Field observations and modeling of waiting pedestrian at subway platform

Information Sciences 504 (2019) 136–160

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Information Sciences journal homepage: www.elsevier.com/locate/ins

Field observations and modeling of waiting pedestrian at subway platform Min Zhou a, Hairong Dong a,∗, Fei-Yue Wang b,c, Yanbo Zhao d, Shigen Gao a, Bin Ning a a

State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, PR China The State Key Laboratory of Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Science, Beijing, 100190, PR China c Center for Military Computational Experiments and Parallel Systems Technology, National University of Defense Technology, Changsha, Hunan, 410073, PR China d Department of Electrical Engineering, University of Southern California, CA, 90089-2560, USA b

a r t i c l e

i n f o

Article history: Received 3 July 2018 Revised 16 May 2019 Accepted 30 June 2019 Available online 11 July 2019 Keywords: Waiting pedestrian Field observation Mathematical modeling Fuzzy logic Behavioral heuristic Waiting mode

a b s t r a c t As a common human activity in subway platform, waiting occupies a large amount of pedestrians’ time and plays an important role in the aggregation, circulation and segregation of pedestrian flows. In order to explore the behaviors and characteristics of waiting pedestrians and their effects on walking behavior of passing pedestrians, we carry out an investigation at two major Beijing’s subway stations to collect the data of pedestrians at subway platforms by using field observations and video recordings. The extension of fuzzy logic based models, incorporating with the behavioral heuristic rules, are proposed to investigate pedestrian’s waiting behaviors based on the waiting modes at subway platform. In addition, the effects of varied environments including train arrival and density variety on pedestrian’s perception are taken into account in the modeling process. Simulations on real life scenarios of a major Beijing subway station are implemented to validate and calibrate the proposed models by contrasting the simulation results with the collected field data. The effectiveness of the proposed models is also demonstrated. Finally, the effects of waiting pedestrians with different modes on the dynamics of passing pedestrians are evaluated and quantified by these simulation models. Simulation results show that the waiting pedestrians under different waiting modes have different influences on the delay time, walking speed and turn angle of passing pedestrians, especially under high density level. Our findings can give some recommendations for the organization of pedestrian flows as well as the layout of facilities and waiting zones at subway platforms. © 2019 Elsevier Inc. All rights reserved.

1. Introduction The subway system is acknowledged as a fast, efficient, convenient and environmentally friendly transportation mode in the world [14]. It provides a feasible solution to alleviate the traffic pressure for those developing countries with a large population and crowded big cities such as China and India. However, many subway stations have to limit the number and ∗

Corresponding author. E-mail address: [email protected] (H. Dong).

https://doi.org/10.1016/j.ins.2019.06.062 0020-0255/© 2019 Elsevier Inc. All rights reserved.

