Research Article Minimizing Metro Transfer Waiting Time with AFCS Data Using Simulated Annealing with Parallel Computing

Hindawi Journal of Advanced Transportation Volume 2018, Article ID 4218625, 17 pages https://doi.org/10.1155/2018/4218625

Xiaobo Liu ,1,2 Minghua Huang ,1 Hezhou Qu ,1,2 and Steven Chien 3

1 School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610000, China 2National Engineering Laboratory of Integrated Transportation Big Data Application Technology, Chengdu, Sichuan 610000, China 3John A. Reif, Jr. Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA

Correspondence should be addressed to Hezhou Qu; [email protected]

Received 16 April 2018; Revised 10 September 2018; Accepted 18 September 2018; Published 4 October 2018

Academic Editor: Luigi Dell’Olio

Copyright © 2018 Xiaobo Liu 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.

Coordinating train arrivals at transfer stations by altering their departure times can reduce transfer waiting time (TWT) and improve level of service. Tis paper develops a method to optimize train departure times from terminals that minimizes total TWT for an urban rail network with many transfer stations. To maintain service capacity and avoid operational complexity, dispatching headway is fxed. An integrated Simulated Annealing with parallel computing approach is applied to perform the optimization. To demonstrate model applicability and performance, the Shenzhen metro network is applied, where passenger fows (i.e., entry, transfer, and exit) at stations are approximated with the automatic fare collection system (AFCS) data. Results show that the total TWT can be signifcantly reduced.

1. Introduction Oyster Card in London, etc.). With the AFCS data in this study, the temporal and spatial passenger entry/exit distri- For large-scale metro networks, large numbers of passengers butions and transfer volumes at stations can be determined. arrive simultaneously at transfer stations, especially during We aim to seek a quick and easy-to-implement method peak periods. Transfer time incurred by passengers has been to efectively reduce TWT without increasing operator’s considered as an index of service quality. Synchronizing cost and operational complexity. To this end, we alter the vehicle arrival times to facilitate efective timed transfer is train departure times from terminals but fx the dispatching desirable. headways. Te research problem is combinatorial, which Transfer time is defned in this study as the elapsed time is difcult to solve with classic optimization methods. An between a passenger alighting from a “delivery” train to integrated Simulated Annealing (SA) with parallel computing boarding a “pickup” train, which consists of walking time (PC) approach is developed to search for the solution that between platforms and transfer waiting time (TWT) for the minimizes TWT. “pickup” train. Walking time is dependent on the layout of Te remainder of this paper is structured as follows. the station and walking speed, while TWT is afected by the Section 2 describes previous research and practices related arrival/departure times of the trains and walking time. To to this study. Te development of the proposed model and minimize TWT for a large metro network, the relationship solution method to solve the study problem are discussed between demand (i.e., spatiotemporal transfer passenger in Sections 3 and 4, respectively. In Section 5, the Shenzhen distribution) and supply (i.e., network confguration, service Metro in China is employed as a case study to demonstrate frequency, and departure time) must be carefully formulated. the efectiveness of the solution algorithm and the benefts of Automatic fare collection systems (AFCS) have been the optimized solution. Finally, the paper concludes with a applied in many metro systems (i.e., Metro Card in New York, summary of fndings and future research needs. 2 Journal of Advanced Transportation

2. Literature Review minimized total transfer wait time. Using GA and the Frank- Wolfe algorithm, Xiong et al. [28] synchronized arrivals of Coordinating train arrivals to facilitate transfer activities in community shuttles linking with a metro service, which a transit network ofers an efective way to reduce transfer yielded the minimum total cost. Due to the absence of the time. Transfer time is an important indicator representing AFCS data, the distribution of passenger arrivals at stations in the service quality and the efciency of public transit systems most previous studies discussed above was either simplifed [1–3]. Previous studies have focused on minimizing total or assumed. Few studies have applied the AFCS data for waiting time [4–8] or maximizing the number of synchro- analyzing passenger demand and route choices [29–31] and nized vehicle arrivals [9, 10] at transfer nodes. Recently, optimizing timetable [32]. several studies focused on the frst and last trains timetabling Te primary contribution of this study is to collect, optimization, with objectives such as maximizing passenger process, and generate the spatiotemporal origin-destination transfer connection headways [11], minimizing the connec- (OD) demand with the AFCS data, approximate transfer tion time between frst trains [12], incorporating bilevel volumes at stations, and apply that to minimize total TWT objectives in which the upper level maximizes social beneft for a large metro network with many transfer stations. Opti- (the number of passengers transferring to the last trains mizing such a coordinated transfer problem is challenging successfully) with minimum total subsidy and the lower because it is combinatorial and difcult to solve with classic level minimizes revenue loss for the operating companies optimization methods. A method that integrates SA with [13], and maximizing the total number of successful transfer PC (SAPC) is developed and implemented to search for the passengers and minimizing waiting times for rail-to-bus optimal solution. passengers [14]. Several studies optimized coordination of transfers at a 3. Methodology single hub station. Feng et al. [15] developed an optimization model for the arrival and departure times of connecting Te mathematical model is formulated and discussed in this trains, which minimized average waiting time. Liu et al. [16] section, and the objective is to minimize total TWT. To developed a multiobjective optimization model to minimize maintain service capacity and avoid operational complexity, the total transfer waiting time, train operating cost, and the preplanned dispatching headways are fxed. Te decision fuctuation of departure interval with given transfer volumes. variables therefore consist of train departure times from the Te optimized results were found using a genetic algorithm beginning terminals of all lines in the study network. Te (GA). Chen and Wang [17] minimized passenger waiting time development of the proposed model is discussed next, and via synchronizing train arrivals and departures and revealed the variables used to formulate the model are summarized in the relationships between three infuencing factors (transfer Table 1. forms, walking distance in the station, and congestion degree of passenger fow) and transfer time. 3.1. A General Metro Network. A general metro network Optimizing coordination among multiple transfer sta- consists of many routes defned as � and a set of stations defned as . A route is represented by two unidirectional tions was conducted by previous studies. Assuming uniform passenger arrivals, Wong et al. [18] presented a mix-integer lines (i.e., outbound and inbound). Line belongs to a set of lines denoted as �. Each line consists of a set of stations programming model to optimize nonperiodic timetable. A ∈ heuristic approach was employed to minimize the waiting �,and � . Each station is given a unique station ID. For example, station ID of line 1 begins with 1 and ends at time by justifying the train running time between stations, +1 dwell times at stations, and departure and turnaround times 1, and then the IDs of stations on line 2 start from 1 and end at 2.Tus,stationsoflinel ( = 2,3,...,) are at terminals. Fang et al. [19] minimized total waiting time +1 yielded by the optimized vehicle arrival and departure times labeled from �-1 through �.Forlinel, the hourly service frequency is denoted as �, and a train is indexed by m (= at transfer stations. Aksu and Akyol [20] optimized integer- 1,2,..., ratio headways to minimize total cost. Considering random �). To formulate TWT incurred by passengers at a passenger arrivals, Liu et al. [21] minimized total waiting transfer station, a link-node diagram is shown in Figure 1 where transfer station is also labelled as � for line as well time by altering the train departure times found by SA. To � ,� ∈ improve transfer efciency, Wu et al. [22] optimized vehicle as �� for line ( � � ). Transfer station has four IDs departure time, headway, running time, and dwell time using associated with four connecting lines. GA. To formulate the proposed model, the following assumptions are made and subsequently explained: Considering probabilistic vehicle travel time, Chowdhury and Chien [23, 24] synchronized vehicle arrivals for an (1) Te platform-to-platform walking time at a transfer intermodal transit network to minimize total cost. Te study station is given (obtainable from a survey or feld network consisted of a train line with multiple transfer observations), which may vary among stations stations and multiple feeder bus routes connecting at the (2) Passenger arrival distributions at stations will not be station. Shrivastava and Dhingra [25, 26] used GA to coor- afected by the change of train departure time dinate an integrated bus-train service which minimized total (3) Te choice of transfer location(s) is determined based cost consisting of user and vehicle operating costs. Li et on the shortest travel time, which is the sum of initial al. [27] optimized bus timetables for a feeder route which waiting time, in-vehicle time, and TWT Journal of Advanced Transportation 3

