Hindawi Journal of Advanced Transportation Volume 2019, Article ID 6830450, 15 pages https://doi.org/10.1155/2019/6830450

Research Article Data-Driven Approaches to Mining Passenger Travel Patterns: (Left-Behinds) in a Congested Urban Rail Transit Network

Xing Chen,1 Leishan Zhou ,1 Zixi Bai ,1 Yixiang Yue,1 Bin Guo ,2 and Hanxiao Zhou1

1 Department of Transportation Management Engineering, School of Trafc and Transportation, Jiaotong University, China 2National Research Center of Rail Transit and Transportation Training and Accreditation, Beijing Jiaotong University, China

Correspondence should be addressed to Zixi Bai; [email protected]

Received 20 November 2018; Accepted 6 March 2019; Published 1 April 2019

Academic Editor: Eneko Osaba

Copyright © 2019 Xing Chen et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Te “lef-behind” phenomenon occurs frequently in Urban Rail Transit (URT) networks with booming travel demand, especially during peak hours in a complex URT network, which makes passenger travel patterns more complicated. Tis paper proposes a methodology to mine passenger travel patterns based on fare transaction records from automatic fare collection (AFC) systems and Automatic Vehicle Location (AVL) data from Communication Based Train Control (CBTC) Systems or tracking systems. By introducing the concept of a sequence, a space-time-sequence trajectory model is proposed to simulate a passenger’s travel activities, including when they are lef-behind. Te paper analyzes passenger travel trajectory links and estimates the weight of each feasible trajectory under tap-in/tap-out constraints. Te station time parameters, including access/egress and transfer walking- time parameters, are important inputs for the model. Te paper also presents a maximum-likelihood approach to estimate these parameters from AFC transaction data and AVL data. Te methodology is applied to a case study using AFC and AVL data from the Beijing URT network during peak hours to test the proposed model and algorithm. Te estimation results are consistent with the results obtained from the authorities, and this fnding verifes the feasibility of our approach.

1. Introduction that we term “lef-behind”; some passengers fail to board the frst departing train afer their arrival at a platform and During the last decade, Urban Rail Transit (URT) in Main- must wait for a later one. Tis occurs mainly because the land China has developed from a total system length of only travel demand exceeds the network supply during a given 763 kilometers ten years ago to 5033 kilometers by the end operational time interval due to train vehicle capacity. of 2017 [1]. With the rapid development of the URT network, To address the above problems, numerous methods travel demand has also experienced a booming increase. In have been proposed and adopted from both the operator’s the past 10 years, the average daily passenger trafc of the perspective and the passenger’s perspective. Guan (2013) [4] Beijing URT system has increased from 1.92 million in 2007 and Yu et al. (2015) [5] developed a model for network design to 10.35 million in 2017, an increase of 439% [2]. Te Mass with the objective of minimizing the number of transfers. Transit Railway system (MTR) in Hong Kong has increased Niu and Zhou [6] presented a methodology to optimize the approximately 131.6% in patronage since 2006 [3]. timetable to minimize waiting time under time-dependent Te signifcant increase in travel demand has resulted travel demands and oversaturation. Tey analyzed the char- in congestion and overcrowding both in stations and in acteristics of passenger fow and formulated a model to train vehicles; this has become a serious problem for URT minimize passengers’ waiting times or minimize the number operators to address, particularly during peak hours. On one of transfers. To better grasp the distribution of URT network hand, congestion brings security risks. On the other hand, passenger fow, methodologies to study passengers’ travel congestion and overcrowding reduce the attractiveness of the patterns have been developed. Tese facilitate a number of URT network, and some passengers will choose other modes applications, including (i) analysis of passengers’ path-choice of transportation. Additionally, a new phenomenon appears preferences, such as minimum time and minimum number 2 Journal of Advanced Transportation of transfers, (ii) prediction of individual passengers’ locations followed by the introduction of the solution algorithm in Sec- and the future distribution of URT network passenger fow, tion 5. Section 6 presents a numerical experiment on a real- (iii) optimizing train scheduling both from the subway line worldnetwork.Tefnalsectionprovidesourconclusions level by identifying the most congested stations and sections and suggestions for future research directions. and from the network level by identifying the transfer hot-spots, and (iv) guiding passengers to avoid congested 2. Literature Review sections as much as possible by informing route suggestions, congestion levels, etc. Many scholars and researchers have studied URT network Tus, this paper attempts to mine passenger travel pat- passenger travel patterns during the last decades. At the terns based on automatic fare collection (AFC) transaction beginning of these studies, it was generally not possible to data and Automatic Vehicle Location (AVL) data. It builds obtain bulk data, including passengers’ tap-in/tap-out infor- on our prior work on the problem [7] and reconstructs a pas- mationandactualtrainmovementdata.Becauseofthelackof senger’s trajectory by introducing the concept of a sequence data, numerous methods were proposed at macroscale level. to describe lef-behind. Te prior work ignored train vehicle Tese methodologies mainly analyzed passengers’ travel pat- capacity constraints and assumed that all passengers lef a terns from a network-fow perspective. Tey generated sets of platform for another subway station by the frst departing feasible paths for each origin-destination (OD) and assigned train afer their arrival at the platform. We propose the passenger fows to each path following specifc principles. concept of sequence to describe the relationships between Te three most well-known principles are the all-or-nothing passenger’s arrival and departure of trains. By separating time principle, the stochastic-assignment principle [8–12], and the periods into segments according to stations, train directions, user-equilibrium-assignment principle [13–18]. and the departure times of trains passing stations, this paper With the wide adoption of AFC systems and rapid reconstructs a passenger’s trajectory and proposes a space- development of train tracking systems such as the Com- time-sequence trajectory model. Te model generates a set munication Based Train Control (CBTC) System, massive of feasible space-time-sequence trajectories that indicate a detaileddatawascollectedandsavedtodatabases.Most passenger’s precise travel patterns and the expected number AFC systems record passenger tap-in/tap-out information of times a passenger is lef-behind on a platform. Ten, a accurately except for some cases such as the New York methodology is presented to estimate the number of lef- City Transit Authority (NYCT) system, in which exit swipe behinds and the probability of each trajectory based on information is not recorded. Te Automatic Vehicle Location the distribution of station access/egress walking time and (AVL) system records train arrival and departure times at sta- transfer walking time. Tese distributions can be obtained tions accurately and in detail. With bulk data collected daily from manual surveys. However, these require substantial automatically and continuously, some novel methodologies labor. Te paper presents a maximum-likelihood estimation for transit performance [19–21] and management [6, 22, 23] methodology based on passengers’ trajectories. have been developed. Te main contributions of this study include the follow- Dai (2015) [22] presented a multimodal evacuation model ing: for metro disruptions based on AFC data in Shanghai, China. (i) A space-time-sequence trajectory model to simulate a Using AFC data of stations in urban areas of Hong Kong, passenger’s travel itinerary in a congested URT system. Te Wang (2015) [21] developed a methodology to analyze metro model introduces the concept of sequence and provides a trip patterns at an aggregate level. Kusakabe and Asakura means to indicate the lef-behind phenomenon. (2014) [24] estimated passengers’ behavioral attributes of (ii) A maximum-likelihood estimation methodology trips with a data fusion methodology using smart cards. based on AFC and AVL data that estimates passenger’s Tey observed and compared continuous long-term changes travel patterns. More automatic data instead of empirical in passengers’ trips as well as personal trip survey data data or manual survey data is used in the methodology; this and constructed a Bayes probabilistic model to estimate minimizes the occasional deviation caused by human factors. the purposes of passengers’ trips. Jin (2015) [19] evaluated Additionally, it reduces the difculty of obtaining data. transit service performance by developing a data-mining (iii) A data-driven method to estimate station walking- logic methodology based on transit smart-card data. time parameters and the expected number of times pas- Some scholars and researchers have analyzed network sengers are lef-behind. Station walking-time parameters, passengerfowattheindividuallevel.Somehaveproposed including access walking time and egress walking time, are a specifc trajectory model to simulate a passenger’s trip the basic parameters for a station. Tey are usually obtained activities and estimated the maximum-likelihood path based by manual survey or observation; however, these require on tap-in/tap-out constraints; numerous assumptions are excessive labor and cost. Te method proposed in this paper embedded into stages of the models’ building process. Poon estimates these parameters using statistical methods based on M.H. (2004) [25] assumed that all passengers have full passengers’ space-time-sequence trajectories. predictive information about present and future network Te remainder of this study is organized as follows. conditions. Chen (2018) [7] assumed that all passengers can Section 2 reviews relevant studies in the literature. Section 3 always board the frst train arriving. Some additional input introduces the main idea of mining passengers’ travel patterns parameters are needed and have a signifcant impact on the and illustrates an example. Section 4 describes the model, accuracy of the estimation result. Journal of Advanced Transportation 3