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rate of arriving passengers because of very high levels of passenger density at subway hall and platform. It may bring about many kinds of potential risks such as overcrowding, panic and trample to passenger crowd themselves, and also challenges to organizers and administrators. Therefore, effective and rapid circulation of passengers in these facilities is indispensable to improve the operational efficiency, especially during peak hours. In the past decades, a number of microscopic pedestrian models, such as social force model [6,17], cellular automation model [12,35], lattice gas model [15], and agent-based model [27], neuro-fuzzy architecture [1], as well as computational experiment-based method [31] are widely used for the study of dynamical characteristics of pedestrian and evacuation flows in the large buildings. Referring to pedestrian behaviors in subway stations, a multiagent-based model including the subway station environment, pedestrian model and interactive rule base has been proposed by Chen et al. [2], which has formed a relatively complete theoretical framework for the simulation of subway station and performed well in reproducing and predicting of pedestrian behaviors in subway station. Passenger boarding and alighting behaviors in metro stations have been studied based on a cellular automata model [35] and a pedestrian traffic micro-simulator with experiments [22]. The effects of pedestrian management strategies and different group sizes in the boarding and alighting performances (time) of passengers at metro stations have also been analyzed. Zheng et al. [37] have investigated the pedestrian movement behaviors in the queuing process in subway stations based on the social force model and the queuing rule. The determining factors of the queuing rule were the desired force, the nearest pedestrian ahead and a self-stopping mechanism. Passengers choice behaviors such as route choice of vertical facilities [24], path choice [11], exit choice [36], and waiting area choice [32], have been investigated from different perspectives. The safety strategies and key influential factors of passenger evacuation in subway stations have been evaluated and investigated in [23] and [9] respectively. The impact of roundabout design on the intersecting pedestrian streams in subway station have been explored by conducting a series of field experiments [25]. The effects of three factors including roundabout size, guiding signs, and a greater number of streams intersect on traffic efficiency have been investigated in the same study. Sun et al. [26] have conducted pedestrian experiments to investigate the effects of funnel shape buffer zone with different angles on traffic efficiency of the bottlenecks. These studies have been proven to be helpful for guiding the design and optimization of safe evacuation strategies and pedestrian facilities in subway stations. In addition, the short-term subway passenger flows have been forecasted by using multi-scale radial basis function networks and transit smart card data [16]. Xu et al. [30] have analyzed the capacity of subway station by using the queuing theory. A theoretical support for agencies has been provided to optimize the operation of subway stations. Previous works have mainly focused on the dynamical behaviors and characteristics of moving passengers. However, a large amount of passengers’ time has been spent on waiting at the subway platform. According to field observations from some real subway stations, waiting occupied over 50% of total time from pedestrians entering to leaving the subway platforms. Waiting crowd group is a key factor influencing passengers walking patterns and times as well as traffic efficiency of subway station but was mostly ignored in the field of pedestrian and evacuation dynamics [3,33]. As a common human activity at subway platforms, waiting has attracted limited attention specifically to study the waiting strategies and models. Pettersson [19] has studied passenger waiting strategies on railway platforms by taking into account the effects of information and platform facilities. They have found that waiting pedestrians at subway platform tend to cluster around entrances and seats or stand close to the doors. Wu et al. [29] have studied effects of installation of platform screen doors and the regional function transition on the waiting behavior and level of service at stations based on a waiting area division method. Seitz et al. [21] have performed a field observation at a train station platform and analyzed some characteristics of waiting pedestrians, such as personal space requirements and choose of waiting positions, the times passengers staying at one position, and safety distance kept to the border of the platform. For the modeling and simulation of waiting pedestrians, a cellular automata based model considering the influence of waiting pedestrians on crowd dynamics have been proposed first by Davidich et al. [3] and its effectiveness have been validated by contrasting field observations at two railway stations with simulation results of the corresponding real life scenarios. The qualitative influences of waiting (standing) pedestrians on the walking time and trajectories of pedestrians passing by have been analyzed by simulations. Johansson et al. [10] have extended to the social force model to waiting pedestrians. Three alternative extensions of the waiting model (the adapting preferred position model, the preferred position model and the preferred velocity model) have been proposed to produce waiting behavior and evaluate their effects on the level of service for passing pedestrians. Simulations of the effects of waiting pedestrians on dynamics of passing pedestrians have been performed. These results have shown that high density level of waiting pedestrians may increase the walking time and walking distance significantly. Waiting pedestrian models proposed by Davidich et al. [3] and Johansson et al. [10] have been specified that they have the ability of reflecting some facts of waiting pedestrians by simulations. However, these models did not or only partially validated and calibrated using experiment/field data. These researches have focused on investigating waiting pedestrians who are scattered in the platform without regularity. Therefore it is less clear whether these models can reproduce collective phenomena and predict microscopic behaviors of waiting pedestrians realistically. From our observations at subway platform, we found that not all of pedestrians choose the scattering mode when they are waiting for a train. On the contrary, orderly waiting modes, such as queuing mode and clustering mode, are occurred much more common than scattering mode because of the constraints of moral codes and/or cultural norms and the guidance of marking lines on the platform. The waiting pedestrians under different waiting modes have different effects on pedestrians’ walking patterns and behaviors, especially under high density level. In order to further explore and improve the research of waiting behaviors and its effects on walking behaviors of passing pedestrians, the extension of fuzzy logic based model is adopted to study waiting pedestrian taking into account waiting modes. The fuzzy logic based pedestrian

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Fig. 1. Schematic diagram (top-down view) of observed platform in the subway station.