Table 1: Notations. Variables Units Description

��/�� - Arrival / Departure time of train m at station i of line l

� trains/hour Train frequency of line l

ℎ� min Headway of line l // -Indexofstations(i, j,∈) � � � / - Index of lines (, ∈� and , =1,2,...,)

� -Tesetoflines � � / - Index of pick-up/delivery trains ( = 1, 2, . . . , �,and =1,2,...,�� ) -Tesetofstations � �� pass/s Number of passengers from stations i to j via transfer station s at t

- Index of routes (∈�,and = 1, 2, . . . , �) � � ��,��,� pass Number of transfer pass from train line to train m line l at s � � ��,��,� pass Number of pass from sta. i to j on train line via train m line l at s

�/�/� min/pass Average TWT at transfer station s /onlinel /onrouter min Total TWT

�/�/� min TWT at transfer station s /onlinel /onrouter

� - Te set of routes

- Index of transfer stations (∈�,and=1,2,...,)

� - Te set of transfer stations -Indexoftime � � ��,��,� min TWT from train of line to train m of line l at station s � �� min Walking time from line to l at transfer station s

�� min Passenger travel time from stations i to j via transfer station s

�� min In-vehicle time from stations i to j via transfer station s

V� min Adjustment of schedule departure time for trains on line l

� min Initial waiting time at station i � � ��,��,� - Binary var., 1 as passengers from train line to train m line l via s;otherwise,0

�� - Binary var., 1 as transfer station s is on line l;otherwise,0

�� - Binary var., 1 as line l belongs to route r;otherwise,0

(4) Te number of passengers making more than two be determined by employing a time-dependent shortest path transfers to reach their destination is negligible algorithm which will be discussed later in Section 3.2.2. Once (5) Train running times between stations and dwell times the transfer location(s) is determined, the passengers who at stations are deterministic within a period; however, enter station at time and exit station via transfer station � they may vary over diferent periods denoted as �� (see Figure 2) can be approximated. Considering required platform-to-platform walking � � 3.2. Demand Characteristics. In this study, the passenger OD time, passengers can take train of line to transfer demand distribution can be derived from the AFCS records. station and wait for train of line . For example, as train � � Passengers who access station are classifed into two types, -1 of line departs from station at time ��−1,�,�� and direct (without transfer) and indirect (with transfer), and � � the following train of line departure time is �� , they must swipe the card when entering and exiting a station. the number of indirect passengers (i.e., the shaded area in Note that indirect passengers do not need to swipe cards at Figure 2) from station to station via transfer station s transfer stations. (denoted as ��,��,�) can be determined by time interval � [��−1,�,�� , �� ), and transfer connection availability 3.2.1. Indirect Passenger Arrival Distribution. With the AFCS �� data, the temporal passenger arrival distribution at any � � ,��,�.Tus, � −1 station and their destination (station j)canbedetermined; �� however, the transfer location is not available. As discussed ��,��,� = �� ,��,�,∀,,,, ,, (1) �=� in assumption (3), passengers would use the shortest travel ��−1,�,�� time paths to reach their destinations. Since passenger arrival time at station and posted train schedule are known, the Note that ��,��,� is a binary variable. It is equal to � � travel path and transfer location(s) for each passenger can 1 indicating that train of line arrives early, so that 4 Journal of Advanced Transportation

Line 4

N3+1 N3

N3+2 N3-1

rm l i,mlj ,s N3+3 N3-2

u4-1 u3+1

u u 1 N N 1 N 1 2 3 1-1 u1 1+ 1-2 1- 1 Line 1 u4 s u3 Line 2 u2 u 1 N N 2 N 1 N2 N2-1 N2-2 u2+1 2- 1+3 1+ 1+

u4+1 u3-1

N4-2 N2+3

N4-1 N2+2

N4 N2+1 Line 3 Intermediate station Inbound Direction End Terminal Outbound Direction Transfer Station Transfer Direction

Figure 1: Confguration of a general transfer station.

t q ijs can be found by applying the Dijkstra algorithm (DA) [33]. Otherwise, an enhanced Dijkstra algorithm (EDA) shall be developed for dealing with the time-dependent travel time. Te train arrival and departure time at various stations will be recorded using actual time schedule, which is diferent from starting at zero time used in DA. A brief discussion of the

D   D   D   D  D   proposed EDA is summarized below. m -3,i,l m -2,i,l m -1,i,l m il m +1,i,l Time t Te travel time of a path is dependent on the passengers’ Figure 2: Temporal distribution of transfer passenger arrivals at arrival time at the origin station. To determine the shortest origin station i. in-vehicle time from station to station k, all links which have their start station ID equal to station and end station ID equal to station can be searched through the network successful transfer can be made to train line at s; otherwise, it is 0. Tus, layout (note that the metro network has specifc direction of operation for each line). For each of these links, the frst train � � � � ,��,� departuretimeatstation which is greater than the passenger � arrival time at station can be obtained by the timetables. Te 1; �� >�� +�� Trains and are connected (2) = train and passenger arrival time at station when traveling by 0; ≤ � � +� �� Otherwise this link is equal to the corresponding departure time of the start station plus the travel time from the start station to 3.2.2. Enhanced Dijkstra Algorithm (EDA). Te shortest path the end station of the link which can be extracted by the of a network where the travel time is not time-dependent timetables, too. Journal of Advanced Transportation 5