Sun (2016) [26] presented a schedule-based passenger’s path-choice estimation model for a multioperator rail tran- sit network using automatic fare collection data. In this paper, a Train Schedule Connection Network (TSCN) was A B constructed,andtheestimatedpassengerpath-choicewas F converted to the problem of generating a feasible set of network paths. Te Fail-to-Board (FtB) phenomenon was D modeled and the weight of each path could be calculated basedonthesetoffeasiblepaths.Teaccuracyoftheresult was highly dependent on inputs, such as FtB parameters. C However, these parameters cannot be obtained directly and are not easy to calculate. E G Poon M. H. et al. (2004) [25] present a schedule-based transit model to solve passenger assignments for a congested network. Tey assumed that all passengers have full predic- tive information about present and future network conditions Station Station Transfer Station and always travel by the minimum-cost path. However, it is not possible for passengers to be informed of full information Figure 1: URT network topology. about network conditions. Furthermore, the minimum-cost path is time-dependent. Frequent URT passengers have their respective perceptions for choosing paths, gaining experience and directions, such as upward and downward directions. For day by day. Additionally, the tap-out times are not taken into example, there are a total of 55 trains passing a station in account when loading network fow. the upward direction between 7:00 AM and 9:00 AM, and Timon Stasko (2015) [20] analyzed passengers’ ridership the frst/last train’s departure time is 07:02:30/08:59:00. Tus, at the train level using actual train movement data. He built the time period is segmented into 56 successive intervals in a customized network representation by estimating train the upward direction; the sequence number of the frst time movements and developing an origin-destination table. Te interval from 07:00:00 to 07:02:30 should be 1. Te sequence methodology formulates a trip trajectory with 10 types of number of the last time interval from 08:59:00 to 09:00:00 arcs. It assigns passengers to trains using a Frank-Wolfe shouldbe56.Tesequencenumbersoftheseintervalsshould approach, with customizations designed for transit. However, also be successive and the sequence number of any time it is unnecessary to infer a destination for most of the interval should be smaller than that of any later time interval. URT network. Finally, the accuracy of the result is highly Assume that there is a passenger travelling from Station dependent on boarding penalties. AtoStationGthroughtheURTsystemshowninFigure1 during peak hours. 3. Problem Description Obviously, there are three feasible spatial routes for this trip: (i) A �→ B �→ C �→ E �→ G; (ii) A �→ B �→ F Time and space are two important attributes of passenger �→ G; (iii) A �→ B �→ D �→ E �→ G. Te passenger travel. Although AFC systems record passenger transaction transfers at Station B if travelling by route (i) or (ii), whereas information in detail, including precise transaction times he/she transfers at Station E if travelling by route (iii). For and locations when the passenger swipes his/her smart this journey, the passenger needs to experience the following card, detailed information on a passenger’s itinerary is not activities: (i) moving from the entry gate to the platform, (ii) included. Tis section describes methods for estimating a waiting at platforms of both the origin and transfer stations, passenger’s detailed travel information in both time and (iii) transfer from Line 4 to Line 2, (iv) egress from platform space. to exit gate, and (v) on-train. Te passenger may be lef- Space-time models attempt to integrate travellers’ time- behind and unable to board the frst-arriving train to leave dependent movements/trajectories with the transportation the platform at both the origin station and the transfer station network and are widely used in transportation geography during peak periods because of crowding on the platforms modeling literature. A space-time trajectory indicates a pas- andinthetrainvehicles.Figure2illustratesthetheoretically senger’s movements among activity locations with respect feasible space-time-sequence trajectories from Station A to to time, providing a useful means to describe both the Station G under tap-in/tap-out constraints. spatial and temporal aspects of a passenger’s travel status. As shown in Figure 2, the concept of an ideal boarding However, the key focus of this paper, the number of lef- node is proposed to distinguish platform waiting from lef- behinds due to crowding, cannot be obtained directly from behind. An ideal boarding node represents a passenger’s a specifc space-time trajectory. To estimate the number of theoretically earliest boarding activity; i.e., it represents the times passengers are lef-behind, a parameter defned as a passenger boarding the frst departure train afer his/her sequence is introduced, and a passenger space-time-sequence arrival at a platform. Te arc linking the entry space-time- trajectory model is developed. sequence node and ideal boarding node indicates that a Te time duration of the study is segmented into a set of passenger moves from the entry gate to the platform and waits successive intervals based on trains’ departure times, stations, until the frst train leaves afer his/her arrival. 4 Journal of Advanced Transportation

t t

j+5 j+5

j+4 j+4 (i+4) train (i+4) train j+3 (i+3) train j+3 (i+3) train j+2 j+2 (i+2) train (i+2) train j+1 j+1 (i+1) train (i+1) train j j i train i train

j-1 j-1 (i-1) train (i-1) train j-2 j-2

Entry A E' E'' G Exit Entry A E' E'' G Exit gate gate gate gate AEGAEG

Entry node Transfer link Entry node Transfer link

Arrival node Walk link Arrival node Walk link

Station node Exit node Station node Exit node

Spatial link Departure node Spatial link Departure node

Space-time link not in path Ideal boarding node Space-time link not in path Ideal boarding node Platform Platform Space-time link in path Space-time link in path