models proposed by Zhou et al. [38,39] have proven to be capable of reappearing crowd motion realistically, which also can make full use of human experience and behavioral heuristics as well as perceptual information obtained from interaction with surrounding environments. In addition, the model can be conveniently used because of the elementary behavioral analysis and weighting integration strategies. We will investigate two major Beijing’s subway stations to collect waiting pedestrian related data such as distribution of waiting pedestrians on waiting zones of the platform, percentages of waiting modes under different density levels, distributions of distance headway, distributions of speed. More importantly, the waiting pedestrians data collected from field observation are used to validate and calibrate the proposed models. We also demonstrate the effectiveness of proposed models and these models can reappear the waiting behaviors realistically. The effect of waiting pedestrians and their modes on dynamics of passing pedestrians are evaluated by simulations of proposed models. The main contributions of this paper are briefly summarized as follows: (i) We discover three waiting modes of waiting pedestrians at subway platform and their effects on patterns and behaviors of walking pedestrians based on the field observations at two subway stations; (ii) The fuzzy logic based models for waiting pedestrians, incorporating with the behavioral heuristic rules, are proposed based on the waiting modes and behavioral characteristics; (iii) The effects of varied environments including train arrival and density variety on pedestrian’s perception are taken into account in the modeling process; (iv) The proposed models are validated and calibrated by contrasting the real field data with the simulation results; (v) The effects of waiting pedestrians and their modes on dynamics of passing pedestrians are evaluated and qualified by simulations. The remainder of this paper is organized as follows. The next section introduces the field observations at two major Beijing’s subway station that collect stationary data of a platform and pedestrian data at tactical level and operational level. In Section 3 the fuzzy logic models for waiting pedestrians are proposed based on the waiting modes and behavioral characteristics. In Section 4 the proposed models are calibrated and validated and the impacts of waiting pedestrians and their waiting modes on the passing pedestrians are quantified by simulations of real life platform scenarios. The Section 5 concludes this paper and proposes some possible problems for future research. 2. Observation and data collection We investigated two major Beijing’s subway stations, i.e., Xidan station and Zoo station, with typical topologies and characteristics of pedestrian flows, which are also representative of transfer station and non-transfer station respectively. The schematic diagram of a typical platform of Beijing subway stations is shown in Fig. 1. These stations adopt the popular island platform with screen doors. The 6-coupled train with 24 doors is equipped in each direction. These doors are numbered with 1 to 24 from left to right in the up direction and with reversed order in the down direction. The train stops in a fixed place with the deviation of 0.3 meters because of the adopting of high precision positioning system and signal system [4]. Waiting zones are specified in advance according to the location of doors when the train stops in the subway station. The stationary data of the platform is shown in Fig. 1. It covers approximately 1440 m2 , which contains waiting area, circulation area, and areas covered by columns, walls and stairs/escalators. The brown lines represent screen doors. The black zones correspond to obstacles (including columns and walls) that pedestrians can’t across. The waiting zones are marked with gray rectangle where pedestrians stand on and wait for a train. All these zones are divided into two categories: the unrestricted waiting zone and the restricted waiting zone (see Fig. 2) according to the sizes of available zones. The main difference between them is that the available zone of the latter category is restricted by obstacles and the former is not. The purple line zone represents the potential waiting zone which will be converted into waiting zone when the number of waiting pedestrians exceeds the capacity of default waiting zone, and it may be further extended with increasing in density of the waiting zone. The walking zone is marked with black line which is reserved as circulation of pedestrians. All these marking lines are used in subway platform to guide pedestrians to wait for a train or leave the platform smoothly rather than compel them to do it. Analysis of field observations and surveillance videos were conducted on these subway stations. We mainly concerned the analysis of pedestrian waiting behaviors such as which waiting mode will be chosen and how waiting pedestrians interact with surrounding people who want to board a train or cross the waiting zones. Our purpose was to investigate which and

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Fig. 2. The waiting zone at the subway platform, (a) unrestricted waiting zone and (b) restricted waiting zone.

( g) Low 1

0

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Fig. 3. Membership functions for global density.

how factors affect the behaviors of waiting pedestrians at the subway platform. Therefore, we mainly focus on the collection of data including: 1) pedestrian waiting mode, 2) waiting zone choice, 3) waiting time distribution, 4) spatial social distance between adjacent waiting pedestrians, 5) effects of walking and waiting pedestrians on waiting behaviors and 6) effects of train arrival and density variety on the distribution of distance headway between two adjacent pedestrians at subway platform. For the field observations in Xidan station, twelve persons investigated pedestrian waiting behaviors at the subway platform during a time period between 07:00 to 19:00 on October 12 to 18, 2015. These investigators were scattered evenly at the upper/lower side of the platform without disrupting the normal subway operation. At first, activities of waiting pedestrians at the tactical level were investigated, which include the distribution of waiting pedestrians on the waiting zones, common waiting modes and their percentages at various density levels. Then, we collected the measurements on the distribution of distance headway kept to the closest pedestrian ahead before and after a train arrival in the station as well as its distribution with the varying of densities on the waiting zones. The operation time of Beijing subway is usually from 5 a.m. to 11 p.m. The time intervals of 5 a.m. to 6 a.m and 9 p.m. to 11 p.m. correspond to low peak period, the time intervals of 7 a.m. to 9 a.m and 5 p.m. to 7 p.m. correspond to peak period. The rest of operation time correspond to flat hump period. The division principle is based on official passenger flow historical data, field observation data, and expert experience and knowledge. The global density ρ g is defined as the quotient between the number of pedestrians and the total available area of the platform. It is represented by the three linguistic fuzzy sets of {Low, Middle, High}, with the trapezoidal membership functions of [0, 0, 0.3, 0.4], [0.3, 0.5, 0.8, 1], and [0.9, 1.2, 2, 2], respectively. The widely-viewed triangular and trapezoidal fuzzy membership function is a good candidate to capture and represent the uncertainty and vagueness of linguistic assessments [8]. The determination of trapezoidal fuzzy memberships is based on the analyses of field observation data and communications with operation and management personnel of subway stations, which were interpreted in detail in the revised version. When the global density is less than a certain value (0.3 p/m2 ), the membership values of μlow (ρ g ), μmiddle (ρ g ), and μhigh (ρ g ) are 1, 0, and 0 respectively. When the global density is large than a certain value (1 p/m2 ), the membership values of μlow (ρ g ), μmiddle (ρ g ), and μhigh (ρ g ) are 0, 0, and 1 respectively. The feasible membership functions for global density were shown in Fig. 3. Compared with Gauss, Triangular, and Sigmoid models, the trapezoidal fuzzy membership is the most appropriate model.