If a transfer is needed at a station, transfer time must be 3.3. Objective Function. It is worth noting that the average included in the travel time of the appropriate link. Note that access time for passengers swiping metro cards, entering the transfer times vary with diferent transfer stations. Te link station, and walking to the boarding area is given, which will which gets the shortest travel time (including the passenger not afect the optimized solution and thus can be omitted. Te initial waiting time at origin station, in-vehicle time, and objective total TWT denoted as is the sum of TWT incurred transfer waiting time) from stations to is chosen as the by all transfer passengers. Tus, shortest path. Te proposed algorithm will fnd the shortest � �� paths for all passengers from the origin station to destination � � � � � = � � � � station. � � ,��,� � � ,��,� (9) � �=1 �=1 �=1 ��=1 ��=1 Transfer passengers �� will select the best transfer location to minimize their travel time denoted as �� .Tus, where ��,��,� is afected by the justifcation of train departure times at the beginning terminal of line l (i.e., the decision min �� ,∀,, (3) variable, denoted as V�). Te objective is to minimize R; therefore, the objective function is Note that �� is the sum of initial waiting time, in-vehicle time, and TWT. Tus, min (10)

= + + � � �� ,��,� (4) 3.4. Constraints. To maintain service capacity without where the initial waiting time, �,isthetimeforpassengers increasing the operation cost, the service headway of each � � who wait for boarding on train of line at station i,which line is not varied. Terefore, the constraints considered is the elapsed time from passenger arrival time to the train in most previous studies, such as capacity and feet size � � departure time � �� .Tus, constraints, will not be our concerns. Te relation among the “delivering” train arrival time, walking time, and “pickup” � =�� − (5) train departure time will be employed to minimize total TWT. When the departure time of train of line at station Te in-vehicle time, denoted as ��,includesthein- � � � vehicletimefromstation of line to transfer station and s ( ��) is greater than the arrival time of train line � � � then to station of line .Tus, ( � �� )pluswalkingtime( � ��), transfers can be successfully made and ��,��,� is equal to 1. Tus,

= � � − � � +! − " �� (6) �� >�� +��,∀,, (11) where �� and �� represent the arrival and departure times � � Note that only one pickup train of line has connectivity of train on line at station i, respectively. Finally, � � ,��,� � � can be calculated by (7). with delivery train of line .Tus,

�� 3.2.3. Transfer Passengers. As discussed earlier, we assume ��,��,� =1, ∀, ,,, (12) that passengers would use transfer station(s), if necessary, �=1 which minimizes their travel time. For passengers who expect � � where � represents the service frequency on line l. to transfer from train of line to train of line at s, the TWT denoted as ��,��,� is determined by the departure time of pickup train denoted as �� and the arrival time of 3.5. Performance Analysis. To evaluate the efectiveness of � delivery train denoted as �� , the platform-to-platform the optimized solution on system operation, we propose to walking time is ��, and transfer connection availability is investigate total and average TWT at diferent level of detail. ��,��,�.Tus, Equations to assess system performance are formulated and discussed below. ��,��,� = �� −�� −�� ,��, (7) 3.5.1. Transfer Waiting Time (TWT). Te station-based total ∀�,�,,, TWT, denoted as �, is the sum of TWT incurred by transfer In the interest of simplicity, the average walking time is passengers at transfer stations .Tus, � distance divided by walking speed. Since each “route” is split � �� into two unidirectional lines, there are eight transfer fows at � = ��,��,��,��,�,∀ (13) a general station . Te number of transfer passengers from �=1 �=1 � � � � � =1 � =1 train of line to train of line at is denoted as ��,��,�, which can be calculated by Te line-based total TWT, denoted as �,isthesumof TWT incurred by transfer passengers at all transfer stations � −1 �� from other lines to line .Tus, ��,��,� = ��,��,�,∀, ,,, (8) �=� +1 �=� +1 � � � �� −1 � � � � = ��,��,��,��,��,∀ (14) Note that ��,��,� can be determined by (1). �=1 �=1 ��=1 ��=1 6 Journal of Advanced Transportation

where �� equal to 1 means that station is on line l;otherwise, Step 2. With initialized information, open the parallel pool (0) it is 0. Tus, and calculate total TWT denoted as (see (9)) with PC (split the execution of calculation in serial over the workers in 1; Transfer station on line (0) a parallel pool). Let � = . Set the index of SA temperature �� = (15) 0; Otherwise iteration z =0.

Teroute-basedtotalTWT,denotedas�,isthesum Step 3. Search for a provisional V� with SA, determine �1�, of TWT consumed on the two lines associated with route . and calculate total TWT denoted as � with PC. Let =+1. Tus, Note that �1� is updated based on V�, which must be satisfed � with = ,∀ � � �� (16) =(0) + V , ∈ [0, ] �=1 �1� �1� � �1� (21) where �� equal to 1 means that line is associated with route where the planning time horizon of departure time is denoted .Otherwise,itis0.Tus, as [0, T]. Terefore, the adjusted departure time �� and arrival time �� at each station can be derived accordingly 1; Line belongs to Route (0) based on the existing departure time �� and arrival time �� = (17) (0) 0; Otherwise ��.Tus, (0) = + V (22) 3.5.2. Average Transfer Waiting Time. Te average TWT at s, �� denoted as �,istotalTWTdividedbythenumberoftransfer (0) �� = + V� (23) passengers. Tus, �� where the allowable adjustment range of V� is deviating within = � ,∀ � � the dispatching headway of line l, denoted as ℎ�.Tus, � �� (18) ∑ ∑ ∑ ∑ � � �=1 �=1 ��=1 ��=1 � � ,��,� ℎ ℎ − � < V < � (24) Te average TWT of line l, denoted as �,is � divided by 2 � 2 the number of transfer passengers of line .Tus, ⩾ Step 4. Compare � and �.If � �,gotoStep5; = � ,∀ = � � otherwise, let � � and denote the current solution as � �� (19) ∑ ∑ ∑ ∑ � � �=1 �=1 ��=1 ��=1 � � ,��,� �� the provisional solution; then go to Step 6. Similarly, the average TWT of route r, denoted as �,is � Step 5. Verify the Metropolis criterion. Calculate �� = divided by the number of transfer passengers of route .Tus, � −�.Ifexp(−��/�)>( is a random number), ∈(0,1),let� =�; otherwise, go to Step 6. = � ,∀ � ∑� (20) �=1 � � Step 6. Reduction criteria of temperature: if >,�+1 = �, repetition counter u =0,gotoStep7;otherwise,goto 4. Solution Algorithm Step 3. Set z = z+1.