Lef behind link Lef behind link (a) (b) t

(j+5) train (j+4) train i+4 (j+3) train i+3 (j+2) train i+2 (j+1) train i+1 j train i (j-1) train i -1 (j-2) train

Entry Exit gate A B' B'' G gate

ABC G

Entry node Transfer link

Arrival node Walk link

Station node Exit node

Spatial link Departure node Ideal boarding node Space-time link not in path Platform Space-time link in path

Lef behind link (c)

Figure 2: Feasible space-time-sequence trajectories. Journal of Advanced Transportation 5

Figure 2 presents three feasible space-time-sequence Table 1: Notations and input parameters. trajectories with given tap-in/tap-out constraints. Tis paper attempts to estimate the maximum-likelihood trajectory to Symbol Defnitions S mining passengers’ travel patterns. Ten, the problem of Set of URT stations estimating the passenger’s travel patterns can be converted N Set of spatial nodes P P into problems of generating feasible space-time-sequence N Setofplatformspatialnodes,N ⊂ N trajectories and weight assignments. C Set of spatial connections, including sections and transfer links E Set of space-time-sequence arcs 4. Methodology W E Set of walking space-time-sequence arcs Te key question in estimating a passenger’s maximum EL Set of lef-behind space-time-sequence space-time-sequence trajectory is how to generate a set of arcs efective trajectories with entry and exit constraints and V Set of space-time-sequence nodes calculate their weights. Given AFC and AVL data, this sec- T Set of activity times tion constructs a passenger’s space-time-sequence trajectory- P Set of passengers estimation model to maximize the weight of a chosen path. �, �� Index of urban railway transit stations, Tables 1 and 2 defne the related notations and estimation �, �� ∈ S variablesusedinthemathematicalformulations. P L� Set of trains passing platform �, � ∈ N P L�(�) Te �th train passing platform �, � ∈ N 4.1. Precise Estimation Model for a Passenger’s Space-Time- � � ∈ P Sequence Trajectory. Within a closed URT system, an Index of passenger, �, � itinerary begins with passing an entry gate and ends with Index of spatial nodes, �, � ∈ N � � swiping a smart card at an exit gate. Te proposed model �, � Index of time stamp, �, � ∈ T � attempts to mine more detailed travel information about a ℎ� Interval time at station at time passenger’s travel using the tap-in and tap-out record. Tis � �, � ∈ S, � ∈ T paper addresses only regular passengers whose travels consist Te station to which node � belongs, �� of some or all of the fve activities present in Section 3. Some � ∈ N, s ∈ S special circumstances such as a passenger forgetting to alight (�, �) Index of spatial connection, (�, �)∈C are not considered. (�, �, �) ,(�, ��, ��) Index of space-time-sequence node, Considering that passengers are independent individu- (�, �, �), (�, ��, �)∈V als, it is reasonable to assume that passengers’ maximum- Index of space-time-sequence arc likelihood space-time-sequence trajectories are mutually � � indicating departing � at � during � time (�, �, �, � , �, � ) � � independent. Furthermore, each passenger’s walking activity interval and arriving at � at � during � � � and the trains running on diferent subway lines are indepen- time interval, (�, �, �, � , �, � )∈E dent from each other. Tus, the weight of each space-time- �,��,�� Te distribution of the time cost of ��,�,� � � sequence trajectory is the product of probabilities of all space- space-time-sequence arc (�, �, �, � , �, � ) time-sequence arcs passed by a passenger and the objective �,��,�� Te mean of the time cost of ��,�,� � � function is represented as follows. space-time-sequence arc (�, �, �, � , �, � ) �,��,�� Tevarianceofthetimecostof �,��,�� ��,�,� � � � � � space-time-sequence arc (�, �, �, � , �, � ) �=∏ ∏ (��,� ,� ) �,�,�,� max �,�,� (1) �,��,�� Te probability that a passenger leaves �∈� � � � � (�,�,�,� ,�,� )∈� �,�,� node � at � and arrives at node � at � �,��,�� Te time that a passenger should spend subject to the following. � � � �,�,� on (�, �, �, � , �, � ) � Space-Time-Sequence Flow Balance Constraints.Ifspace- ��,� ,�� Te number of times passengers who �,�,� (�, �, �, ��, �, ��) time-sequence node (�, �, �) is an entry node, then travel by are lef-behind � � Te arrival and departure times at � � ��,�, ��,� P ∑ ��,� ,� − ∑ ��,�,� =1 platform � of the �th train, � ∈ N �,�,�,� �,��,��,� (2) � (�,��,��)∈V (�,��,��)∈V Te upper error limit of function value P ��,� Te � interval time of platform �, � ∈ N If it is an exit node, then

� � ∑ ��,� ,� − ∑ ��,�,� =−1 �,�,�,� �,��,��,� (3) (�,��,��)∈V (�,��,��)∈V Constraints (2)-(4) ensure fow balance at the network entry, exit and intermediate space-time-sequence nodes, (�, �, �) If is an intermediate node, then respectively. �,��,�� ∑ � − ∑ ��,�,� =0 � � �,�,�,� �,��,��,� On-Train Constraints. If (�, �, �, � , �, � ) indicates on-train � � � � (4) (�,� ,� )∈V (�,� ,� )∈V activity, the train at the start point should be the same as that 6 Journal of Advanced Transportation

