Managing Recurrent Congestion of Subway Network in Peak Hours with Station Inflow Control

Home , Line 15 (Beijing Subway), Line 17 (Beijing Subway)

Hindawi Journal of Advanced Transportation Volume 2018, Article ID 6931025, 16 pages https://doi.org/10.1155/2018/6931025

Research Article Managing Recurrent Congestion of Subway Network in Peak Hours with Station Inflow Control

Qingru Zou,1 Xiangming Yao ,1 Peng Zhao,1 Fei Dou,2 and Taoyuan Yang 1

1 School of Trafc and Transportation, Beijing Jiaotong University, Beijing 100044, China 2Beijing Mass Transit Railway Operation Corporation, Ltd., Beijing 100044, China

Correspondence should be addressed to Xiangming Yao; [email protected]

Received 27 August 2017; Revised 27 November 2017; Accepted 20 December 2017; Published 31 January 2018

Academic Editor: Taha H. Rashidi

Copyright © 2018 Qingru Zou 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.

Station infow control (SIC) is an important and efective method for reducing recurrent congestion during peak hours in the Beijing, Shanghai, and Guangzhou subway systems. Tis work proposes a practical and efcient method for establishing a static SIC scheme in normal weekdays for large-scale subway networks. First, a trafc assignment model without capacity constraint is utilized to determine passenger fow distributions on the network. An internal relationship between station infows and section fows is then constructed. Second, capacity bottlenecks are identifed by considering the transport capacity of each section. Ten, a feedback-based bottleneck elimination strategy is established to search target control stations and determine their control time and control strength. To validate the efectiveness of the proposed approach, a decision support system coded in the C# programming language was developed, and the Beijing subway was used as a case study. Te results indicate that the proposed method and tool are capable of practical applications, and the generated SIC plan has better performance over the existing SIC plan. Tis study provides a practical and useful method for operation agencies to construct SIC schemes in the subway system.

1. Introduction Up to now, a practical and efcient method to generate SIC schemes for large-scale transit networks is still lacking. 1.1. Motivation. Station infow control (SIC) is to relieve Current SIC scheme is established almost depending on congestion and ensure operational safety by controlling the operator’s experience. According to the regulations on oper- number of passengers entering a station [1]. It is usually ation safety management for urban rail transit, which was applied during excessive congestion such as peak hours and released by the Beijing municipal commission of transport, other expected high passenger fows. Tough SIC causes a station should be controlled when passenger infows reach travel delays and inconvenience to passengers, it plays an thewarningstateof70%oftheloadcapacityofthestation important role in maintaining safety when travel demand [1]. Tis regulation is the only ofcial guidance for carrying greatly exceeds capacity. In April 2011, the Beijing subway out SIC actions. However, it does not provide a clear and frst employed SIC at 17 stations during morning peak hours system-wide optimization approach. For instance, congestion [2]. Since then, SIC has been gradually implemented in of a certain station may not be caused by large infows but other subway systems in China, such as the Guangzhou by limited train capacity. Hence, a system-wide optimization and Shanghai subways. With the continuous growth of approach that considers not only large infows but also train travel demand, the number of controlled stations and the capacities should be constructed. length of control time have increased greatly. At the end To address the SIC issue in subway systems, previous of 2016, the number of controlled stations in the Beijing works have proposed mathematical optimization models to subway reached 74, covering almost 25% of all stations establish a cooperative SIC plan within multiple stations [3]. [4, 5]. Nevertheless, these methods have low computational 2 Journal of Advanced Transportation efciency and lack capability to address the problem in large- 80 4.0 scalenetworks,becauseofcomplexsolutionandoversimpli- 70 3.5 fcation of the practical problem in formulating model. It is 60 3.0 well known that capacity bottlenecks are the critical reason 50 2.5 for congestion. Hence, we start from this basic point and con- 40 2.0 struct a new feedback-based bottleneck elimination strategy 30 1.5 to determine the SIC plan. Compared to the existed math- 20 1.0 ematical models, the proposed method has direct meaning 10 0.5 Annual ridership (billion) ridership Annual

Number of controlled stations controlled of Number 0 0.0 and high computational efciency and can be easily expanded 2011 2012 2013 2014 2015 2016 by considering practical factors in diferent situations. Te Year major characteristics of the model include the following. (a) A feedback-based bottleneck elimination algorithm is used to Controlled stations generate the control scheme, which can provide quantitative Annual ridership support for operation managers, including control stations, Figure 1: Te number of controlled stations and annual ridership of control times, and control strength. (b) Te method has high the Beijing subway. computational efciency and capability for applications in large-scale rail transit networks. (c) Te proposed approach has good extensibility with regard to practical factors, such as platform load capacity and trafc environment outside the SIC plan. First, station masters only make decisions based station. on a single station’s crowdedness, not from the system wide. Second, there is no scientifc method to support operation managers to decide which station should be controlled. 1.2. SIC Applications in Beijing Subway. Te Beijing subway Moreover, a SIC scheme only determines which station and developed rapidly in recent years, consisted of 18 lines with what time should be controlled, not including the control a total length of 574 km by the end of 2016. Te ridership strength. reached 3.66 billion trips in 2016 (based on the count of unlinked trips, as every transfer in the system is counted as an additional trip), which means more than 10 million 1.3. Objective and Organization. Tis work aims to provide a trips per day [6]. To relieve congestion, train headways in practical method for generating static SIC schemes for large- some lines have been reduced to the minimum time (less scale subway networks only in peak hours and guides SIC than two minutes). However, travel demand is much greater actions through a quantization reference of control strength. than the transport capacity, and the congestion is becoming A proper SIC scheme could ensure operational safety and serious. improve the service level for passengers. TeBeijingSubwayfrstlyemployedSICmeasuresin Te remainder of this paper is organized as follows. Sec- April of 2011, which controlled seventeen stations in Line tion 2 provides related works on SIC actions and congestion 1 and Line BT [2]. Te control time starts from 7:00 am remission measures for rail transit system. Te methodology to 9:00 am on weekdays. Ten, the number of controlled to determine a control plan based on a feedback-based bottle- stations continues to grow as travel demand increases. Fig- neck elimination approach is given in Section 3. Aferwards, ure 1 presents the number of controlled stations and annual a discussion of its implementation in the Beijing subway ridership in the last fve years. is provided in Section 4. Finally, conclusions and future In practice, three control levels are generally employed research are discussed. based on the crowding extent in a station. Te frst level limits passengers entering platform when platform capacity 2. Literature Review is insufcient. Te second level limits passengers going to purchasing area, such as the area close to ticket gates. If the Congestion is an intractable problem for worldwide trafc congestion cannot be relieved by these two control actions, and transit systems. Two important strategies are usually used then a third level is adopted, which limits passengers entering to manage congestion, which are capacity enhancement and station by setting fences to slow down fow speed or closing travel demand management. For subway systems, it is difcult station gates. Control level increases with the extent of to improve capacity because physical facilities have upper congestion growth. Representative SIC measures applied in limits on capacity, and a long time is required to build new theBeijingsubwayareshowninFigure2. lines. Measures of demand management become efective According to a survey of the Beijing subway, SIC schemes and positive tools for relieving congestion. In practice, two will be updated every three months in accordance with the types of congestion-relief measures are widely used. Te variation of travel demand. If a station meets with heavy frst one is time-varying price approach which has been congestion, station masters will apply for a SIC action to the used in the London [7], Melbourne subway systems [8, Beijing Subway Operation Company. Ten, operation agen- 9], and so on. Te second is station infow control which cies decide whether to authorize the application depending is broadly implemented in the subway systems of China. on fow status and previous experience. However, there exist Next,wewillsummarizetherelatedworksonthesetwo drawbacks in the redesign process for establishing a new aspects. Journal of Advanced Transportation 3