To minimize total TWT for a large metro network consisting Step 7. Check if the stop criteria (e.g., maximum iteration Z) of multiple lines intersecting at many stations, the study are satisfed. If positive, go to Step 8; otherwise, go to Step 3. problem is combinatorial with large feasible solution spaces. Te developed model is therefore difcult to solve with classic Step 8. Terminate SA search and output the optimized solu- ∗ ∗ ∗ ∗ ∗ optimization methods. With SA, the computation time could tions V �, �1�, ��, ��,and . Update train arrival be long due to large passenger demand, number of running and departure times at each station based on the results from trains, and the size of the study network. Te primary reasons ∗ (0) ∗ for using PC (splitting large problems into smaller ones that �� =�� + V� (25) are solved simultaneously) are to save time, to solve larger ∗ (0) ∗ problems, and to provide concurrency [34]. �� =�� + V� (26) We thus apply an integrated SA with PC (using MATLAB sofware) to search for the optimized solution and compute 5. Case Study the objective total TWT. Te procedure is discussed below and illustrated in Figure 3. 5.1. Study Metro Network and Associated Data. Te case study employs the year 2013 metro network in Shenzhen, China, Step 1 (initialization). Input SA parameters (i.e., initial solu- consisting of 5 routes intersecting at 13 transfer stations. Con- tion, temperature, upper and lower bounds, etc.) and baseline sidering inbound and outbound trafc, the network is repre- model parameter values (i.e., train arrival and departure sented by 10 directional lines with 262 stations as shown in times of the existing timetable. Figure 4. Te baseline model parameter values were provided Journal of Advanced Transportation 7

Start Initialization

－！４，！＂Ⓗ workers (0) R parfor Calculate with initial －！４，！＂Ⓗ solution using PC client (0) (Rx=R ), z=0

u=0

Search provisional l with SA

u=u+1

－！４，！＂Ⓗ workers

parfor R －！４，！＂Ⓗ Calculate y client using PC

Yes Ry

exp(-ΔRxy /tz )>? Yes ∈( 0, 1)

No Rx=Ry

No u>U ?

Yes

z=z+1

Reduce Temperature tz+1= tz

No z>Z?

Yes ∗ ∗ ∗ ∗ ∗ Output optimized solution  l, D m1l, D mil, A mil and R End

Figure 3: Step procedure of the proposed SAPC. by the operating agency, including a spatiotemporal passen- am) and of-peak (i.e., 12:00 pm ∼ 1:00 pm). Tere are 111,887 ger OD demand matrix, timetables, and average passenger and 17,984 transfer passengers in AM peak and of-peak, walking time from one line to another at each transfer station. respectively, which resulted in transfer volumes of 138,702 Te ridership distribution over time on a typical weekday and 22,107 because some passengers need more than one is shown in Figure 5. In addition to minimizing total TWT, transfer. Te input data include train departure and arrival the beneft before and afer the implementation of the times, transfer walking time, and other operator parameters, optimized solution will be assessed. which are summarized in Appendices A and B. To demonstrate the model performance applied in dif- ferent levels of congestion for the metro network, we apply 5.2. Passenger Demand. When a passenger either enters the AFCS data collected in the AM peak (i.e., 8:00 am ∼ 9:00 or exits a station, the time is reported and archived in 8 Journal of Advanced Transportation

Line 1 Route A Line 2 Line 3 Route B Line 4 Line 5 Route C Line 6 Line 7 Route D Line 8 Line 9 Route E Line 10 Transfer Station Outbound Inbound Figure 4: Te studied Shenzhen metro network.

350000 trip from Station 33 of line 2, transfer at station 2,andthen 300000 ended that trip at Station 86 of line 3. 250000 As shown in Table 3, the transfer demand matrix at a 200000 transfer station 1 records transfer volume at each of 8 transfer 150000 directions (see Figure 1). 100000 50000 5.3. Optimized Results. Te SA parameter values include Number of Passengers (Pass) Passengers of Number 0 initial temperature 0=10,000, reduction parameter of tem-

0~1 1~2 2~3 3~4 4~5 5~6 6~7 7~8 8~9 perature =0.9, number of temperature iterations Z = 1,000, 9~10 10~11 11~12 12~13 13~14 14~15 15~16 16~17 17~18 18~19 19~20 20~21 21~22 22~23 23~24 and number of iterations at current temperature U=100. Time For the AM peak, the computation time to search for Figure 5: Temporal distribution of ridership. the optimized solution using SA requires 85.7 hours to yield the minimum total cost (Intel(R) Xeon(R) CPU E5- 1620 v4 @3.50 GHz 3.50 GHz with 32.0 GB RAM and 64- bit Operating System). However, SAPC requires 8.5 hours to AFCS.Tus,thepassengerin-andout-fowdistributions yield the optimized result. can be accurately derived. Table 2 illustrates the sample data For the of-peak, the computation time with SA only was extracted from the AFCS database, which include passen- 8.5 hours, which is signifcantly less than that for the AM ger ID, transaction time (entering and exiting a station), peak because of less transfer demand and reduced service line/station ID where a transaction occurred, and transac- frequency. It was found in Table 4 that as the transfer demand tion type. Te sample data represent trips initiated by two is reduced (i.e., of-peak) using SAPC seems inefcient (i.e., passengers (i.e., ID 32286198 and ID 322357672). Passenger 9.5 hours) which costs more computation time to fnd the 32286198 began his/her journey from Station 218 and ended at optimized solution than that of solely using SA (i.e., 8.5 Station 230 on line 9, who traveled without transfer. Te same hours). Tis computing in serial loops generally does not passenger initiated the 2nd trip in the afernoon on the same beneft from conversion into PC method for a relatively day. On the other hand, passenger 322357672 began his/her simple computational task in of-peak. Because the time Journal of Advanced Transportation 9

Table 2: Sample data from AFCS.