Table 2: Estimation variables. words, the distributions of access walking time, egress walking time, and transfer walking time are also similar Variable Defnition � to normal distributions. An access space-time-sequence � � � ∈ S � � Te mean of access walking time at station , . (�, �, �, ��, �, � ) � � arc means that the passenger departs node � �� Te variance of access walking time at station �, � ∈ S. � �,� ,�� � at time � and arrives node � before time � .Tus,��,�,� can �� Te mean of egress walking time at station �, � ∈ S. � be calculated as follows. �� Te variance of egress walking time at station �, � ∈ S. �,��,�� � � � � Te mean time consumed transferring from to �,�,� �,�� ��, �, �� ∈ S . 2 �,��,�� � � { ��−� (�−� ) Te variance of time consumed transferring from to { 1 �,�,� ��,�� � � { � � , �, � ∈ S {∫ � � exp (− )��, �=� . { �,� ,� � � 2 { 0 √2�� 2(��,� ,� ) (10) � Te mean of platform waiting time at station � during �,�,� �,�,� � = 2 � { �,��,�� of-peak hours, � ∈ S. { ��−� (�−� ) { 1 �,�,� {∫ (− )��, �=�̸ � � Te variance of platform waiting time at station � { � � exp 2 � { ��−�−� �,� ,� �,��,�� � �,�� √2�� 2(� ) during of-peak hours, � ∈ S. { �,�,� �,�,� Te mean number of times passengers are lef-behind ��,� � � on platform �. Similarly, if (�, �, �, � , �, � ) is a transfer space-time- � � 0-1 binary variables: 1 if trajectory of passenger sequence arc, its probability can also be calculated by (10). ��,� ,�� � � �,�,�,� contains space-time-sequence arc (�, �, �, � , �, � );0 Equation (10) can be integrated using characteristics of the otherwise. normal distribution, and the result is given as follows.

� � ��,� ,� of the end point. If the train runs in the upward direction, �,�,� � �,��,�� �,��,�� then { � −�−� −� {Φ( �,�,� )−Φ( �,�,� ), �=�� { � � � � � { ��,� ,� ��,� ,� (11) L� (�) = L� (� ) (5) = �,�,� �,�,� { � �,��,�� � �,��,�� { � −�−� � −�−��,�� −� {Φ( �,�,� )−Φ( �,�,� ), �=�̸ � { � � � � Sequence Constraints. According to the defnition of a space- ��,� ,� ��,� ,� time-sequence, if (�, �, �) is an ideal boarding node or train { �,�,� �,�,� departure node, then In (11), Φ(�) is the standard normal distribution function; � its numerical values can be found in the tables. �=�� ,� (6) � � ������� If (�, �, �, � , �, � ) is a lef-behind space-time-sequence or else arc,thenumberoftimesthepassengerislef-behindandcan � � be calculated as follows. �� ,�−1 ≤�<�� ,� (7) ������� ������� �,��,�� � ��,�,� = � − � (12) Notethatthesequencenumberoftheendnodeofa space-time-sequence arc should not be less than that of the Because that passenger can board the frst train afer their � � start node. Tus, if (�, �, �, � , �, � ) is a lef-behind space- arrival at a platform during of-peak hours, the number of time-sequence arc, then times passengers is lef-behind and ��,� should be zero. Simi- � � ��,� ,�� � ≤ � (8) lar to the on-train space-time-sequence arc, �,�,� should be equal to 1 during of-peak hours.

4.2. Calculation of Weight of Space-Time-Sequence Arc. � ��,� ,�� =1 According to the objective function, the precise estimation �,�,� (13) problem for a passenger’s detailed travel patterns is converted into a problem of the generation and weight assignments and of a feasible trajectory set. Among a passenger’s travel �� = � activities within the URT system, access, egress, and transfer (14) are walking activities. Once passengers board a train, their Provided that all passengers in line board the train movements with respect to time are the same as those of train � � following the frst-come-frst-served principle during peak vehicles and correspond to AVL data. Tus, if (�, �, �, � , �, � ) �,��,�� hours, the closer the number of lef-behinds is to its mean �,��,�� is an on-train space-time-sequence arc, ��,�,� should be value, the greater the probability ��,�,� is. It is similar equal to 1. to the progressive distribution. Here, we adopt (15) as its �,��,�� distribution function. ��,�,� =1 (9) � −(��,� ,��−� )2/2 �,��,�� 1 �,�,� �,� According to Shi [27], the distribution of passengers’ ��,�,� = � (15) walking times is similar to a normal distribution. In other √2� Journal of Advanced Transportation 7

� � 4.3. Estimation of Station Walking-Time Parameters where �� =�� =�,and(�, � , � ) is an exit space-time- sequence node. � � Estimation of Platform Waiting-Time Parameters. Platform If (�, �, �, � ,�,� ) is an entry space-time-sequence arc waiting time is defned as the elapsed time afer a passenger’s and its time consumption consists of two parts, (i) access arrival at a platform and before the departure time of the walking time and (ii) platform waiting time, thus, the mean frst departing train. During of-peak hours, the capacity of and variance of the access walking-time distribution can be the transit service supply is greater than trafc demand, and calculated by all passengers can board the frst departing train afer their arrival at a platform. Te actual boarding nodes are the same � �,��,�� � � = � − � (20) as the ideal boarding nodes in this situation. Additionally, � �,�,� � the platform waiting time should be less than the interval � 2 (��)2 =(��,� ,��) −(��)2 between the departure times of sequential trains passing � �,�,� � (21) the station. Since the times passengers arrive at a platform arerandom,thedistributionattheplatformistheuniform where �� = �� = � and (�, �, �) is an entry space-time-sequence distribution. Te mean and variance of the platform waiting- node. time distribution are given as follows. Similarly, the parameters of the distribution of transfer walkingtimescanbecalculatedasfollows. � � ℎ � � = � (16) �� = ��,� ,�� � 2 �,�� �,�,� (22) 2 � 2 2 �,��,�� (ℎ ) (�� ) =(� ) (23) (��)2 = � (17) �,�� �,�,� � 12 � � where �� = �, �� = � and �(����)=� (����). Estimation of Station Walking-Time Parameters. According to Section 2, there are three types of walking activities at a 5. Solution Algorithm station: access at an origin station, egress at the destination � � station, and transfer(s) at transfer station(s). If (�, �, �, � , �, � ) Te objective function presented in Section 4 is a product and �,��,�� is nonlinear; it is difcult to optimize. Tis section presents is an exit space-time-sequence arc, � is equal to the �,�,� an algorithm to estimate the maximum space-time-sequence egress walking time. Tus, it has the same distribution trajectory for all passengers with given AFC data. function. Te mean and variance of the time consumption of (�, �, �, ��, �, ��) Te objective function can be converted to a sum using canbecalculatedasfollows. properties of the logarithm function.