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Fig. 4. Distribution of waiting pedestrians on waiting zones of the platform along the up direction of the train under different density levels.

Fig. 5. Illustration of pedestrians waiting on the platform with (a) queuing mode, (b) clustering mode, and (c) scattering mode.

The universe of discourses of density is set to [0, 2] p/m2 based on the field observation data and expert experience and knowledge. The fuzzy sets of ‘Low’, ‘Middle’, and ‘High’ represent three typical degrees of crowding. For the low density, pedestrians can move freely on the station platform with desired speeds. They have enough space for waiting and circulation. For the middle density, pedestrians can move with normal speed and they are beginning to be affected by the surrounding neighbors. For the high density, it is difficult to maintain desired, or even normal speed due to the aggregation of large numbers of passengers on the subway platform. The personal space is severely restricted by the surrounding neighbors and the movement speed or/and headway are significantly reduced. We collected data about the distribution of waiting pedestrians on waiting zones of the upper side of the platform (see Fig. 4), which were collected from three different time periods, i.e., peak period, flat hump period and low peak period. From Fig. 4 we can see that the distribution presents a saddle-shape along the train operation direction under any density level. More pedestrians were willing to choose waiting zones close to the entrances of the platform, which shows two obvious peaks in the distribution curve. Conversely, the zones far from the entrances was less chosen by waiting pedestrians. The distribution of pedestrians on the platform is mainly affected by the density of waiting zones and the distance to the waiting zones. While higher density leads to a more even distribution on the platform, and vice versa. Obviously, pedestrians do not distribute uniformly over the platform, which is not accord with a common hypothesis made in many simulation models. The hypothesis of uniform distribution was rejected based on the field observations in many researches [3,21]. Three common waiting modes i.e., queuing mode, clustering mode and scattering mode were also observed during waiting processes (see Fig. 5). Queuing mode is an orderly waiting mode that pedestrians follow with and keep a certain distance from the front pedestrian. Clustering mode is characterized by pedestrians spontaneously gathering together at both side of waiting zones with different shapes. The randomness is the most visible trait that distinguishes scattering mode from other modes. An arbitrary available location within a waiting area may be chosen as the standing position. It is worth noting that the multiline queuing mode would be occurred when the number of waiting pedestrians exceeds the capacity of waiting zone in uniline queuing mode, which may occurred more frequently in the restricted waiting zone than in the unrestricted waiting zone under same density conditions. However, the reason of occurrence of multiline queuing mode is much more than the above-mentioned incentive. The situations that pedestrians wait in uniline or multiline at waiting zones are known collectively as queuing mode. According to the line marks mounted on the waiting zones of the platform, the reserved zones are set for the pedestrians who want to alight the train and walk through waiting zones. In general, the reserved zones are not occupied by the

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Table 1 Four categories of spatial social distance at waiting zones. Category

Object

Hall (1966)

Observed value

Intimate distance

Close relationships Family members Friends Associates Strangers Newly formed groups New acquaintances Public

dc1 < 0.45 m

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Personal distance Social distance

Public distance

pedestrians who are waiting for a train with queuing mode. However, they may be compressed in the clustering mode. One possible explanation is that the number of waiting pedestrians exceeds the capacity of the predefined waiting zone. Pedestrians waiting in the scattering mode are characterized by that an arbitrary location within waiting area may be chosen as the standing position. So, the restriction of reserved zones is disappeared. The classifications of waiting modes are not absolutely identical with above definitions. For instance, a situation that pedestrians are waiting in line with several individuals outside the queue is often viewed as queuing mode too. With further observations, the data about the percentages of waiting modes under various density levels were also collected at restricted and unrestricted waiting zones (see Fig. 6). Notice that the word “density” here represents the local density ρ l , which is defined as the number of pedestrians per unit area on the (potential) waiting zone. The local density ρ l is divided into three fuzzy levels {Low, Middle, High} based on the observed field data with the trapezoidal membership functions of [0, 0, 1, 1.5], [1, 2, 3, 4], and [3, 3.5, 8, 8], respectively. As shown in Fig. 6, with the increase in density, the percentage of queuing mode is decreased nonlinearly. The changing trend of the percentage of clustering mode is opposite with that of the queuing mode. For scattering mode, the percentage keeps low value with small fluctuation all the way. We observed significant differences between Fig. 6(a) and (b). The clustering mode occurs more commonly at restricted waiting zone than unrestricted zone under condition of the same density level. In addition to activities of waiting pedestrians at the tactical level, the waiting behaviors at the operational level were also investigated. The spatial social distances between pedestrians were collected. According to the analyses of Seitz et al. [21], the behavior and social interactions, such as interactional distances to different members, are regulated by physical environment, social environment and cultural norms. Following the research of Hall [5], spatial social distances between people are divided into four categories and their features are shown in Table 1. Pedestrians’ psychological expectation of personal space varies in different physical environments, social environments, moral code and cultural norm which regulate their behaviors and social interactions. From our field observations at subway stations, The values of distances are reassigned shown in Table 1. We found that the observed values of four categories of distances are not consistent with that proposed by [5]. The possible reason for this situation is that Hill’s [1966] results were presented in the situation of less dense and it is not suit for crowded urban environment. It is difficult to meet personal space requirements when being in dense communities, such as crowded trains, subway platform, or shopping mall. In such situations, pedestrians might lower their expectation for the requirement of personal physical space. We also collected the data of distributions of distance kept to front pedestrians. The investigation covered all three periods, i.e., peak period, flat hump period and low peak period, to guarantee data integrity. We took 1028 photos of waiting pedestrians who were standing in the waiting zones of platform by using handheld cameras over a week (see Fig. 7(a)). A total of 9230 valid samples, containing distance information at different density levels and waiting modes, were collected for the validation of waiting behavior models. The data of distance headway between adjacent pedestrians was collected