Passenger Card ID Transaction time stamp Line ID Station ID Transaction type No. 322861698 2013-10-16 08:26:18 9 218 Entry 322861698 2013-10-16 09:00:35 9 230 Exit 1 322861698 2013-10-16 13:31:17 10 241 Entry 322861698 2013-10-16 14:07:50 10 253 Exit 322357672 2013-10-1607:54:19 2 33 Entry 322357672 2013-10-16 08:50:52 3 86 Exit 2 322357672 2013-10-16 11:40:27 4 93 Entry 322357672 2013-10-16 12:57:47 1 28 Exit

Table 3: Train-to-train transfer demand at station 1.

Line ID 1 2 3 4

1--��1,�3,�1 ��1,�4,�1

2--��2,�3,�1 ��2,�4,�1

3 ��3,�1,�1 ��3,�2,�1 --

4 ��4,�1,�1 ��4,�2,�1 --

Table 4: Results from diferent solution algorithms.

AM peak (Of Peak) Computation time Minimized TWT Reduced TWT Solution algorithm (hr) (min) (min) SAPC 8.5 (9.5) 276,194.1 (65,464.7) 41,851.9 (9,822.8) SA 85.7 (8.5) 283,626.3 (65,481.1) 34,419.7 (9,806.4)

×105 needed for data transfer is signifcant compared with the time 3.5 needed for computation, therefore, the results show that the AM peak PC method can be useful for some loop iterations that require 3 Of-peak long times to execute with big data. Te total TWT of the studied AM peak and of-peak were 2.5 signifcantly reduced by 41,851.9 minutes and 9,822.8 minutes, respectively, afer implementing the adjusted train departure 2 times at the beginning stations. Te yielded minimum total TWT by the solutions found using SA and SAPC are fairly 1.5 close, which indicates that SAPC is very efcient. TWT (Min) Total Figure 6 shows the relationship between total TWT and 1 the number of iterations using SAPC. It is notable that total TWT was reduced quickly at the frst 200 iterations and then 0.5 stably converged to a constant afer the 500th iteration. 0 200 400 600 800 1000 1200 Results under existing operation (EO) and optimized Iteration operation (OO) are compared in this section. EO refers to Figure 6: Total TWT vs. iteration with SAPC (AM and of-peak). train departures following the existing timetable, while OO refers to the fact that trains will be dispatched based on the optimized departure times. Te diference between the departure times at the beginning terminal with EO and OO the existing schedule (i.e., negative values: -179, -174, -103, -55, -209, -142, -38, -82, -46, and -112 sec). of line denoted as V� is shown in Figure 7. It was found that the trains of lines 1, 4, 5, 8, and 10 should be dispatched later than the existing schedule (i.e., 32, 150, 14, 29, and 43 seconds, 5.4. Before and afer Analysis. With SAPC, the proposed respectively),whiletrainsoperatingonlines2,3,6,7,and9 model is applied to optimize train departure times from the should be dispatched earlier (i.e., -2, -104, -50, -72, and -45 terminals in the studied time periods. Tere are 148 trains seconds) in the AM peak. However, in the of-peak hour all dispatched during the AM peak and 85 trains dispatched in the trains’ departure times should be dispatched earlier than the of-peak. 10 Journal of Advanced Transportation

200 0

150 AM peak −50 100

50 −100

0 −150 −50 −200 −100 Of-peak

Adjustment of Departure Time (sec) Time Departure of Adjustment −150 Adjustment of Departure Time (sec) Time Departure of Adjustment −250 12345678910 12345678910 Line ID Line ID Figure 7: Optimized adjustment of departure times with SAPC (AM and of-peak).

60,000 50,000 45,000 50,000 40,000 40,000 35,000 30,000 30,000 25,000 20,000 20,000 15,000 Total TWT (Min) Total 10,000 TWT (Min) Total 10,000 5,000 0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 0 s s s s s s s Transfer Station ID 3 1 5 4 2 6 7 Transfer Station ID for Line 1 AM EO Of-peak EO AM OO Of-peak OO AM EO Of-peak EO AM OO Of-peak OO Figure 8: Total TWT with EO and OO at various transfer stations. Figure 9: Total TWT with EO and OO at transfer stations on line 1.