�,��,�� �,��,�� �,��,�� � = �� (18) �=∑ ∑ � ∙ � �,�,� � max ln �,�,�,� ln �,�,� (24) �∈P (�,�,�,��,�,��)∈EW∪EL 2 �,��,�� 2 (� ) =(��) (19) �,�,� � By substituting (10)-(12), (14), and (16) into (24) we get

max ln �

� �,��,�� � �,��,�� � � � −�−� max {0, � −�−��,�� }−� � � � � 2 = ∑ ∑ ��,� ,� ∙ (Φ ( �,�,� )−Φ( �,�,� )) − ∑ ∑ ��,� ,� ∙(��,� ,� −� ) − ∑ ∑ √2� (25) �,�,�,� ln �,��,�� �,��,�� �,�,�,� �,�,� �,� ln �∈P (�,�,�,��,�,��)∈EW �∈P (�,�,�,��,�,��)∈EL �∈� (�,�,�,��,�,��)∈EL ��,�,� ��,�,�

Provided that the mean and variance of a walking space- Te algorithm assigns a feasible trajectory for all passen- � �,��,�� �,��,�� � gers randomly and estimates station time parameters with time-sequence arc, Φ((� −��,�,� )/��,�,� ),andΦ((max{0, � − �,��,�� �,��,�� MLE. Te estimation of passengers’ maximum-likelihood �−� � }−� )/� ) �,� �,�,� �,�,� arefxedandcanbecalculated space-time-sequence trajectories and station time parameters � � �,� ,� 2 will not stop until the optimal result is obtained. easily, similarly, (��,�,� −��,�) can also be calculated. Tus, the weights can be calculated for all trajectories. Inverting this Algorithm 1 (iterative optimization algorithm). Input: pas- argument, if all passengers’ space-time-sequence trajectories sengers’ feasible space-time-sequence trajectory sets are given, these trajectories can be used as samples to estimate Output: station time parameters and passengers’ these parameters with the maximum-likelihood estimation maximum-likelihood space-time-sequence trajectories algorithm. To solve the station time parameters estimation problem and a passenger’s trajectory-estimation problem, Step 1 (initialization). Input AFC data and AVL data, initialize 0 an iterative optimization algorithm is proposed in this parameters of algorithm. Set (ln �) =0, �=10, � =1,where paper. � is the index of calculation generation. 8 Journal of Advanced Transportation

Step 2 (feasible space-time-sequence trajectories generation). weights of all space-time-sequence arcs are fxed and can be Generate a feasible space-time-sequence trajectory set and calculated. Tus, the passenger’s travel-patterns estimation select a trajectory randomly and assign it to all passengers. problem can be converted into a shortest-path problem. Te passenger’s travel-patterns estimation algorithm is presented Step 3 (estimate station parameters using the maximum- as follows. likelihood estimation algorithm). Given the detailed infor- mation of all passengers’ space-time-sequence trajectories, Algorithm 2 (passenger’s travel-patterns estimation algo- a passenger’s time consumption at any station can be cal- rithm). Input: station time parameters culated. Ten, the mean and variance can be estimated Output: passengers’ space-time-sequence trajectories accordingto(27)and(28). Step 1 (initialize algorithm parameters). Set � =1, � is the �,��,�� �,��,�� countofpassengers. � � ∑�∈P ∑(�,�,�,��,�,��)∈EW � ∙� ��,� ,� = �,�,�,� �,�,� Step 2 (weight calculation). Update weights of all space-time- �,�,� �,��,�� (26) ∑�∈P ∑(�,�,�,��,�,��)∈EW ��,�,�,� sequence arcs according to the following equations.

�,��,�� � � 2 �,� ,� ln ��,�,� (��,�,� ) � � � � 2 { (��,� ,� −��,� ,� ) { �,�,� �,�,� 1 � � W �,��,�� �,��,�� �,��,�� {− + , (�, �, �, � ,�,�)∈ (27) { � � 2 ln �,��,�� E ∑ ∑ � � W � ∙(� −� ) { �,� ,� √ (29) �∈P (�,�,�,� ,�,� )∈E �,�,�,� �,�,� �,�,� 2(� ) 2���,�,� = = { �,�,� �,��,�� { � � 2 {−(��,� ,� −� ) , (�, �, �, ��,�,��)∈ L ∑�∈P ∑(�,�,�,��,�,��)∈EW � { �,�,� �,� E �,�,�,� { {0, ��ℎ������ During peak hours, the mean of lef-behind can also calculated. Step 3 (estimate a passenger’s maximum-likelihood space- �,��,�� �,��,�� time-sequence trajectory). Calculate the weight of each feasi- ∑ ∑ � ∙� �∈P (�,�,�,��,�,��)∈EL �,�,�,� �,�,� ble space-time-sequence trajectory following (25) and assign � = (28) �,� �,��,�� the shortest path for the �th passenger. ∑�∈P ∑(�,�,�,��,�,��)∈EL ��,�,�,� �>� � Step 4 (algorithm loop judgement). If ,gotoStep4; Step 4 (deviation calculation). Calculate (ln �) according to otherwise, go to Step 2. � �−1 (25). If (ln �) −(ln �) <�,thengotoStep6.Otherwise, set � = � +1andgotoStep5. Step 5 (algorithm end). Output all passengers’ space-time- sequence trajectories. Step 5 (passenger’s travel pattern estimation). Assign the most likely space-time-sequence trajectory for all passengers by executing the passenger’s travel-patterns estimation algo- 6. Case Study rithm. Ten, go to Step 3. To verify the proposed methodology, the model was tested on real-world data from the Beijing railway transit network. Step 6 (algorithm end). Calculate station time parameters We propose an approach to validation that addresses the lack based on (16)-(23). Output the station time parameters and of actual passengers’ itineraries. Te approach is to analyze all passengers’ space-time-sequence trajectories. the estimation results statistically and compare them with We implemented the following iterative procedure to existing results. A sofware system has been developed using solvetheproblems,assummarizedinFigure3. C#, Windows Presentation Foundation (WPF) and Human- As shown in Figure 3, we have extended the Beijing computer interaction technology based on the model pro- rail transit network topology by replacing a station with posed in this paper. four types of spatial nodes (entry, exit, platform, and track) from which we generate the set of feasible space-time- 6.1. Beijing Railway Transit Network. Construction started sequence trajectories using the methodology in [7]. Te set on the Beijing railway transit network in 1965, and the frst of passengers’ feasible space-time-sequence trajectories is line began operation on January 15, 1971. By the end of the basis for solving the station time parameters estimation 2016, Beijing railway transit had developed into a large-scale problem and the passenger’s space-time-sequence trajectory- network, and its average daily passenger trafc was close to estimation problem. Te mean and variance of passengers’ 10 million. During this period, the metro operations were time consumption at a station can be estimated with MLE divided into two companies: (i) and (ii) once all passengers’ space-time-sequence trajectories are Beijing MTR. Figure 4 shows the real-world Beijing railway assigned. Ten, the key to the station time parameters esti- transit network topology at the end of 2016. mation problem is the passenger assignment problem. Afer AsshowninFigure4,thereareatotalof17railway estimating station time parameters, all space-time-sequence lines and 338 stations, including 53 transfer stations. Unlike arc time-consumption distribution functions are known. Te other railway lines, the airport line, labeled JC in Figure 4, is Journal of Advanced Transportation 9