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Fig. 7. Illustration of (a) the photos for pedestrians waiting on the platform, and (b) the method for data collection of distance headway between adjacent pedestrians.

Fig. 8. Illustration of the video frames for pedestrians waiting on the subway platform.

manually by contrasting with edge of floor tile. The measurement error was ± 0.03 m under normal circumstances and can meet our demand (Fig. 7(b)). The F statistical test was performed for Xidan subway station to collect data for estimating the parameters of fuzzy variable of distance, which is represented by two linguistic fuzzy sets ‘Close’ and ‘Far’. The respondents should be familiar with the concepts of fuzzy variables and possess the capability of expressing them approximately with quantity. They were asked to answer a question that how far do you think a distance between two adjacent pedestrian is ‘Close/Far’ when you are waiting a train at platform? The test was included under the conditions of middle density level of pedestrians and no trains stopped at the station. In this test, the respondents contained young, middle-aged, and old, whose ages range from 14 to 65. A total of 218 sets of useful data were collected in subway platform over a week of test. At two stations four fixed gun video surveillance cameras were placed in the ceiling position (top-down view) at 2.75 m height from the floor. These cameras worked throughout the whole service hours of stations and covered the whole platform and buffer zone between waiting zones and stairs/elevators. They captured the pedestrians’ movement behaviors and dynamics at the subway platform. The video frames are shown in Fig. 8. The size of captured image was 80 0∗ 60 0 pixels, and the videos were captured at 30 frames/s. We were mainly concerned with the pedestrian waiting behaviors on the operational level. One of the most important observations was how waiting pedestrians interact with adjacent person (including waiting and/or walking pedestrians) who were often considered to be main stimuli affecting pedestrian waiting behaviors. We also investigated how the speeds of waiting pedestrians vary over time under different waiting modes and how long does it take pedestrians to wait for a train at different locations of the platform. First, the behaviors of waiting pedestrians at the platform were analyzed from a qualitative perspective based on video observations. For pedestrians who waited in queuing mode, we observed three common behaviors, i.e., the front pedestrianfollowing behavior, walking pedestrian-conceding behavior and goal-seeking behavior during the waiting process. They followed with and kept a certain distance from the closest pedestrian ahead. A wave-like propagation phenomenon of the gap between the successors had been observed. They would also like to make a room for walking pedestrians who want to

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Fig. 10. A general framework for the decision process of pedestrian behavior.