(a) Limit to enter platform (b) Close ticket gates

Figure 2: Representative SIC measures in the Beijing subway.

2.1. Time-Dependent Pricing. Te diferential price approach demandinadirectandforcedway,byremovingthemountain to shif demand from peak periods is not new to either peak of the demand. For a mature subway system, pricing research or practice, which has been implemented in many strategy is more preferable than control actions, while in large cities in the US from the 1970s [10]. Tere are two basic developing subway systems where travel demand grows and strategies of diferential pricing measure, peak surcharges and fuctuates greatly, infow control is an efcient measure for of-peak discounts. In the feld of subway system, Santiago reliving congestion and maintaining operational safety. underground system frstly employed time-varying pricing strategy to reduce peak congestion in 1986 [11]. Tereafer, 2.2. Station Infow Control. Station infow control has been many subway systems have implemented the varying price widely implemented in the subway systems of China, includ- strategy to manage peak demand. A recent review by LEK ing Beijing, Tianjin, Shanghai, Guangzhou, and Chengdu fnds that around 40% of urban rail networks worldwide subway. With the peak congestion being serious, how to per- provide some form of peak surcharge and/or of-peak dis- form SIC actions becomes an absorbing topic for researchers count [12]. Te most famous diferential pricing strategy is “early bird tickets” in Melbourne metro, which provides free and practitioners. Previous works can be divided into three tickets if trips are completed before 7:00 am. Afer a half categories: macroscopic principles for SIC strategy, meso- year of the implementation of the policy, it is found that scopic methods for constructing a SIC plan, and microscopic 23% of commuters transfer from peak hours to of-peak measures for carrying out SIC actions in a station. Tis periods, and the departure time of travelers moves forward work falls into the second category on how to construct SIC about 42 minutes in average. Te pricing strategy reduces schemes. peak demand and relieves congestion signifcantly [9]. More Macroscopic principles provide overall guidance for SIC. applications of diferential price policy in subway systems can Liu and Jiang pointed out earlier that SIC actions should refer to the reviews of Hale and Charles [13] and Liu and be executed at three levels of “station-line-network” [15]. Charles [14]. In practice, congestion of a station may not be caused by Te mechanism of diferential pricing for congestion large infows but for limited train capacity, because the relief is to infuence passenger’s travel behaviors and even the stations ahead of the congestion station occupy most of the demand in temporal-spatial domains. Pricing strategy can train capacity. Hence, collaborative control within multiple intervene with the choices of passengers on departure time, stations should be considered. Based on a balance principle, destination, travel mode, and travel route. Usually the efect Liu et al. proposed a cooperative control strategy between of a new price policy needs a long time to appear. Compared twostations[16].Huangetal.studiedpropagationpatternof with the elastic pricing strategy, infow control manages peak congestion and proposed a collaborative control strategy in 4 Journal of Advanced Transportation

Trafc demand (OD matrix) Train timetable

Assignment model

Transport capacity Inter-relationship of Section fow infows and link fows of sections

Response time Bottleneck detection Elimination Trafc conditions algorithm outside the station Bottleneck elimination

Platform load capacity SIC scheme generation Factors for bottlenecks elimination Control stations Control time Control strength