Initialize parameters

Feasible space-time trajectory set generation

Assign space-time trajectory for passengers randomly

Estimate station parameters using MLE algorithm

Passenger trajectory assignment algorithm Calculation deviation

   k k−1 No (ＦＨ z) −(ＦＨz)  <?

Yes

Algorithm end

Figure 3: Solution methodology procedure.

CP 15 5

14 JC 13

10 2 8 1 BT

6 14 7

9 YZ

FS 4

Figure 4: Topology of Beijing rail transit network. independent; passengers must swipe their smart cards when from manufacturer to manufacturer, the basic information they transfer from/to the airport line. used in this paper was recorded. An automatic ticketing system was launched in Beijing 6.2. Input Data Preparation. Te case study employs AFC railway transit on June 9, 2008. Dozens of types of infor- transaction data and AVL data obtained from Beijing Subway mation are recorded and saved to a database. Passengers’ and Beijing MTR Corporation. Although these data vary tap-in and tap-out information was extracted, and Table 3 10 Journal of Advanced Transportation

Table 3: AFC transaction data from Dongwuyuan to Chongwen- According to Tables 5(a), 5(b), and 5(c), the estimation men. results are close to the manual survey results. Te relative CardID Entry Time Exit Time deviations between estimation results and manual survey are less than 5% except for the access walking time of 15093414604 17:34:00 18:08:16 Dongwuyuan. As the access walking time is approximately 30 15094844706 18:09:00 18:43:23 seconds, the absolute deviation is only three or four seconds 15094957624 18:08:00 18:42:11 and is acceptable, although the relative deviation exceeds 5%. 15095055101 17:29:00 18:01:21 15094845984 17:47:00 18:17:21 6.3.2. Lef-Behind. Te distribution of the estimated number 15095014893 17:27:00 17:56:18 of lef-behinds is shown in Figure 6. During of-peak hours, 15093507376 17:25:00 17:54:17 only approximately two percent of passengers are lef-behind, 15093510397 17:43:00 18:12:17 and the vast majority of passengers board the frst train. 15095109950 18:04:00 18:33:02 Tese lef-behind passengers may have been waiting for a companion. Most passengers lef-behind during peak hours due to train vehicle capacity constraints miss only one train, shows some AFC data from Dongwuyuan to though some passengers miss as many as three. observedduringpeakhoursonMay9,2016.Tetimeformat is hh:mm:ss. 6.3.3. Passenger Travel Patterns. A space-time-sequence indi- Five types of information are extracted directly from the cates a passenger’s travel information in detail. Te number database. Te Card ID is the unique identifer of a smart card of times the passenger is lef-behind and the specifc train(s) and represents an individual passenger. It is critical to match taken can be found directly. Figure 7 shows the space-time- tap-in and tap-out records. Te time and location of tap-in sequence trajectory-estimation result of a passenger whose and tap-out are recorded by the AFC system when passengers Card ID is 15093414604. Tis passenger passed the Dong- pass the entry/exit gates and swipe their smart cards. Te data wuyuan entry gate at 17:34:00 and lef from Chongwenmen at areaccurateandrecordtothenearestsecond. 18:08:16. Table 6 shows the station-time parameters estimated AVL data is actual train operation information; arrival in Sections 6.3.1 and 6.3.2. and departure times at each station of all trains are recorded AsshowninFigure7,therearetheoreticallymore in detail, and then they are collected by tracking systems or than ten feasible space-time-sequence trajectories. Partial CBTC, generally in one of two formats within the Beijing trajectories are given in Table 7. railway transit (see Tables 4(a) and 4(b)). In Table 7, columns 3-5 indicate the total time consumed Te sofware system uses a unifed data structure for with no lef-behinds at the origin, transfer, and destination trains to analyze passengers’ travel behavior at the network stations. Te total time consists of two components at both level and improve computation efciency. the origin and transfer stations: the access/transfer and platform waiting times. In general, the total time consumed at 6.3. Estimation Results and Discussion. Te accuracy of the the destination station should be the egress time. According estimation results is the key measure in evaluating the model to the estimation, this passenger chose the fourth trajectory proposed in this paper. Accuracy is evaluated at both the for the journey. individual and network levels. Te passenger arrived at platform of Dongwuyuan before 17:35:28, the departure time of train 1S443. He/she did not 6.3.1. Estimation Results for Station Parameters. Station-time leave Dongwuyuan by 1S443 until the departure of the next parameters are the basic attributes that tell the approximate train, 1Q445, because of crowding. Similarly, he/she was time consumed, including access, egress, and transfer walking lef-behind once at and boarded train 322223 for times for a transfer station. A maximum-likelihood estima- his/her destination. tion algorithm was developed to estimate these station time parameters by analyzing passengers’ space-time-sequence 6.3.4. Distribution of URT Network Passenger Flow. Te trajectories. Figure 6 shows the distribution of station-time distribution of the URT network passenger fow is one of parameters during of-peak hours and peak hours. Te most important network characteristics for URT operations. distributions of access walking time in Dongwuyuan station It refects the time-dependent travel demand and is the basis during of-peak hours and peak hours are shown in Figures for the transportation plan. Figure 8 shows the distribution of 5(a) and 5(b). Figures 5(c) and 5(d) show the distribution URT network passenger fow during peak hours. of egress walking time and the last two fgures present the During peak hours, as shown in Figure 8, the URT distribution of transfer walking time. network is crowded, and the maximum train load is up to AsshowninFigure5,thedistributionsareobviously 140%. Te more congested sections are located mainly in similar to a normal distribution. Te actual times consumed the center of Beijing, consistent with that during of-peak are concentrated over a certain range. Table 5(a) compares hours [7]. Table 8 compares the estimated results of section the estimated access walking time with a manual survey passenger fow and the results provided by Beijing TOCC for result provided by the Beijing Transportation Operations the top fve subway sections during peak hours. Coordination Center (TOCC). Tables 5(b) and 5(c) show As shown in Table 8, the estimated results are consistent comparisons of egress and transfer walking times. with the results from TOCC. Compared with of-peak hours, Journal of Advanced Transportation 11