move through the queue. All the while, a tendency of moving in directions to their goals regardless of external environments was also found from analysis of videos. Pedestrians who were chosen the clustering mode spontaneously gathered together at both side of waiting zones with different shapes, which was similar to the formation of clogging phenomenon. A pedestrian waiting in the scattering mode may select an available location within the waiting areas as his/her standing position without thinking too much about the moral code and/or cultural norm, in which they may get the upper hand to board the train. We analyzed several recorded videos of different times of the day, including peak period, flat hump period and low peak period, each having a runtime of train running interval. The positions of pedestrians were extracted from these video clips and their coordinates were recorded at every time step based on semiautomatic approach. We adopted a method similar with that proposed by Teknomo [28] to complete this work. A mouse pointer was used to indicate the centre of foot of a pedestrian on-screen at every time step. Then, the time stamp, local density, waiting mode and 2D coordinates were stored in memory for later use. Repeat above procedure until all of the pedestrians appeared in the video were captured. The recorded data were geometrically corrected and converted into 2D coordinates in realistic scenarios. The time step of 0.5 s was chosen in this program to, i.e., picking a point every 15 frames. We collected 7715 set of valid samples and each sample contains information of time stamp, local density, waiting mode and 2D coordinates. Finally, the quantitative data about waiting time distribution on the platform was calculated from above dataset. In Fig. 9, the mean waiting time was measured for each measurement cell with side lengths of 1 m. Warmer colours indicate the positions where pedestrians waited more time. We observed longer time of waiting at the positions near the entrances compared to that are far from the entrances, which was in accordance with the results of Fig. 4. The mean waiting time between two different operation directions (upper and lower part of the platform) was symmetrical in general. Additionally, only very few pedestrians were waited a long time at locations close to the wall/escalators in the middle of the platform. So the waiting zones are located in certain areas rather than the whole platform. 3. Modeling of pedestrian waiting behavior Modeling and simulation of pedestrian dynamics plays an essential role in acquaintance of complicated motion features and self-organized phenomena under normal and emergency situations. The fuzzy logic based model proposed by Zhou et al. [38] has been proven to be capable reappearing crowd motion realistically, which also can make full use of human experience, behavioral heuristics and perceptual information obtained from interaction with surrounding environments. In addition, the model can be conveniently applied and extended because of the elemental behavioral analysis and weighting integration strategies. A general framework for elemental behavior matching process of pedestrian behavior is given in Fig. 10. Take the activity of waiting for a train as an example, pedestrians choose to queue in front of screen door. The three components i.e., front pedestrian-following behavior, walking pedestrian-conceding behavior, and goal-seeking behav-

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ior, are matched during waiting process, which are regarded as elemental behaviors of queuing waiting mode. Therefore, the extension of fuzzy logic based model is adopted to study pedestrian waiting behavior. According to the definition of Seitz et al. [21], waiting is the behavior of individuals remaining at a position until an event they expect occurs. For example, pedestrians wait for a train on the subway platform until the train is arriving. We mainly concern pedestrian waiting behaviors happened at the waiting zones of the subway platform during the waiting. These behaviors are modeled at tactical and operational levels based on the definition of Hoogendoorn et al. [7]. On the tactical level, the behaviors consist of pedestrian waiting mode choosing and waiting zone choosing. Modeling and analysis of tactical behavior are not the focus of this paper. So no more details will be given at the tactical level. However, the observed results are used as the input data of simulations. Finally, waiting also includes behavior on the operational level, i.e., how to choose waiting location and react to environments while waiting. As noted before, we focus on pedestrian waiting behavior at the subway platform where the screen door and marking line are configured. According to the results of field observations, there are three common modes i.e., queuing mode, clustering mode and scattering mode existing in the waiting process. The probability of scattering mode is comparatively lower than that of other two modes at subway platform because the waiting zone is specified in advance according to the locations of screen door or marking line. Waiting with scattering mode appears frequently in the railway station platform where the train stopping position is uncertain and screen doors are not installed in advance [3,21]. The pedestrians who choose different waiting modes exhibit various waiting behaviors. The waiting pedestrian model is proposed based on the following behavioral heuristics extracted from human experience and field observations: (1) Get close to the screen door; (2) The distance kept to neighbors affected by the social relationships between them (Keep a social distance to neighbors); (3) Follow the front pedestrian; (4) Decreases the distance headway with the increase of local density on the waiting zone; (5) The waiting pedestrians are compressed when the train is arriving. In this paper, the proposed behavioral heuristics are formalized and implemented in waiting pedestrian models based on a fuzzy logic approach. 3.1. Queuing waiting model Queuing is the most common waiting mode at the subway platform. A queue can be seen as a complete social system where agent’s behavior is governed by complex social rules and norms [13,18]. The waiting process of queuing mode can be described as follows. Once pedestrians enter a waiting zone, they begin to scan their visual field and detect a queue tail near the screen door. Then they set the queue tail as target (waiting location) and try to join the tail of the queue. A pedestrian in the queue follows with and keeps a certain distance from the front pedestrian. We proposed three possible reasons for the formation of queuing mode based on field observations and living experiences. (1) Line markings mounted on the waiting zones of platform guide pedestrians to stand inside waiting zones along the markings. These lines and arrows are likely to guide the pedestrians to wait in line along the direction of arrows and thus may suggest the queuing mode; (2) Waiting in a queue is a commonly accepted moral code and/or cultural norm, and they urge waiting pedestrians to stand in line and supervise behaviors of other people. Whoever violates codes and/or norms will be subjected to moral criticism; (3) Knowledge and common sense that waiting in line is an effective way to improve the efficiency of boarding and alighting and reduce the waiting time also benefit to the formation of queuing mode. These three aspects of the factors may encourage the formation of queue phenomenon. In the queue, we assume that all pedestrians are cooperative forming a line without queue-jumpers and line cutting. The illustration of the decision maker interacting with environments and following the social rules and norms while waiting with queuing mode is shown in Fig. 11. In the queuing waiting model, the desired direction θ d is directed toward the front pedestrian and the desired speed Vd is to keep pace with the front pedestrian. The waiting behavior is determined by the integration of recommendations of the front pedestrian-following behavior, walking pedestrian-conceding behavior and global goal-seeking behavior. The front pedestrian-following behavior makes the decision maker follow the movement of front pedestrian when he/she is waiting in the queue on a waiting zone of subway platform. This behavior is constrained by the front pedestrian who is waiting in the queue too. A fuzzy inference system is proposed to describe this behavior. The antecedents of the fuzzy inference system are the speed of front pedestrian, the distance and angle between the decision maker and front pedestrian f f f which are denoted with Vp , d p and θ p , respectively. The consequents are turning angle α 1 and movement speed V1 . The formulation of the front pedestrian-following behavior is summarized as follows:

  α1 V1



= R1 Vpf , d pf , θ pf



(1)

where R1 is the set of IF-THEN rules whose definitions of the antecedents and consequents are similar with those proposed in [38]. The terms “Large-Pos”, “Large-Neg”, “Small-Pos”, “Small-Neg” are short for “Large-Positive”, “Large-Negative”, “Small-Positive”, “Small-Negative”, respectively. These terms are five linguistic terms (fuzzy sets) which are used to cover the

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145

Fig. 11. Illustration of the decision maker facing waiting pedestrians under the queuing mode.

Table 2 Inference rule R1 for the front pedestrian-following behavior. Rule No.

Input

θ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

f p

Large-Pos Large-Pos Large-Pos Large-Pos Large-Pos Large-Pos Small-Pos Small-Pos Small-Pos Small-Pos Small-Pos Small-Pos Zero Zero Zero Zero Zero Zero Small-Neg Small-Neg Small-Neg Small-Neg Small-Neg Small-Neg Large-Neg Large-Neg Large-Neg Large-Neg Large-Neg Large-Neg

Output d pf

Vpf

α1

V1

Near Near Near Far Far Far Near Near Near Far Far Far Near Near Near Far Far Far Near Near Near Far Far Far Near Near Near Far Far Far

Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast Stop Slow Fast

Large-Neg Large-Neg Large-Neg Large-Neg Large-Neg Large-Neg Small-Neg Small-Neg Small-Neg Small-Neg Small-Neg Small-Neg Zero Zero Zero Zero Zero Zero Small-Pos Small-Pos Small-Pos Small-Pos Small-Pos Small-Pos Large-Pos Large-Pos Large-Pos Large-Pos Large-Pos Large-Pos

Stop Slow Fast Slow Fast Fast Stop Slow Fast Slow Fast Fast Stop Slow Fast Fast Fast Fast Stop Slow Fast Slow Fast Fast Stop Slow Fast Slow Fast Fast

turning angle α of a waiting passenger. For a more detailed descriptions see our previous works [38,39]. A total of 30 items of IF-THEN rules (R1 ) are constructed in Table 2 to motivate the pedestrian to follow the movement of the front pedestrian. f The human experience and behavioral heuristics extracted from field observations are reflected in inference rules. If the d p f

is Far and/or v p is Fast, the decision maker improves the speed to follow in the front pedestrian, and vice versa. The walking pedestrian-conceding behavior is that pedestrians who are queuing up to wait the train make room for walking pedestrians who want to move through the queue. The precondition is that the location of walking pedestrian belongs to the decision maker’s visual field, i.e., Pw ∈ VF. The interactions with walking pedestrians are considered in the

146

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160 Table 3 Inference rule R2 for the walking pedestrianconceding behavior. Rule No.

1 2 3 4 5 6 7 8

Input

Output

d pf

θ

Far Far Far Far Near Near Near Near

A A D D A A D D

w p

dw p

V2

Near Far Near Far Near Far Near Far

Stop Stop Stop Stop Fast Slow Stop Stop

model. The antecedents of the fuzzy inference system are the front pedestrian distance and the angle and distance between f f the decision maker and walking pedestrian which are denoted with d p , θ p and dw p , respectively (Fig. 11). The formulation of the walking pedestrian-conceding behavior is summarized as follows:

 α2 = 0,



V2 = −R2 d pf , θ pw , dw p



(2)

where the negative value of speed represents walking backward, and α2 = 0 corresponds to maintaining the current direction. It is unusual for a pedestrian to walk backward with directional variations. A total of 8 items of IF-THEN rules (R2 ) are constructed to dominate the waiting pedestrian to make way for walking pedestrians (Table 3). ‘A’ and ‘D’ are short for f ‘Approach’ and ‘Deviation’, respectively. The conceding behavior will happen if and only if the value of distance d p is ‘Near’ and a walking pedestrian is approaching the decision maker. The goal-seeking behavior is a kind of global behavior which reflects a tendency that the decision maker always moves in directions to his/her goal regardless of external environments. The formulation of the global goal-seeking behavior is summarized as follows:

  α3 V3

= R 3 ( d g , θg )

(3)

where dg and θ g denote the goal distance and goal angle between the decision maker and the goal, respectively. The rule set R3 dominates the decision maker to reduce the speed and turn to the goal direction sharply without missing the goal when the pedestrian is near to but not facing the goal. Conversely, the decision maker moves freely along the goal direction with fast speed when he/she is facing the goal. The final outputs of turning angle α and movement speed V are determined by integration of recommendations of front pedestrian-following behavior and goal-seeking behavior with mutable weighting factors by using the weighted average method.