Figure 3: Framework for generating a SIC scheme. a single line [17]. Cooperative infow control within multiple crowded exits [24]. However, it is difcult to use a normalized stations has been a consensus agreement for carrying out SIC method to determine control actions, because each station actions. has specifc physical structure and organization rules. How On the mesoscopic level of method construction for SIC to establish detail SIC actions is out of range of this work. plans, Zhao et al. frstly proposed a mathematical optimization model to establish SIC schemes for a single line, with 3. Methodology the objective of minimizing travel delay and maximizing the turnover of passenger fows [4]. Lu et al. also proposed a Tis section discusses a feedback-based bottleneck elimina- linear integer programming model on the basis of network tion algorithm for generating SIC schemes. Firstly, the frame- topology and defnition of passenger demand; however, the work to generate SIC scheme is provided. Ten, the inter- model is only for a line [18]. Ten, Yao et al. established a nal relationship between station infows and section fows coordinated passenger infow control model for networks. In is established using a capacity-unconstrained assignment order to improve the efciency and capability of the model for model, which provides important parameters for construct- a network, a static assignment model is used to establish the ing SIC plans. Tirdly, capacity bottlenecks are identifed internal fow relationship [5]. With the view of reducing travel by considering section fows and corresponding transport delay, Guo et al. built a cooperative model for a network with capacities. Fourthly, the elimination processes for a single constraints on the capacity of stations [19], and Wang et al. bottleneck and multiple bottlenecks are presented separately. established an integer programming model based on an anal- Lastly, the fowchart for generating a time-dependent SIC ysis of passenger delay and alight and board processes [20]. In plan for a network is given. conclusion, these models try to use optimization method to solvetheSICproblem.Toughcooperativecontrolstrategy 3.1. Framework for Generating an SIC Scheme. It is well can be considered, large numbers of parameters and complex known that bottleneck caused by the imbalance between solution limit their capability in real large-scale networks. supply and demand is the origin of congestion. We proceed Te critical point of these models is establishing internal from this point to establish a feedback-based elimination fow relationships, whose complexity increases greatly with algorithm to remove bottlenecks and then search the cor- network scale grows. In practice, congestion usually takes responding target control stations. Usually, a SIC scheme placeinaregionalwide.WhenweconstructaSICplan,there contains three parts, namely, control stations, time, and is no need to consider the stations far away from the target strength. Te framework for SIC scheme generation is shown congestion station. Diferent from optimization methods, we in Figure 3. establish a heuristic infow control algorithm to establish SIC schemes. 3.2. Flow Relationship Construction. In a rail transit system, Moreover, some works focus on SIC actions implemented transport capacity has an upper limit, and passengers should in stations, such as ticket gates optimization and physical wait for the next train if the capacity of the incoming train fences setting for infow control [21]. Dou et al. provide a is insufcient. In order to obtain the original status of fow cloud model to determine what time to start control actions distributions on a network, the capacity limitation of section for a station [22]. Xie studied the detail control actions for is not considered in our trafc assignment model but will be transfer stations [23]. In addition to normal control actions, taken into consideration later. A Logit-based stochastic user Coulson et al. propose a new strategy of monetary incentives equilibrium (SUE) assignment model is applied to establish to reduce congestion by redirecting of passengers to less the relationship between station infows and section (link) Journal of Advanced Transportation 5

m i Train direction 100 100% 80% 60% 50% 20% i 30% 150 m 1000 800 600 500 50% 250

AB CD E AB CD E (a) Te station-section travel rate (b) Te section-station capacity occupation rate

Figure 4: Schematic of relationship between station infows and section fows. fows [25]. In the model, there are mainly two types of Suppose the OD matrix at time � is given, which can relationships: (1) the infows of a station that travel through be accurately determined from automatic fare collection given sections and their corresponding travel through rates (AFC) records. Take an OD pair (�, �) as an example to show and (2) the link fows of a section that comes from particular the process of establishing the internal fow relationship. stations and their corresponding capacity occupation rates. According to the Logit-based SUE model, the probability for A subway network is represented by a directed graph passengers in OD pair (�, �) choosing the �th route is given � = (�, �),where� = {1,2,...,�, �}is the set of stations by (2) and the fow volume of the �th route can be computed (nodes) and � = {1,2,...,�,�}is the set of sections (links). using (3). Te analysis time (such as 7:00 am to 9:00 am) is divided into (� /�) short time spans with the same length, which are denoted by exp �� = {1,2,...,�} � (�) �� = , .Let �� bethetraveldemandfromstation �� ∑� (� /�) � to station � in time interval �,where��(�) and ��(�) are �� (2) the section fow and transport capacity of section � at time ∀� ∈ �, � ∈ �, � ∈� , �,respectively.Defne�� as the set of feasible routes for the �� OD (Origin-Destination) pair (�, �),and�� as the �th route, � (�) =� (�) ⋅� , ∀� ∈ �, � ∈ �, � ∈� , � ∈� � � �� (3) �� .Let �� be the generalized travel cost of the th route. � � Te route cost is represented by a generalized cost where �� is the choice probability and is the average cost function which is composed of four parts: (1) access and of all feasible routes in the OD pair (�, �). egress walk time; (2) on-board time; (3) waiting time; and Assign the whole demand of the OD pair (�, �) to all (4) transfer time. Te walk time contains access and egress feasible routes; then passenger fows of section � that comes walk time, which can be calculated by the distance corre- from this OD can be determined, as shown in the following: sponding to the walk link and the average walking speed � of travelers. Normally, the on-board time for passengers �� travelling through sections is constant, which can be fxed � (�) = ∑� (�) ⋅� , ∀� ∈ �, � ∈ �, � ∈ �, � �� (4) � from train schedules (timetable). Te waiting time includes �� two components: (a) waiting time at the origin station; (b) �� waiting time at the transfer station if a transfer is required. where ��(�) refers to the passenger fow of section �,which (�, �) �� Te average waiting time at an origin/transfer station is equal comes from OD pair ,and �� is a binary variable: if to half of the train headway time. Te transfer time is similar �� =1 � � �� = �� ,section belongs to the route �� ;otherwise �� to the access or egress walk time. Ten the generalized cost of 0. a feasible route can be formulated as follows: Next, assign all demands of all OD pairs to the network; � � =�� (�access +�egress)+��board the total section fow of section canbecalculatedby �� (1) � � +�� (�� wait +�� wait )+��transfer, � (�) = ∑ ∑ �� (�) ,∀�∈�,�∈�. �� (5) �=1 �=1 � � .��,��, where �� is the generalized cost of the route �� In this work, two important parameters are defned to � ,� are weight factors for the cost corresponding to describe the internal relationship between station infows and diferent travel processes; �=1if there is a transfer; section fows. Tese are the station-section travel through rate �=0;�� wait �� wait � � otherwise, �� and �� are waiting time at �� and the section-station capacity occupation rate ��.Te origin and transfer station, respectively. Te weight factors for two parameters describe the correlation from opposite per- � diferent travel processes can be estimated by the maximum spectives, where �� starts from station view to explain that likelihood method through travel surveys. Referring to the the infow of a station will go through specifc sections, and � previous work on trafc assignment for the Beijing subway �� aims to explain that section fows come from particular � � � � [26], � = 0.21, � = 0.14, � = 0.28,and� = 0.37.Te stations. An example of these two parameters is shown in value of factors may be variant for diferent subway systems. Figure 4. 6 Journal of Advanced Transportation

Train direction Low congestion Heavy congestion

AB C Δq DEAB CΔq D E C-D C-D (a) Single control (b) Cooperative control

Figure 5: Schematic of the single bottleneck elimination process.