Table 4

(a) AVL data of Line 2 Xizhimen Chongwenmen Train Num Arrive Time Depart Time Arrive Time Depart Time Arrive Time Depart Time 302108 10:12:30 10:13:30 10:24:31 10:25:01 10:31:07 10:31:52 322109 10:16:00 10:17:00 10:28:01 10:28:31 10:34:37 10:35:22 192110 10:20:30 10:21:30 10:32:31 10:33:01 10:39:07 10:39:52 362111 10:25:00 10:26:00 10:37:01 10:37:31 10:43:37 10:44:22 382112 10:29:30 10:30:30 10:41:31 10:42:01 10:48:07 10:48:52 402113 10:34:00 10:35:00 10:46:01 10:46:31 10:52:37 10:53:22 62114 10:38:30 10:39:30 10:50:31 10:51:01 10:57:07 10:57:52 (b) AVL data of Line 10 Rail Line Train Num Station Arrival Time Departure Time ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ 10 2278 Jinsong 17:48:50 17:49:25 10 2278 Shuangjing 17:50:52 17:51:22 10 2278 Guomao 17:53:30 17:54:20 ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ 10 2302 Liuliqiao 19:44:20 19:45:15 10 2302 Xiju 19:47:06 19:47:51 10 2302 Niwa 19:49:01 19:49:31

Table 5 Te diference is that a large number of passengers get of work and travel to the suburbs through the URT network (a) Dongwuyuan access walking-time parameter comparison table during late peak hours. Survey (s) Estimation (s) Relative deviation Peak 34 37 8.82% 7. Conclusion (b) Chongwenmen egress walking-time parameter comparison table As the objective of URT service, passenger fow is the basis Survey (s) Estimation (s) Relative deviation for the URT transportation organization. Te characteristics Peak 169 177 4.73% ofthepassengerfowdistributionhavealargeimpactonthe transportation plan and efciency. To better understand the (c) Transfer walking-time parameter comparison table composition of passenger fow and its characteristics, we have Transfer Estimation Relative developed a data-driven approach to estimate passengers’ Station Survey (s) Direction (s) deviation travel pattern. A space-time-sequence trajectory model was Xizhimen Line 4�→ Line 2 219 225 2.74% constructed based on AFC transaction data and AVL data to simulate passengers’ travel processes. Xuanwumen Line 4 �→ Line 2 240 229 4.58% An iterative maximum-likelihood estimation algorithm is presented to estimate the most likely space-time-sequence trajectory and station time parameters. A space-time- Table 6: Station parameters expectation at each subway station. sequence trajectory indicates a passenger’s travel activities Station parameter Expected value and time consumed. Additionally, the number of lef-behinds Access time at Dongwuyuan 37 s canbecalculatedbyanalyzingtherelationshipbetweena Transfer time from Line 4 to Line 2 at Xizhimen 225 s passenger’s arrival time at a platform and the train sequence. Te space-time-sequence trajectory is useful in mining Egress time from Chongwenmen 169 s passengers’ path-choice behaviors and further assists URT Lef-behind at Dongwuyuan 1 operations to better predict the future operations status of the Lef-behind at Xizhimen 1 URT network. Ourfutureresearchwillfocusontwomajorareas:frst, mining passengers’ travel pattern in cases of emergency and the distribution of relatively congested sections during peak analyzing the impact of an emergency on passengers’ path hours is similar. Te relatively congested sections mainly choices and the URT network passenger fow distribution; focus on the out-of-Beijing direction and are located around second, how to optimize the URT timetable based on passen- Central Business Districts (CBD) during of-peak and peak. ger travel demand and rescheduling in emergencies. 12 Journal of Advanced Transportation

Table 7: Detailed information of theoretical feasible space-time-sequence trajectories. No. Board Train Origin Transfer Destination Lef-behind 1S443, 1 88 s 65 s 676 s none 422219 1Q445, 2 88 s 205 s 489 s once at Dongwuyuan 162221 1Q445, 3 88 s 205 s 339 s once each at Dongwuyuan and Xizhimen 022222 1Q445, 4 88 s 355 s 189 s once each at Dongwuyuan and Xizhimen 322223 1A447, 5 88 s 235 s 189 s twice at Dongwuyuan and once at Xizhimen 322223

700 600

600 500

500 400 400 300 300 200 200

100 100

0 0 3 6 9 2 4 6 8 36 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 10 12 14 16 18 20 22 24 26 28 30 32 34 (a) Of-peak, Dongwuyuan access walk time (b) Peak, Dongwuyuan access walk time 140 350

120 300

100 250

80 200

60 150

40 100

20 50

0 0 100 110 120 130 140 145 150 155 160 165 170 180 190 200 100 110 120 130 140 150 155 160 165 170 175 180 190 200 210 220 230 240 250 260 270 (c) Of-peak, Chongwenmen egress walk time (d) Peak, Chongwenmen egress walk time 350 450 400 300 350 250 300 200 250

150 200 150 100 100 50 50 0 0 100 130 160 180 190 200 210 220 230 240 250 260 270 300 330 360 390 420 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 330 360 390 420 (e) Xizhimen transfer walk time (f) Xuanwumen transfer walk time Figure 5: Estimation result of distribution of station-time parameters. Journal of Advanced Transportation 13

Table 8: Section passenger-fow comparison results.

Section name TOCC Estimate Relative deviation Xuanwumen - Caishikou 33458 33392 -0.20% Caishikou – Taoranting 31898 31890 -0.03% Jintailu – shilipu 31502 31576 0.23% Hujialou – Jintailu 30171 30287 0.38% Taoranting – Beijing South 28638 28651 0.03%

800

700

600

500

400

300

200

100

0 01234 Figure 6: Distribution of number of lef-behinds at Dongwuyuan.

t 18:08:16 18:05:37

192225 052224

322223

022222

162221

17:48:00 102220 1Q453 422219 1S451 17:45:30 17:43:15 1Y449 17:43:00 1A447 17:41:25 1Q445 17:39:25 17:37:28 1S443 17:35:28 17:34:00 Entry gate

Dongwuyuan Xizhimen Chongwenmen

Figure 7: Space-time-sequence trajectory-estimation result. 14 Journal of Advanced Transportation

Network passenger fow distribution (17:00 - 18:00)

load

150% 0% fux (p/h)

35k 0 Figure 8: Distribution of URT network passenger fow during peak hours.