5.4.1. TWT at Transfer Stations. As indicated in Table 5 and However, for line 2 (the opposite direction of line 1), only Figure 8, total TWT was reduced by 13.2% (i.e., 41,851.9 2,069.1 minutes were reduced, even though there is a transfer minutes) afer adjusting the departure times within the AM volume of 20,023 passengers. Since the average TWT of line peak. Te greatest TWT saving occurred at station 10, 2 is the shortest (1.39 min) among all lines at EO, the room to whereas increased TWT was found at 6, 8,and13 with reduce average TWT was limited. relatively low transfer volumes. On the other hand, in the of-peak, there is a transfer In the of-peak period (see Table 5), total TWT was volume of 3,525 passengers who transfer from lines 3 through reduced by 13.0% (9,822.8 minutes) compared to that with 10 to line 1, which accounts for 15.9% of total transfer demand. EO. Te greatest saving was found at 5 and the least average Under OO, the TWT reduced by 2,228.6 minutes and 2,529.0 TWT was found at 10. It is worth noting that the choice minutes on lines 1 and 2, respectively. Te average TWT in the of transfer location(s) is based on the shortest travel time, AM peak is less than that in the of-peak because of shorter which has been discussed in the assumptions. Te transfer headways. However, the reduction of average TWT in the of- volumes before and afer optimization at transfer stations peak is greater than that of the AM peak. It appears that longer have changed because passengers selected diferent locations headway in the of-peak ofers more fexibility to justify the to make transfer, since the justifed train departure times have departure times at the beginning terminals. altered their shortest paths. 5.4.3. TWT by Routes. Te comparison of TWT on a route 5.4.2. TWT by Lines. Te comparison of TWT by lines is basis with EO and OO is conducted and the results are shown in Table 6. For the AM peak on line 1 (outbound summarized in Table 7. It seems that routes with heavy direction of route A, Figure 9), there is a transfer volume demand experience the greatest reductions in TWT; however, of 33,183 passengers who transfer from lines 3 through 10, it increases at some light-demand routes. which accounts for 23.9% of the total transfer demand. For route A in the AM peak, there is a transfer volume of Afer adjusting the train departure times from the beginning 53,206 passengers from routes B through E, which accounts terminal, the TWT consumed on line 1 was reduced by for 38.4% of the total transfer demand. Afer implementing 21,778.2 minutes, thus yielding the greatest saving of any line. the adjusted departure times, TWT reduced by 23,847.3 Journal of Advanced Transportation 11 -7.7% -7.9% -7.4% -3.3% -9.8% -0.2% -2.6% -5.4% -5.4% -6.0% -0.6% -17.6% +3.4% +4.0% -11.4% +4.0% -13.2% -12.2% -12.7% -10.3% -12.2% -13.0% +15.1% -33.4% +11.0% -50.9% -42.5% -42.9% change Percentage 74.2 26.2 -27.4 -48.0 -181.3 304.6 -227.3 -108.3 -610.3 -730.2 1,143.5 -850.0 -240.4 1,103.7 -1,114.4 -1,515.3 -3,811.6 -1,359.2 -1,223.2 -1,408.7 -1,626.6 -2,763.3 -9,822.8 -3,930.7 -4,338.2 -41,851.9 -13,769.8 -14,442.7 Diference (min) 3.11 1.51 1.21 1.61 3.31 1.53 3.21 1.28 OO 2.16 1.68 1.99 2.37 3.85 3.25 2.25 3.05 3.92 2.85 2.83 3.20 2.02 3.07 3.47 3.34 2.09 2.94 2.96 3.44 EO 2.51 3.51 3.01 3.19 1.77 1.82 2.01 3.41 2.61 1.69 3.33 1.80 3.72 3.32 2.57 3.57 3.30 2.03 2.79 3.50 3.28 2.29 3.68 3.06 3.48 3.49 3.80 3.00 Average TWT (min/pass) Of-peak AM peak OO 200.0 4,717.0 1,951.4 9,737.8 6,372.1 3,987.4 1,629.9 2,091.2 9,341.6 7,099.0 5,325.8 5,270.3 3,770.0 5,260.4 11,165.9 24,517.6 21,461.3 51,749.4 27,383.0 13,294.9 21,443.3 28,801.8 29,595.4 14,805.4 10,400.0 20,286.9 65,464.7 276,194.1 (min) Table 5: Comparison of station-based TWT. Total TWT EO 173.8 7,731.3 1,877.2 2,853.1 2,318.5 9,037.0 7,709.3 5,441.7 9,256.5 4,010.4 4,095.7 11,915.3 4,744.4 6,000.5 21,913.5 31,194.6 75,287.5 21,509.3 15,655.4 10,852.2 28,451.9 56,087.6 10,062.2 27,064.7 25,926.3 43,244.5 24,206.6 318,046.0 51 603 507 OO 7,163 1,528 1,726 1,247 1,452 1,229 2,210 1,065 8,833 3,339 3,655 2,823 2,052 10,611 2,466 6,440 14,177 10,381 12,156 17,590 13,357 23,821 10,327 22,107 138,702 (pass) Transfer volume 50 EO 610 537 1,331 7,163 1,718 2,721 1,425 1,022 1,240 2,199 2,100 8,833 3,632 2,595 3,350 1,464 6,432 17,579 12,126 10,381 14,177 10,619 10,327 13,454 23,724 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 ID Total 22,107 Total 138,702 Transfer station 12 Journal of Advanced Transportation -1.1% -7.5% -5.1% -7.8% -7.6% -0.1% -9.2% -3.6% -0.4% +1.7% -11.0% +3.4% +9.4% -13.2% -19.9% -37.6% -16.7% -13.0% -13.0% -25.3% -25.6% -26.9% change Percentage -6.0 -26.5 528.4 402.6 -131.2 (min) -437.6 -258.2 -705.0 -970.6 2,426.3 -5,927.1 -1,577.6 -1,610.3 -1,051.0 -2,069.1 -9,822.8 -2,529.0 -2,830.9 -2,228.6 -10,895.1 -41,851.9 -21,778.2 Diference 3.51 2.81 1.92 OO 1.28 2.61 1.99 1.48 1.09 2.55 2.33 3.43 2.59 3.65 3.23 3.49 2.92 2.45 2.77 3.46 2.64 2.96 3.48 EO 3.18 1.43 3.51 3.19 3.12 1.74 3.41 3.14 3.10 1.39 3.41 3.43 3.97 3.45 2.62 2.29 2.68 3.90 2.49 2.96 3.06 4.06 Average TWT (min/pass) Of-peak AM peak OO 6,511.0 7,001.7 5,182.3 5,193.2 7,352.6 8,977.6 7,026.3 4,759.7 4,839.4 8,620.9 48,111.4 28,177.6 11,703.4 29,627.7 15,885.2 23,516.4 27,868.9 29,568.4 25,668.8 36,066.3 65,464.7 276,194.1 (min) Total TWT Table 6: Comparison of line-based TWT with EO and OO. EO 6,537.5 5,188.3 9,881.6 7,259.9 5,810.0 8,077.3 9,325.9 5,630.8 6,370.0 23,113.8 27,737.9 11,834.6 25,751.3 11,206.2 31,205.3 75,287.5 15,356.8 57,844.5 54,038.5 30,699.8 40,463.5 318,046.0 OO 3,151 1,412 1,419 1,872 2,017 1,823 3,471 4,771 1,880 2,395 9,903 6,707 2,667 8,069 11,641 10,751 18,201 33,218 22,107 15,434 20,007 138,702 (pass) Transfer volume EO 2,311 1,814 1,916 1,991 1,332 1,802 1,462 3,525 2,720 3,234 4,754 9,908 8,067 6,698 11,657 33,183 18,228 10,736 15,448 20,023 Total 138,702 10 6 7 5 8 9 4 6 7 8 Total 22,107 9 10 5 2 3 2 4 Line ID 1 1 3 Journal of Advanced Transportation 13 -8.8% -5.4% -4.6% +1.5% +5.8% -19.3% -13.2% -27.9% -13.0% -14.0% -14.6% -22.6% change Percentage 397.2 -731.5 -695.8 2,828.9 -1,616.3 -4,757.6 -2,021.6 -7,504.7 -9,822.8 -41,851.9 -23,847.3 -13,726.0 Diference (min) 1.16 1.78 OO 2.61 1.99 3.33 2.27 2.47 3.50 3.07 3.46 2.96 2.86 EO 1.61 3.31 3.12 3.13 2.81 1.76 3.41 2.85 3.67 3.42 2.29 4.02 Average TWT (min/pass) Of-peak AM peak OO 9,942.0 15,131.9 57,437.3 77,739.1 61,735.1 11,865.7 12,194.9 16,330.2 27,588.6 51,694.0 65,464.7 276,194.1 (min) Total TWT EO 27,191.4 11,558.3 13,887.3 71,163.3 21,087.8 75,287.5 15,863.4 12,890.7 48,865.1 85,243.8 85,582.4 Table 7: Comparison of route-based total TWT with EO and OO. 318,046.0 OO 6,621 3,242 3,429 4,267 4,548 15,522 14,775 22,107 25,337 53,226 29,842 138,702 (pass) Transfer volume EO 4,113 3,146 3,453 6,759 4,636 14,765 15,490 29,885 25,356 53,206 Route ID A A D B C E B Total 138,702 D E C Total 22,107 14 Journal of Advanced Transportation 620605 08:33:14 08:31:30 08:34:51 513003 08:31:51 08:30:14 08:28:30 621903 08:28:51 08:27:14 08:25:30 514303 08:25:51 08:24:14 08:22:30 Train No. 621203 08:21:14 08:22:51 08:19:30 Table 8: Sample of existing train departure timetables. 514103 08:19:51 08:18:14 08:16:30 621103 08:16:51 08:15:14 08:10:32 08:13:32 08:16:32 08:19:32 08:22:32 08:25:32 08:28:32 08:13:30 08:06:13 08:09:13 08:12:13 08:15:13 08:18:13 08:21:13 08:24:13 08:08:30 08:11:30 08:14:30 08:17:30 08:20:30 08:23:30 08:26:30 08:02:0608:04:02 08:05:06 08:07:02 08:08:06 08:10:02 08:11:06 08:13:02 08:14:06 08:16:02 08:17:06 08:19:02 08:20:06 08:22:02 08:00:00 08:03:00 08:06:00 08:09:00 08:12:00 08:15:00 08:18:00 9 8 Station ID 1 2 3 4 5 6 7 Journal of Advanced Transportation 15 8/7 8/8 8/7 10/9 10/10 Of-peak - 1.5 1.5 4.5 4.5 4.5 4.5 Baseline values 17/19 10/10 16/16 10/10 20/20 AM Peak - min min min min min min Units Trains/hr Trains/hr Trains/hr Trains/hr Trains/hr 2 4 6 8 10 �,8 �,9 �,10 �,11 �,12 �,13 - / / / / � � / � � � � � � � � � � 1 3 5 7 9 Variables 6/6 6/6.7 7.5/7.5 7.5/8.5 7.5/8.5 Of-peak Table 9: Baseline values of model parameters. 1.5 1.5 3.5 2.5 2.5 2.5 6.5 Baseline values 3/3 6/6 6/6 3.5/3.2 3.75/3.75 AM Peak min min min min min min min min min min min min Units 2 4 6 8 10 /ℎ /ℎ /ℎ /ℎ /ℎ �,1 �,2 �,3 �,4 �,5 �,6 �,7 1 3 5 7 9 � � � � � � � � � � � � � � ℎ ℎ ℎ Variables ℎ ℎ 16 Journal of Advanced Transportation minutes (57.0% of the total reduced TWT). However, for 71671147 and supported by the Sichuan Key Research and route E with a transfer volume of 14,765 passengers (the least Development Program No. 2017GZ0371. transfer volume among the 5 routes), TWT increased by 2,828.9 minutes (5.8%). References