In Figure 4(a), assume the infow volume of station the theoretical capacity. Here, the peak hour factor (PHF) is A is 1000 passengers and the fows traveling through the used to describe the reduction of transport capacity [27] and subsequent sections are 1000, 800, 600, and 500. Terefore, is determined using (11). � the station-section travel rates � are 100%, 80%, 60%, � � (�) =� ⋅�⋅� ⋅�, and 50% respectively. Te station-section travel rate can be � � PHF (10) computed by where �� is the number of trains running through section � � �� during time t, D means the nominal load capacity for a train ∑�=1 �� (�) �� (�) = ,∀�∈�,�∈�,�∈�, (usually 1440 passengers per train), �PHF is the PHF (0.25 ≤ � � (6) � ≤ 1.0 � � ≤ 130 ∑�=1 �� (�) PHF ), and is the permissible overload rate ( %).

� � where � (�) represents the percentage of passengers who � = 60 , � PHF 4⋅� (11) depart from station � traveling through section � at time �. 15

SupposethesectionfowsbetweenstationsCandD where �60 istheinfowsofacertainlineinanhourand�15 is are 500 passengers, as shown in Figure 4(b), in which the the maximum peak fow during 15 minutes in this hour. numbers of passengers from stations A, B, and C are 100, 150,and250,respectively.Ten,thesection-stationcapacity 3.4. Single Bottleneck Elimination Algorithm. Te elimination occupation rates are 20%, 30%, and 50%. Te formulation of algorithm for a single bottleneck is the basis for removing the section-station capacity occupation rate is given by multiple bottlenecks. We will describe how to remove a single � �� (�) bottleneck frst. Tere are two types of control strategies for �� (�) = ∑ � ,∀�∈�,�∈�,�∈�, eliminating a bottleneck: single-station control and coopera- � � (�) (7) �=1 � tive multistations control, as shown in Figure 5. Consider the bottleneck in Figure 5 as an example to show the elimination � where ��(�) represents the percentage of passenger fows process. Suppose section C-D is a capacity bottleneck and Δ� Δ� from station � in all fows traveling through section � at time C-D is the overload fow. While C-D is low, the bottleneck �. canberemovedbycontrollingstationB(assumethefows � of section C-D mainly come from station B). When the Te section-station capacity occupation rate �� should satisfy congestion is heavy, multiple stations, such as stations A, B, and C, should be controlled. Two important questions should � � be answered when we remove the bottleneck, that is, (1) how ∑ �� (�) =1, ∀�∈�,�∈�. (8) to select the target control station/stations and (2) how to �=1 determine the control strength of each station that ensures the bottleneck can be removed. 3.3. Capacity Bottlenecks Identifcation. Abottleneckemer- ges when section fows exceed its transport capacity. In 3.4.1. Target Control Stations Selection. Te purpose of tar- practice, passengers should queen on the platform for unable get control station selection is to determine which sta- boarding. Note that there is no capacity limitation in our tion/stations should be controlled. Tere is no doubt that trafc assignment model; then the bottleneck is exhibited as it is more efective to control the stations with larger fows Δ� thesurplusfowratherthansectioncapacity.Defne � as traveling through the bottleneck section. We can choose the surplus fow of section m, as shown in the following: the target control stations according to the section-station � capacity occupation rate ��. Defne overload rate � as the Δ�� (�) =�� (�) −�� (�) ,∀�∈�,�∈�. (9) congestion pressure of the bottleneck, as shown in Te transport capacity can be calculated from the train � �= � . timetable directly or from train headways, as shown in (12) �� (10). Because of the randomness of passengers’ arrival and imbalance in the distribution of passengers on diferent Te higher the congestion pressure is, the more the stations vehicles, the available capacity of a train is usually less than should be controlled. Moreover, the more stations controlled, Journal of Advanced Transportation 7

Table 1: Te proposed values for determining the number of target to describe the bus operation condition in this work. control stations. Usually,themorethebuslines,thehigherthecontrol strength. Overload rate (�) Number of target control stations (�) � < 110%1(4) Platform load capacity: platform load capacity is 110% ≤�<125%2 another major factor that determines the control 125 ≤�<140 strength,whichcanbemeasuredbasedontheplat- % %3 form area and the designed fow density. It is safer and 140% ≤� 4 robust for a platform with a larger capacity. Hence, if the platform capacity of a station is insufcient, greater control strength should be used to maintain the lower control strengths that are executed. Terefore, safety. thereisnotjustonecontrolstrategyforremovingacertain bottleneck. In this work, a suggested value determined by Te station weight can be expressed as a function of the above referring to management experience and congestion pressure factors, as shown in isusedtoidentifythenumberoftargetcontrolstations.By mining and analyzing the distribution characteristics of the �� 1/Δ�� Beijing subway, proposed values were determined and are �� =� � +� � +� � � 1 � 2 � 3 � ∑ � � ∑ � 1/Δ� ∑ � � provided in Table 1. Once the number of control stations �∈�� ∈�� ∈�� is determined, the top � stations according to the section- (13) � station capacity occupation rate can be selected as the target � � +� � +� � , control stations. 4 5 � ∑�∈�� ∑ � � � �∈��

3.4.2. Station Weight Calculation. If we only consider the � where �� is the set of target control stations for bottleneck internal relationship between station infows and section � section �; Δ�� is the train running time between station � fows, the control strength can be determined directly. How- � � ever, in practice, other factors should be taken into consider- and bottleneck �; �� is the area of the station square; �� is � � ation. Defne a station weight �� to describe the contribution the area of platform; � is the number of bus lines around the of the control station � to eliminate the bottleneck �.Four station; � indicates the importance of these factors. In this typical factors are considered in this work. work, �1 = 0.4, �2 = 0.1, �3 = 0.1, �4 = 0.1, �5 =0.3. For a given bottleneck, the weights of target control (1) Flow relationship: the section-station capacity occu- stations should satisfy the constraint of (14). Te station pation rate represents the capacity utilization of sec- weights can be normalized by (15). tions. It is the most important parameter used to determine the control station weight. Te larger the ∑ �� (�) =1, rate, the more important the station in removing the � (14) �∈�� bottleneck. � (2) Response time: response time describes the temporal �̂� (�) �� = � , connection between control stations and bottlenecks, � ( ) � (15) ∑�∈�� ̂� (�) which is expressed by the running time of the train � between the control station and the bottleneck. When � � the control station is near the bottleneck, the efect of where �� (�) is the fnal station weight and �̂� (�) is the initial the control action is more obvious. control weight from (13). (3) Trafc conditions outside the station: trafc condition isassistantfactorwhenwecarryoutSICactions. 3.4.3. Control Strength Calculation. Afer the target control Two representative factors are considered in this stations and the corresponding control weights are obtained, work, which are the area of the square outside the the control strength needs to be determined. Te infow station, and the bus operation condition. First, there control rate is defned to quantify the control strength, which should be sufcient space for passengers queuing isthepercentageofpassengerswhoarelimitedtoentering outside the station. Te smaller the station square, the station relative to the travel demand, as shown in the the lower the control strength. Second, if there are following: enough buses around the station, travelers have high possibilitytotransfertoabusinsteadofmetro.In �� (�) fact, the frequency, service area, and level of buses � (�) = � ⋅ 100 ,∀�∈�,�∈�, (16) � � (�) % infuent passengers’ transfer behavior. However, it is � a hard work to consider these infuences in depth, because each bus line has its specifc service area and where ��(�) is the control rate, ��(�) is the whole travel demand � characteristics. For available data, a simple index of of station � at time �,and�� (�) is the number of passengers the number of bus lines outside the station is used whoarelimitedtoenteringthestation. 8 Journal of Advanced Transportation

Control stations for bottleneck C-D Infow control Train direction d (t) A

AB C D E AB C D E Control stations for C-D(t) D-E(t) bottleneck D-E A A (a) Schematic for eliminating multiple bottlenecks (b) Flow relationship among multiple bottlenecks

Figure 6: Schematic for the internal relationship between multiple bottlenecks.

To remove bottleneck � with overload fow Δ��(�),the (3) Update the section fows of the related sections using efective infows that need to be controlled can be calculated (19). � by Δ��(�)�� (�).Notethatthisistheefectivefow,notthereal fow, because not all passengers who enter station � will travel (4) Identify the bottlenecks on the network afer updating through bottleneck �. Here,wecanusethestation-section the section fows. travel through rate to revise the control infows, as shown in �� (�) (5) If all the bottlenecks are removed, the SIC plan is � � =Δ� � ⋅ � �� ( ) � ( ) � . (17) fnished; otherwise, go to step (1). �� (�) Te control rate of the stations is given by 3.6. SIC Scheme Generation for a Network. Based on the Δ� (�) ⋅�� (�) /�� (�) above approach for generating a SIC plan for a single time � (�) = � � � ⋅ 100 ,∀�∈�� . � � (�) % � (18) interval, the algorithm for construction of a SIC scheme � throughout the peak hours (7:00 am to 9:00 am) will be established in this section. A SIC scheme usually contains 3.5. Multibottlenecks Elimination Algorithm. Tere are always three elements, namely, control stations, control time, and many bottlenecks on the network, and these bottlenecks are strength. Discretize the continuous time into short time interconnected through passenger fows. For example, if we periods of equal length (such as 30 minutes). For each time remove a bottleneck with heavy congestion, another light span, the proposed algorithm can be used to generate a bottleneck close to this bottleneck may disappear. Consider portion of the SIC plan. the example in Figure 6, which shows the elimination process It should be noted that the passengers who are limited for multiple bottlenecks. Suppose both section C-D and to entering the station in time interval � will infuence section D-E are bottlenecks, and their target control station �+1 { , , } { , , } thetraveldemandinnexttimeperiod .Moreover, sets are A B C and B C D , respectively. When we control travel behaviors of passengers can be infuenced by SIC the infows of stations A, B, and C to remove bottleneck actions, such as travel mode change and departure time C-D, the link fows through section D-E may reduce, or reschedule. Ten the temporal-distribution of demand can be the bottleneck may even disappear. Hence, the connections changed. However, it is very hard to consider the interactive among bottlenecks should be considered when eliminating infuence when we construct the SIC plan. In this work, it multiple bottlenecks. Te internal fow relationship among is supposed that travel demand is constant, and passengers these bottlenecks is illustrated in Figure 6(b). Te reduced will wait outside the station and not transfer to other travel fows of the related links can be computed by the station- modes. section travel through rate, as shown in Ten,thetraveldemandattime�+1should be updated � � � �� (�) =�� (�) − ∑ �� (�) ⋅�� (�) ,∀�∈�,�∈�, by considering the passengers delayed at time ,asshownin � (19) �∈�� (20).Moreover,thesectionfowsrelatedtothecontrolstation should also be updated, as shown in (21). where ��(�) is the updated section fow of section � afer station � is under control. � To rationally remove all bottlenecks, an iterative elimina- �� (�+1) =�� (�+1) +�� (�) , ∀�∈�,�≥1, (20) tion algorithm is employed in this work:

(1) Sort all bottlenecks according to their overload rate in where ��(�) is the updated infow of station � in time �+1,if descending order and select the frst one as the target the station is controlled in time �. bottleneck. (2) Establish the infow control plan for the target bot- � � �� (�+1) =�� (�+1) +�� (�) ⋅�� (�+1) , tleneck by using the single bottleneck elimination (21) algorithm; see Section 3.4. ∀�∈�,�≥1, Journal of Advanced Transportation 9

Start

Initialization (OD matrix, etc.), t=0

t=t+1

Passenger fow assignment Capacity calculation

Flow relationship Transport capacity construction Section fow

Identify capacity bottlenecks

Sort capacity bottlenecks

Get the maximal capacity bottleneck

Single-bottleneck elimination algorithm

Select control stations Determine control Update link strength fows

All bottlenecks No are removed?

