Effects of Random Delay on Travel Behavior of Subway Commuters
during Peak Hour based on Equilibrium Models
Jianan Cao
a
Beijing Jiaotong University, China
Keywords: Random Delay, Travel Behavior, User Equilibrium, Peak Hour, Commuting Model.
Abstract: This paper discusses the influence of random delay on the travel behavior of subway commuters in the peak
hour. We consider the situation that commuters need to take bus to complete the rest of the journey after
getting off the subway. We assume that the buses have random delay
T
that follows a uniform distribution
in the range
bT 0
. And it is found that
T
has an impact on the commuting model. It is shown that with
the increase of
b
, three different scenarios emerge. The start time and end time of the peak hour, the expected
value of travel cost, and the queuing time have been derived under the three scenarios. It is shown that the
start time of rush hour monotonically decreases (i.e., the start time becomes earlier and earlier) and the travel
cost monotonically increases with the increase of
b
.
1 INTRODUCTION
Subway is becoming more and more popular among
people, especially commuters, as a comfortable and
punctual means of transportation. However, as the
number of commuters increases, the subway has
become increasingly congested during the rush hour.
Since Vickrey proposed the classic bottleneck model
to characterize the commute behavior (Vickrey 1969),
many extensions and applications of the model have
been made (Arnott 1990, Laih 2004, Lindsey 2012),
considering, e.g., elastic demand and general queuing
networks (Braid 1989, Arnott 1993, Yang 1998), the
uncertainty of road bottleneck capacity (Xiao 2015,
Zhu 2019).
The bottleneck model has also been used to study
the subway commuting behavior. For example, Kraus
and Yoshida (Kraus 2002) investigated the optimal
fare and service frequency to minimize the long-term
system cost. Yang and Tang (Yang 2018) proposed a
fee feedback mechanism to manage the passenger
flow during peak hours and minimize the system cost
while ensuring the same revenue for the authorities.
However, in the vast majority of cases, the
subway does not go directly to a commuter's place of
work. Passengers often need to take a bus to reach
workplace after getting off the subway. During the
a
https://orcid.org/0000-0003-1000-9538
morning rush hour, a random delay of buses is very
common. Motivated by the fact, this paper studies the
impact of random delay on commuters' travel
behavior and travel cost.
The paper is organized as follows. Section 2
introduces the subway bottleneck model considering
random delay and derives the commuter travel cost in
user equilibrium. Section 3 discusses the impact of
random delay on commuters' departure time choice
and travel cost. Section 4 summarizes the paper.
2 THE TRAFFIC BOTTLENECK
MODEL CONSIDERING
RANDOM DELAY
2.1 Symbol Definition
: the unit cost of queuing time
: the unit cost of early arrival
: the unit cost of late arrival
: the unit cost of random delay on the bus
)(mq
: Queuing time of taking the
m
th train
)(me
: Early arrival delay for commuters on the
m
th train