6. Conclusions [1] M. H. Rapp and C. D. Gehner, “Transfer optimization in an interactive graphic system for transit planning,” Transportation Tis study develops a quick and easy-to-implement method Research Record, vol. 619, pp. 27–33, 1967. to minimize total TWT with the AFCS data provided by [2] J. Bookbinder and A. Desilets, “Transfer optimization in a Shenzhen Metro in China in which the train departure times transit network,” Transportation Science,vol.26,no.2,pp.106– 118, 1992. from the beginning terminals were optimized. Te metro users can gain substantial beneft (reduced TWT) without [3] A. Adamski, “Transfer optimization in public transport,” in Computer-Aided Transit Scheduling, vol. 430 of Lecture Notes bearing additional operator’s cost. in Economics and Mathematical Systems,pp.23–38,Springer Since the transfer information is not available in AFCS, an Berlin Heidelberg, Berlin, Heidelberg, 1995. enhanced Dijkstra algorithm (EDA) was developed to search [4] W. D. Klemt and W. Stemme, “Schedule synchronization for for transfer station(s) for each indirect passenger based on public transit networks,” in Computer-Aided Transit Scheduling, their arrival time at station and posted train schedule. With pp. 327–335, Springer Berlin Heidelberg, Berlin, Heidelberg, that, the transfer volume at each station can be estimated. 1988. Te average TWT was found to be reduced more in the [5]F.CevallosandF.Zhao,“Minimizingtransfertimesinpub- of-peak period than the AM peak period because longer lic transit network with genetic algorithm,” Transportation headway ofers more fexibility to justify the train departure Research Record: Journal of the Transportation Research Board, time. Te average and total TWT based on station, line, and vol.1971,no.1,pp.74–79,2006. routewereassessed.Ingeneral,moreTWTcanbesaved [6] S. Voß, “Network design formulations in schedule synchro- at stations with greater transfer volume, albeit increasing at nization,” in Computer-Aided Transit Scheduling, vol. 386 of stations with light transfer volume. Lecture Notes in Economics and Mathematical Systems,pp.137– In addition, the developed SAPC is fairly efcient in 152, Springer Berlin Heidelberg, Berlin, Heidelberg, 1992. searching for the solution. It signifcantly outperforms SA, [7] J. R. Daduna and S. Voß, “Practical experiences in schedule especially in the peak period when the transfer demand is synchronization,” in Computer-Aided Transit Scheduling,vol. 430 of Lecture Notes in Economics and Mathematical Systems, large. As would be expected, the computational efciency is pp. 39–55, Springer Berlin Heidelberg, Berlin, Heidelberg, 1995. highly dependent on the size of solution spaces. [8] R. M. P. Goverde, “Synchronization control of scheduled train As an immediate extension of this study, we intend services to minimize passenger waiting times,” in Proceedings to enhance the developed model by considering realistic of the Transport, Infrastructure and Logistics; Competition, train operational issues (i.e., probabilistic train travel time Innovation and Creativity,vol.2,4thTRAILAnnualCongress, between stations and dwell time at stations), probabilistic 1998. passenger walking time [35] within the transfer station, and [9]A.Ceder,B.Golany,andO.Tal,“Creatingbustimetables passengers making more than two transfers to reach their with maximal synchronization,” Transportation Research Part destination. Tis enhancement would permit the developed A: Policy and Practice,vol.35,no.10,pp.913–928,2001. model to better optimize dynamic train departure times at the [10] T. Liu, A. Ceder, and S. Chowdhury, “Integrated public trans- beginning station and holding times at intermediate stations. port timetable synchronization with vehicle scheduling,” Trans- portmetrica A: Transport Science,vol.13,no.10,pp.932–954, 2017. Appendix [11] L. Kang, J. Wu, H. Sun, X. Zhu, and Z. Gao, “A case study on the coordination of last trains for the Beijing subway network,” A. Transportation Research Part B: Methodological,vol.72,pp.112– 127, 2015. See Table 8. [12]X.Guo,J.Wu,H.Sun,R.Liu,andZ.Gao,“Timetable coordination of frst trains in urban railway network: a case B. study of Beijing,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, See Table 9. vol. 40, no. 17-18, pp. 8048–8066, 2016. [13]H.Yin,J.Wu,H.Sun,L.Kang,andR.Liu,“Optimizinglast trains timetable in the urban rail network: social welfare and Conflicts of Interest synchronization,” Transportmetrica B,pp.1–25,2018. Te authors declare that they have no conficts of interest. [14]L.Kang,X.Zhu,H.Sun,J.Wu,Z.Gao,andB.Hu,“Lasttrain timetabling optimization and bus bridging service management in urban railway transit networks,” Omega,2018. Acknowledgments [15] X. Feng, X. Wang, and H. Zhang, “Passenger transfer efciency optimization modelling research with simulations,” Interna- Tis research was fnancially supported by the National tional Journal of Simulation Modelling,vol.13,no.2,pp.210–218, Natural Science Foundation of China under grant No. 2014. Journal of Advanced Transportation 17