Yes No Update station All t? demand Yes End

Figure 7: Algorithm for constructing SIC plan in whole peak hours.

where ��(�) is the updated section fow of section � in time on the iterative bottleneck elimination algorithm and auto- �+1. matically exporting the plan in the form of a report; (c) Te iterative algorithm based on the bottleneck elimina- evaluating the performance of the generated SIC plan; (d) tion approach to generate the whole SIC scheme during peak tracking the detailed elimination process for a particular hours is presented in Figure 7. bottleneck.

4. Method Implementation 4.2. Timeframe for Updating SIC Plan. Tough the proposed method has no limitation on the iteration step length for 4.1. Tool Description. Adecisionsupporttoolbasedonthe updating SIC plan, other factors from applicability and proposed method was developed in the C# programming robustness should be considered in practice. Firstly, we will languageandisusedtovalidatetheefciencyandperfor- analyze the stability of the model inputs, which are time- mance of the approach. Te tool was executed on an Intel dependent OD tables. Te relative deviation shown in (22) PC under Windows 7 with a 3.8 GHz CPU and 4 G RAM. is used to measure the stability of OD fows. Figure 9 shows Figure 8 shows the main interfaces of the tool. Tanks to the deviations of OD fows between two related weekdays the Beijing Subway Operation Co. Ltd. for providing data, (the day and the same weekday of last week) in diferent time the tool has been tested in the Beijing subway system. Te intervals. It can be clearly found that the deviations increase results demonstrate that it has high efciency for applications greatlywiththetimeintervalshortening.Ifthetimestepis in large transit networks, and reasonable SIC plans can be fve minutes, the average deviation is over 50%. Tere is no obtained. doubt that SIC plans are not credible if a short time span is chosen to update the plan. Temaincapabilitiesofthetoolincludethefollowing:(a) � � constructing time-dependent internal-relationship between � � � � �� (�) − �� (�)� /�� (�) station infows and section fows and representing them in (�) = ∑ ∑ � � × 100 , RE � % (22) graphical visualization; (b) generating SIC schemes based �=1�=1,�=�̸ 10 Journal of Advanced Transportation

(a) Te station-section travel through rate (b) Te section-station capacity occupation rate

Figure 8: Main interfaces of the decision support tool.

100

20 Relative deviations (%) deviations Relative

0 5:00 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00 Time

5 min 30 min 1 d 10 min 1 h 15 min 2 h Figure 9: Relative deviation of OD fows in diferent time interval. where RE(�) is the average relative deviation of OD fows in 4.3. Case Study of Beijing Subway time interval �; � is the total number of OD pairs; and �� (�) � (�) 4.3.1. Data. Te Beijing subway, one of the largest and most and �� mean the volume of fows in a certain day and the congested transit systems in China, was analyzed as a case contrastive day of last week, respectively. study. To avoid the fuctuating infuence of travel demand, Secondly, the feasibility of implementation of control the average travel demand over fve weekdays from Monday actions should also be considered when we make the plan. April 10th to Friday April 14th in 2017 is used in the model. Because rail transit stations lack fexible control equipment, it Te demand was obtained from the automatic fare collection is difcult to change control actions frequently, such as fences. (AFC) system. Time-dependent infows of each line are Consider the variation of travel demand and the feasibility provided in Figure 10. Te SIC action is usually carried out of implementation in practice; we suggest that the timeframe during the morning and evening peak hours. However, only (time length) for updating SIC plan should not be less than morningpeakhours(7:00amto9:00am)arediscussedinthe 30 minutes. study. Journal of Advanced Transportation 11

×104 25 20 15 10 (/person) 5 Number of infows infows of Number 0 Line 1 Line 2 Line 4 Line 5 Line 6 Line 7 Line 8 Line 9 Line Line 10 Line 13 Line 14 Line 15 Line 16 Line JC Line Line FS Line BT Line Line CP Line YZ Line name 07:00–07:30 07:30–08:00 08:00–08:30 08:30–09:00 Figure 10: Time-dependent infows of each line during morning peak hours.

Line 2 Line 6

Line 1 Line BT

Line 14 Line 10 Line 7 Line 9 Line YZ Line FS Line 4

Cancelled Newly added Te same Figure 11: Distribution of the generated and actual SIC plans for the network (morning peak hours).

Te time span for updating the SIC scheme is set to be fromtheSICscheme.Temainreasonisthediferent 30 minutes. Hence, there are four small time intervals during operational concepts between the Beijing subway and MTR the morning peak hours. Transport capacity is an impor- Corporation. Regular SIC actions are never applied to these tant parameter for identifying bottlenecks. In this work, lines. the train timetable is employed to calculate the transport capacityforeachlineorsection,whichispresentedin 4.3.2. Results. In April of 2017, the Beijing subway controlled Table 2. 61 stations during morning peak hours. Te generated SIC Moreover, trafc conditions around the station (such as planfromtheproposedmethodincludes63stations.Com- the bus and square area) are obtained from a trafc survey, paring with the actual SIC plan, 52 stations are the same as and platform load capacity is determined from the design the actual controlled stations, 9 stations should be cancelled, map of stations. Tese parameters are crucial to determining and 11 new stations should be controlled. Figure 11 shows the station weight when removing a particular bottleneck. the distribution of the actual and generated SIC plans for Considering the copious amount of information in these the network, in which the “canceled” means the station is parameters, they are not represented here in detail. controlled in practice but not included in the generated plan, Note that Line 4, Line 14, and Line 16, which belong to and “newly added” has an opposite meaning. Table 3 presents Beijing Mass Transit Rail (MTR) Corporation, are excluded the detailed plan of each line. 12 Journal of Advanced Transportation 5230 21910 11340 17427 12258 33091 30514 14709 12240 24681 16092 35850 22027 25943 30789 23984 34638 29609 5230 6 18 22027 15 23235 15 23984 13 16092 10 12258 12 14709 18 29609 19 18450 10 11340 10 12240 16 25943 25 26853 27 34638 24 30789 30 35850 30 29782 20 24681 Frequency (trains/h) Transport capacity (person/h) 7:00–8:00 8:00–9:00 7:00–8:00 8:00–9:00 0.81 20 0.85 10 0.83 30 0.85 10 0.85 22 0.85 18 0.85 12 0.77 27 0.79 10 0.97 6 0.89 27 0.89 24 0.80 16 0.86 18 0.86 15 0.86 13 0.86 20 0.84 16 896 1920 1920 1860 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 Table 2: Transport capacity for each line during peak hours. 8 8 6 6 6 6 6 6 6 6 6 6 6 4 6 6 6 6 310 224 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 Line YZ Line 15 Line 6 Line 7 Line CP Line BT Line FS Line JC Line 14 Line 16 Line 10 Line 13 Line 5 Line 9 Line 2 Line 4 Line 8 LineLine 1 Vehicle capacity (person) Train formation (vehicles) Train capacity (person/train) PHF Journal of Advanced Transportation 13

