22 41.36 58.41

4 1.0 0.18 185.14 44.78 0.24 37.95 61.81

Figure 3: Trade-off between delay and waiting time under

various holding strategies (inbound direction)

It is worth noting that in the case of longer headways, when

passengers arrive at stops according to the schedule and in

case of high importance for transfer coordination, a

schedule-based strategy that improves schedule adherence

will result in shorter waiting times. The preceding-headway

strategy together with the no control scenario and the

restricted mean-headway strategy compose the set of non-

dominated strategies in our analysis. As the threshold ratio

is set higher, there is a larger gain in terms of reduced

waiting time but also an increase in passenger delay due to

0

5

10

15

20

0 5 10 15 20 25 30 35

Ave

rage

red

uct

ion

in w

aiti

ng

tim

e p

er

pas

sen

ger

[sec

on

ds]

Average increase in passenger in-vehicle time caused by holding [seconds]

s=0 s=1 s=2, α=0.6 s=2, α=0.7 s=2, α=0.8 s=3 s=4

holding times. This relationship seems to have a linear

pattern within the recommended range of values. In order to

determine which alternative is the optimal strategy for a

specific case, it is common to compose a compensatory

function by defining the relative importance for each of the

different objectives. For example, if passenger waiting and

in-vehicle time are the only two relevant objectives, and

assuming the common ratio of 2 between their relative

importance (passenger waiting time is twice as important as

passenger in-vehicle time), all the non-dominated strategies

are beneficial. It is expected that with shorter headways, the

extra in-vehicle time is lower, making the holding strategies

even more efficient.

V. CONCLUSIONS

A simulation-based evaluation enables to analyze the effects

of real-time holding strategies on bus performance and level

of service by capturing the interactions between traffic

conditions, transit operations and passenger demand.

Several holding control strategies aimed to improve service

regularity were implemented in BusMezzo, a mesoscopic

transit simulation model. The simulation model represents

schedules, boarding and alighting processes, passengers left

behind, dwell time, layover and recovery time and trip

chaining. The holding strategies were applied on a real-

world high-demand line in the Tel Aviv metropolitan area.

All candidate holding strategies improved service regularity

substantially. In particular, an analysis of the results

suggests that a holding strategy based on the mean headway

from the preceding bus and the next bus, restricted by a

maximum allowable holding time, is especially efficient.

This strategy yields significant gains in terms of improved

service regularity and shorter passenger waiting times. In

addition, its narrower distribution of headways has the

potential to compensate for the increase in total travel time,

by requiring a smaller fleet size for carrying out the same

service frequency under a given layover policy.

Future work will focus on the implementation of additional

control strategies such as conditional transit signal priority,

expressing and short turns, enabling evaluation of

integrative control schemes. These control strategies will

allow compensating for delays caused by holding strategies

and have the potential to reduce late arrivals. Holding

strategies based on headway-based dispatching are also

subject for a future study. A detailed representation of

passenger demand draws an additional interesting direction

for future research as it would enable to capture the

interaction between transit operation strategies and

passenger route choice and to capture the role of missed

transfers.

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