[16] L. Liu, X. Yang, and K. Yang, “Research on the multi-objective [32]X.Guo,H.Sun,J.Wu,J.Jin,J.Zhou,andZ.Gao,“Multiperiod- transfer coordination optimization of urban rail transit trains,” based timetable optimization for metro transit networks,” Journal of Information and Computational Science,vol.12,no.5, Transportation Research Part B: Methodological,vol.96,pp.46– pp. 1855–1864, 2015. 67, 2017. [17] X. Chen and B. Wang, “Coordination and optimization of [33] E. W. Dijkstra, “A note on two problems in connexion with connecting trains in a transfer station of urban mass transit,” in graphs,” Numerische Mathematik,vol.1,pp.269–271,1959. Proceedings of the 16th COTA International Conference of Trans- [34] B. Barney, “What is parallel computing,” in Introduction to portation Professionals: Green and Multimodal Transportation Parallel Computing,2012. and Logistics, CICTP 2016, pp. 901–912, China, July 2016. [35] M. Xiao, S. Chien, and D. Hu, “Optimizing coordinated transfer [18]R.C.W.Wong,T.W.Y.Yuen,K.W.Fung,andJ.M.Y.Leung, with probabilistic vehicle arrivals and passengers’ walking time,” “Optimizing timetable synchronization for rail mass transit,” Journal of Advanced Transportation,vol.50,no.8,pp.2306– Transportation Science,vol.42,no.1,pp.57–69,2008. 2322, 2016. [19] X. Fang, L. Zhou, and M. Xia, “Research on optimization of urban mass transit network schedule based on coordination of connecting time between diferent lines,” in Proceedings of the 2010 Joint Rail Conference,pp.465–477,Urbana,IL,USA,2010. [20] D. T. Aksu and U. Akyol, “Transit coordination using integer- ratio headways,” IEEE Intelligent Transportation Systems Maga- zine,vol.15,no.4,pp.1633–1642,2014. [21]X.Liu,H.Qu,S.Chien,L.Spasovic,B.Ran,andM. Huang, “Optimizing passenger transfer coordination in a large scale rapid rail network,” in Proceedings of the Transportation Research Board 94th Annual Meeting,Washington,DC,USA, 2014. [22]J.Wu,M.Liu,H.Sun,T.Li,Z.Gao,andD.Z.W.Wang, “Equity-based timetable synchronization optimization in urban subway network,” Transportation Research Part C: Emerging Technologies,vol.51,pp.1–18,2015. [23] M. S. Chowdhury and S. I.-J. Chien, “Dynamic vehicle dispatching at the intermodal transfer station,” Transportation Research Record,no.1753,pp.61–68,2001. [24] S. M. Chowdhury and S. I.-J. Chien, “Intermodal transit system coordination,” Transportation Planning and Technology,vol.25, no.4,pp.257–287,2002. [25] P. Shrivastava, S. L. Dhingra, and P. J. Gundaliya, “Application of genetic algorithm for scheduling and schedule coordination problems,” Journal of Advanced Transportation,vol.36,no.1,pp. 23–41, 2002. [26] P. Shrivastava and S. L. Dhingra, “Development of coordinated schedules using genetic algorithms,” Journal of Transportation Engineering,vol.128,no.1,pp.89–96,2002. [27]J.Li,D.Fan,andL.Lei,“Transferschedulingformetro-bus integration in mega cities,” in Proceedings of the 14th COTA International Conference of Transportation Professionals: Safe, Smart, and Sustainable Multimodal Transportation Systems, CICTP 2014, pp. 1465–1478, China, July 2014. [28] J. Xiong, Z. He, W.Guan, and B. Ran, “Optimal timetable development for community shuttle network with metro stations,” Transportation Research Part C: Emerging Technologies,vol.60, pp. 540–565, 2015. [29] Y. Sun and P. M. Schonfeld, “Schedule-based route choice estimation with automatic fare collection data for rail transit passengers,”in Proceedings of the Transportation Research Board 93rd Annual Meeting (No. 14-0834),2014. [30] F.Zhang,J.Zhao,C.Tian,C.Xu,X.Liu,andL.Rao,“Spatiotem- poral segmentation of metro trips using smart card data,” IEEE Transactions on Vehicular Technology,vol.65,no.3,pp.1137– 1149, 2016. [31]J.Zhao,F.Zhang,L.Tuetal.,“Estimationofpassengerroute choice pattern using smart card data for complex metro systems,” IEEE Transactions on Intelligent Transportation Systems, vol.18,no.4,pp.790–801,2017. International Journal of Rotating Advances in Machinery Multimedia

Journal of The Scientifc Journal of Engineering World Journal Sensors Hindawi Hindawi Publishing Corporation Hindawi Hindawi Hindawi www.hindawi.com Volume 2018 http://www.hindawi.comwww.hindawi.com Volume 20182013 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018

Journal of Control Science and Engineering

Advances in Civil Engineering Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018

Submit your manuscripts at www.hindawi.com

Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018

VLSI Design Advances in OptoElectronics International Journal of Modelling & International Journal of Simulation Aerospace Navigation and in Engineering Observation Engineering

Hindawi Hindawi Hindawi Hindawi Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 Volume 2018 Hindawi www.hindawi.com www.hindawi.com www.hindawi.com Volume 2018

International Journal of International Journal of Antennas and Active and Passive Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration

Hindawi Hindawi Hindawi Hindawi Hindawi www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018 www.hindawi.com Volume 2018