Table 3: Te number of controlled stations in each line. 4.3.3. Performance Evaluation. Measuring the performance of SIC schemes is important for carrying out a new plan in Line Actual Generated Canceled Newly added stations practice. However, it is difcult because the actual plan of the name plan plan stations Beijing subway is not clear. We can only know the control Line 66−1 1 stations and a rough range of control times (such as 7:00 am 1 to 9:00 am), and we do not know pivotal information about Line 000 0 the control strength of each controlled station. Terefore, 2 the number of delayed passengers cannot be determined. Line 000 0 In this work, the section fows are used to evaluate the 4 performance in an indirect way. First, time-varying link Line 16 11 −5 0 fowsofeachsectionundertheactualSICplancanbe 5 obtained from the Revenue Clearance Center (RCC) of the Line Beijing subway, which represents the performance of the 99−1 1 6 practical plan. Ten, section fows under the generated SIC Line scheme can be gained from the fow assignment model. Te 20−2 0 7 relative deviation of section fows between the practical and Line generatedplanisusedtomeasuretheSICperformance,as 130 2 8 shown in Line � �� 220 0 (�� (�) −�� (�))/�� (�) 9 � (�) = ∑ ∗ 100 , � % (23) Line �∈�� 550 0 10 �(�) Line where is the average relative deviation of all section 440 0 �� (�) � � 13 fows, � is the section fow of section at time �� (�) Line using the generated SIC scheme, � is the actual fow 000 0 � 14 from the RCC, and � is the set of sections with � ele- Line ments. 000 0 15 Table6showstheaveragerelativedeviationofsection fows in each line. Note that the travel demand used to gen- Line 000 0 16 erate SIC plan is the average OD tables from fve consecutive weekdays in April of 2017. Terefore, the actual section fows Line 9110 2 are the corresponding mean value. Te following can be seen: BT Line (1) In examining the results over all the peak hours, 130 2 YZ the change of relative deviations is very small. It is Line easy to understand that SIC action only infuences 680 2 CP the departure time of travelers rather than the travel Line demand. Hence, the total fows through the section 010 1 FS will not change greatly. Line 000 0 (2) In view of the small time span, the section fows in the JC controlled lines generally increase during 7:00 am∼ SUM 61 63 −9 11 8:00 am and decrease during 8:00 am∼9:00 am to a certain degree. Tis indicates that passengers enter the station earlier and that the new plan has a positive impact on reducing passengers’ travel delays. Consider too many items in the SIC scheme, only an example of the detailed plan for Line 1 and BT is shown (3) Te larger the section fow values change, the more in Table 4. Te control rate represents the control strength, controlled stations there are in these lines, such as which equals the percentage of limited passengers and all Line 1 and Line 5. Tese lines are the most congested infows.Itcanalsoberegardedasthereductionofspeedof lines on the network. Put another way, it is necessary passengers entering the station. In Table 4, the station names to adjust the actual SIC plan in these lines to improve are represented by their acronyms. the fow management. Table 5 provides the detailed elimination process for key bottlenecks (the heaviest congestion) in Line 1 and BT 4.3.4. Guidance for SIC Actions. Afer the SIC scheme for between 7:30 am and 8:00 am. For a certain bottleneck, the a network is obtained, there is another important work target control stations, station weights, and control volumes that should be considered, which is how to determine the can be tracked. Trough tracking the bottleneck elimination detail control actions for a specifc station. In practice, process, we can determine the function of each control station station masters decide how to control fows according to for a certain bottleneck. their experience and the specifc operational environment 14 Journal of Advanced Transportation

Table 4: An example of the generated SIC scheme.

Control rate (%) ID Station name Line name 7:00–7:30 7:30–8:00 8:00–8:30 8:30–9:00 9:00–9:30 (1) PGY Line 1 4.56 34.53 41.92 / / (2) GCL Line 1 1.74 15.93 15.51 / / (3) BJYLY Line 1 / 25.00 18.72 / / (4) BBS Line 1 4.33 33.47 36.66 / / (5) YQL Line 1 / 24.99 / / / (6) WKS Line 1 / 24.97 / / / (8) SH Line 1 / / 49.72 / / (9) SHD Line 1 / / 9.73 / / (10) CMDX Line BT 22.85 59.63 40.26 / 41.60 (11) SQ Line BT 41.11 52.05 52.75 38.80 47.90 (12) GZ Line BT 44.26 69.17 47.25 16.14 / (14) TZBY Line BT 24.98 50.00 49.95 / / (15) GY Line BT 50.00 70.00 70.00 28.13 / (17) LY Line BT 54.17 70.00 70.00 27.70 / Note. Te “/” represents no control.

Table 5: Elimination processes of certain bottlenecks (7:30 am∼8:00 am).