Data Availability References Te data used to support the fndings of this study have not [1] “Urban rail transit statistical analysis report,”http://www.camet been made available because AFC transaction data and AVL .org.cn. data are recorded during actual operations. Tese data can [2] “National bureau of statistics of China,” http://www.stats be mined for too much information and relate to passenger .gov.cn/. travel privacy as well as trafc safety. Readers can access [3] “Transport department of the government of the hong kong the distribution of Beijing URT network passenger fow at special administrative region,” http://www.td.gov.hk. https://map.bjsubway.com/. If necessary, we can process the [4]J.F.Guan,H.Yang,andS.C.Wirasinghe,“Simultaneous data and provide it. optimization of transit line confguration and passenger line assignment,” Transportation Research Part B: Methodological, vol. 40, no. 10, pp. 885–902, 2006. Disclosure [5] B. Yu, Z. Yang, C. Cheng, and C. Liu, “Optimizing bus transit network with parallel ant colony algorithm,” in Proceedings of Te data in this paper are based on research supported by the the Eastern Asia Society for Transportation Studies,vol.5,pp. Beijing TOCC. 374–389, 2005. [6] H. Niu and X. Zhou, “Optimizing urban rail timetable under time-dependent demand and oversaturated conditions,” Trans- Conflicts of Interest portation Research Part C: Emerging Technologies,vol.36,pp. 212–230, 2013. Te authors declare that they have no conficts of interest. [7] X. Chen, L. Zhou, Y.Yue et al., “Data-driven method to estimate the maximum likelihood space-time trajectory in an Urban Rail Transit system,” Sustainability,vol.10,no.6,article1752,2018. Acknowledgments [8]C.O.TongandS.C.Wong,“Astochastictransitassignment model using a dynamic schedule-based network,” Transporta- Tis work was fnancially supported by the Fundamen- tion Research Part B: Methodological,vol.33,no.2,pp.107–121, tal Research Funds (Grant T17JB00040), the Fundamen- 1999. talResearchFundsfortheCentralUniversities(Grant [9] C. O. Tong and S. C. Wong, “A schedule-based time- 2018RC012), and National Key R&D Program of China dependent trip assignment model for transit networks,” Journal (2018YFB1201402). of Advanced Transportation,vol.33,no.3,pp.371–388,1999. Journal of Advanced Transportation 15

[10] J. Moller-Pedersen, “Assignment model for timetable based [25] M. H. Poon, S. C. Wong, and C. O. Tong, “A dynamic schedule- systems (TPSCHEDULE),” in Proceedings of 27th European based model for congested transit networks,” Transportation Transportation Forum, Seminar F, pp. 159–168, Cambridge, Research Part B: Methodological,vol.38,no.4,pp.343–368, England, 1999. 2004. [11] O. A. Nielsen and G. Jovicic, “Alarge-scale stochastic timetable- [26] Y. Sun and P. M. Schonfeld, “Schedule-based rail transit path- based transit assignment model for route and submode choices,” choice estimation using automatic fare collection data,” Journal in Proceedings of 27th European Transportation Forum, Seminar of Transportation Engineering,vol.142,no.1,article04015037, F, pp. 169–184, Cambridge, England, 1999. 2016. [12] R.-H. Xu, Q. Luo, and P. Gao, “Passenger fow distribution [27]J.Shi,F.Zhou,W.Zhu,andR.Xu,“Estimationmethodof model and algorithm for urban rail transit network based on passenger route choice proportion in urban rail transit based multi-route choice,” Journal of the China Railway Society,vol. on AFC data,” Journal of Southeast University (Natural Science 31,no.2,pp.110–114,2009. Edition),no.1,pp.184–188,2015. [13] Y. Hamdouch and S. Lawphongpanich, “Schedule-based transit assignment model with travel strategies and capacity con- straints,” Transportation Research Part B: Methodological,vol. 42,no.7-8,pp.663–684,2008. [14] M. E. Ben-Akiva, S. Gao, Z. Wei, and Y. Wen, “A dynamic trafc assignment model for highly congested urban networks,” Transportation Research Part C: Emerging Technologies,vol.24, pp.62–82,2012. [15] M. Cepeda, R. Cominetti, and M. Florian, “A frequency- based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria,” Transportation Research Part B: Methodological,vol. 40, no. 6, pp. 437–459, 2006. [16] R. D. Connors and A. Sumalee, “A network equilibrium model with travellers’ perception of stochastic travel times,” Trans- portationResearchPartB:Methodological,vol.43,no.6,pp.614– 624, 2009. [17] J.-D. Schmocker,¨ M. G. H. Bell, and F. Kurauchi, “A quasi- dynamic capacity constrained frequency-based transit assign- ment model,” Transportation Research Part B: Methodological, vol. 42, no. 10, pp. 925–945, 2008. [18] C. O. Tong and S. C. Wong, “Apredictive dynamic trafc assign- ment model in congested capacity-constrained road networks,” Transportation Research Part B: Methodological,vol.34,no.8, pp.625–644,2000. [19] J. K. Eom, J. Y. Song, and D.-S. Moon, “Analysis of public transit service performance using transit smart card data in Seoul,” KSCE Journal of Civil Engineering,vol.19,no.5,pp.1530–1537, 2015. [20]T.Stasko,B.Levine,andA.Reddy,“Time-expandednetwork model of train-level subway ridership fows using actual train movement data,” Transportation Research Record: Journal of the Transportation Research Board,vol.2540,no.1,pp.92–101,2016. [21]W.L.Wang,S.M.Lo,andS.B.Liu,“Aggregatedmetro trip patterns in urban area of hong kong: evidence from automatic fare collection records,” Journal of Urban Planning & Development, vol. 141, no. 3, pp. 2692–2704, 2015. [22] R. Xu, Y.Li, W.Zhu, and S. Li, “Amulti-modal evacuation model for metro disruptions: based on automatic fare collection data in Shanghai, China,” in Proceedings of the 95nd Annual Meeting of the Transportation Research Board,2015. [23] H. Niu, X. Zhou, and R. Gao, “Train scheduling for minimizing passenger waiting time with time-dependent demand and skip- stop patterns: nonlinear integer programming models with linear constraints,” Transportation Research Part B: Methodolog- ical,vol.76,pp.117–135,2015. [24] T. Kusakabe and Y. Asakura, “Behavioural data mining of transit smart card data: a data fusion approach,” Transportation Research Part C: Emerging Technologies,vol.46,pp.179–191, 2014. International Journal of Rotating Advances in Machinery Multimedia

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