Line name Bottleneck Target control stations Control weight Control volume (Person) Infows (Person) Control rate (%) PGY 0.314 2109 6107 34.53 BBS 0.160 588 3693 15.93 GGL 0.077 961 3842 25.00 Line 1 WSL->GZF BBYLY 0.127 992 2964 33.47 YQL 0.217 814 3257 24.99 WKS 0.105 537 2151 24.97 LY 0.240 1971 2815 70.00 GY 0.264 1798 2569 70.00 Line BT CMDX->GBD CMDX 0.093 1412 2368 59.63 GZ 0.125 1593 2303 69.17 SQ 0.096 1039 1996 52.05

of the station. Tis is a difcult work because each station 5. Conclusion may have diferent physical structure, organization rules for passenger fows, fow characteristics of diferent entrances In this study, an algorithm based on a bottleneck elimination and exits, and so on. Tis work cannot provide a nor- strategy for generating SIC schemes was proposed, which has malized method to determine the detail station control high computational efciency for application to large-scale actions. subway networks. Te approach has a clear meaning and However, the control rate/strength of the scheme could can be expanded easily by considering other factors. A tool provide a guidance for setting control actions. Te control based on the proposed method has been developed in the C# rate represents the percentage of passengers who are limited programming language. A case study of the Beijing subway to entering the station relative to the travel demand, which validates that there are good performance and practical value canalsoberegardedasthefowspeedreductionrate.Ten, ofthemodel.Testudycansupportmanagersinconstructing what we need to do is to use some proper measures to scientifcally SIC plans and help station masters adopt proper slow down the infow speed. We think the microsimulation actions in reference to the control rate. tool, such as LEGION and VISSIM, which is widely used A static SIC plan is suitable for recurrent congestion for evacuation evaluation for stations, is a useful method to during peak hours because commute travel is very stable in determine the detail actions. the subway system. However, there are also sudden changes Journal of Advanced Transportation 15

Table 6: Deviations of section fows between the new scheme and the actual scheme.

Relative deviation (%) ID Line 7:00–7:30 7:30–8:00 8:00–8:30 8:30–9:00 9:00–9:30 Average ∗ (1) Line 1 4.66 5.66 4.78 −7. 7 5 −12.19 −0.97 (2) Line 2 0.54 3.58 −0.12 0.49 −1.07 0.68 (3) Line 4 1.83 2.77 1.49 1.03 −0.81 1.26 ∗ (4) Line 5 10.33 8.95 −6.24 −7. 2 1 −8.97 −0.63 ∗ (5) Line 6 3.88 7.11 −7. 4 0 −6.50 −3.93 −1.37 ∗ (6) Line 7 0.32 0.73 0.67 0.29 0.33 0.47 ∗ (7) Line 8 6.16 7.75 −7. 31 −3.78 −1.61 0.24 ∗ (8) Line 9 0.22 −1.79 −2.14 0.83 −1.58 −0.89 ∗ (9) Line 10 −1.17 0.84 −0.84 1.38 0.51 0.14 ∗ (10) Line 13 −1.15 −0.89 1.35 −1.06 0.28 −0.29 (11) Line 14 0.10 0.10 −1.07 −0.47 0.03 −0.26 (12) Line 15 0.72 −0.54 0.96 −0.27 −1.33 −0.09 (13) Line 16 0.34 −0.21 1.63 −1.15 −1.71 −0.22 ∗ (14) Line BT −0.29 1.02 0.31 −0.13 1.26 0.43 ∗ (15) Line YZ −1.93 1.71 −1.21 −0.35 −0.26 −0.41 ∗ (16) Line CP −1.90 3.12 4.31 −5.58 −1.07 −0.22 (17) Line FS 0.65 6.37 −3.42 −4.64 −2.96 −0.80 (18) Line JC −1.11 0.03 −0.01 0.55 1.10 0.11 Note. ∗ means there is control stations on these lines. in congestion pattern caused by mass fows, unexpected [4] P.Zhao, X. M. Yao, and D. D. Yu, “Cooperative passenger infow accidents, severe weather, and so on. Online self-adaptive control of urban mass transit in peak hours,” Journal of Tongji control approaches can be developed in the future by consid- University,vol.42,no.9,pp.1340–1443,2014. ering real-time passenger fow status, such as passenger fow [5]X.Yao,P.Zhao,K.Qiao,andD.Yu,“Modelingoncoordinated density on the platform and train. passenger infow control for urban rail transit network,” Journal of Central South University (Science and Technology),vol.46,no. 1, pp. 342–350, 2015. Conflicts of Interest [6] “Beijing Transportation Research Center, Report on Beijing Te authors declare that there are no conficts of interest Trafc Operation, Beijing Transportation Research Center, Bei- jing, China, 2016,” Tech. Rep. regarding the publication of this work. [7]Y.LiuandP.Charles,“Spreadingpeakdemandforurbanrail transit through diferential fare policy: a review of empirical Acknowledgments evidence,” in Proceedings of the 36th Australasian Transport Research Forum, ATRF 2013,Australasia,October2013. Te authors would like to acknowledge the Beijing subway [8] G. Currie, “Quick and efective solution to rail overcrowding: for data support. Tis research is supported by the National Free early bird ticket experience in Melbourne, Australia,” Natural Science Foundation of China (Grants nos. 71701011 Transportation Research Record, no. 2146, pp. 35–42, 2010. and 51478036) and Research Project of Beijing Mass Transit [9] M. Afabuzzaman, G. Currie, and M. Sarvi, “Modeling the Railway Operation Co., Ltd. (Grant no. 2017000501000003). spatial impacts of public transport on trafc congestion relief in Melbourne, Australia,” Transportation Research Record,no. References 2144, pp. 1–10, 2010. [10] R. Cervero, “Time-of-day transit pricing: comparative US [1] Beijing municipal commission of transport, Regulations on the and international experiences: foreign summaries,” Transport operational safety management of urban rail trafc (DB11/T 647-, Reviews,vol.6,no.4,pp.347–364,1986. 2009, Beijing municipal administration of quality and technology [11] S. R. Jara-Diaz, “Alternative pricing schemes for the Santiago supervision, Beijing, China, 2009. underground system,”in 14th Summer Annual Meeting of Public [2] Te Beijing News. Current station infow control mode of Bei- Transport Planning and Operation,pp.281–290,Sussex,UK, jing Subway http://bj.bendibao.com/news/201373/109047.shtm. 1986. [3] Beijing Subway. Adjustment of station infow control mode [12] P. Aitken, “Meeting the Funding Challenges of Public Trans- andcontrolperiodofBeijingSubwayforDecember2016, port,” Report prepared for Tourism & Transport Forum, Aus- http://bj.bendibao.com/news/20161215/236752.shtm. tralia, 2010. 16 Journal of Advanced Transportation

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