⎧ ⎨α =

⎩V=

δ p f ·α1 +

δ pc ·α2 +

δsg ·α3 ,

δ +

δ +

δ pf

pc

sg

δ p f ·V1 +

δ pc ·V2 +

δsg ·V3

δ +

δ +

δ pf

pc

(4)

sg

where denotes the crisp value of the counterpart fuzzy set which is calculated by using the Center-of-Gravity defuzzification method. The definitions of weighting factors

δp f ,

δ pc and

δsg are similar with those proposed in Zhou et al. [38], which are represented by the three fuzzy sets {Low, Middle, High}. The formulation of the weighting’s assignment principle is summarized as follows:

 δp f   δ pc = R4 d pf , θ pw , dwp , dg δsg

(5)

The weighting’s assignment rules (R4 ) are constructed to integrate multiple elementary behaviors and resolve potential conflict (see Fig. 12). The weighting factors are adjusted dynamically according to the perceptual information obtained from surrounding environments. The final decisions are dominated by the walking pedestrian-conceding behavior if and only if there are walking pedestrians who want to cross the queue from the front space of the decision maker and the front space is relatively tight. The front pedestrian-following behavior plays a key role in final outputs if the decision maker does not encounter the crossing pedestrians. The weight of goal-seeking behavior is not going beyond ‘Middle’ at all times.

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Fig. 12. Weighting’s assignment rules.

3.2. Clustering waiting model From the field observation during the peak periods, clustering mode is characterized by pedestrians spontaneously gathering together and clogging in waiting zones in front of each screen door along the marking lines on platforms (Fig. 5(b)). There are two main and essential reasons about the formation of clustering waiting mode: (1) With the accumulation of waiting pedestrians, a limited waiting zone can’t hold so many pedestrians if they are waiting in queuing mode or scattering mode; (2) Because of the limited dwell time of a train, the rear pedestrians who want to board the train in time should to choose a position near the screen door and/or easy to board the train. According to the results of field observations, the probability of clustering mode appearing is high when the local density of waiting pedestrians is high, and vice versa. When an assigned waiting zone is not enough to hold so many waiting pedestrians, a part of walking zone (potential waiting zone) is converted into waiting zone and the reserved zone is compressed (Fig. 5(b)). From our field observations at subway platforms, the pedestrians waiting in front of the platform screen door under the clustering mode can be seen as two clogging groups who squeeze each other so that they can board the train as soon as possible. It is worth mentioning that the reserved zone acts as an invisible obstacle for waiting pedestrians which prevent them from standing in this zone. The fuzzy logic based model proposed by Zhou et al. [38] has been shown to be a suitable model for reappearance and description of pedestrian evacuation behaviors at the bottleneck scenario. This model is adopted to simulate pedestrians waiting behavior in clustering mode during waiting process. 3.3. Scattering waiting model There are other kind of waiting pedestrians who are less constrained by physical environment, moral codes and/or cultural norms. Pedestrian waiting behaviors in scattering mode are characterized by its randomness. Previous model has been proposed by Davidich et al. [3] based on a precondition that an arbitrary location within predefined waiting zone is chosen as the next destination once their have reached this zone. The pedestrian stands at the chosen location for a period of time until a expected thing is happen, for instance, a train is arriving at the station. An arbitrary location within waiting area may be chosen as the standing position. However, the location choosing behavior is not at all irregularity. Moreover, the waiting pedestrian is not motionless once he/she has chosen a location in advance but may move to a certain extent because of a varied physical environment. Based on field observations at subway station, combining with previous research results [5], pedestrians’ waiting behaviors and social interactions in scattering mode are regulated by the following two behavioral heuristics: (1) Keeping a certain distance from nearby person to regulate private space and privacy; (2) Ignoring the effects of moral codes, cultural norms and/or line markings mounted on the platform. Once a passenger enters the waiting zone, a advantage location will be chosen as his/her initial standing location according to the physical environment and social environment on the premise that the psychological expectation of personal space is met. The group of pedestrians waiting on a scattering mode can be seen as a clogging crowd who gather together in front of platform screen door with advantage and comfortable locations, the fuzzy logic based model [38] is adopted to simulate pedestrians waiting behavior in scattering mode during waiting processes.

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The initial standing location may be changed when a pedestrian’s personal space is encroached by other pedestrians. Then he/she will search for a better location to move to and re-establish personal space by adjusting social interaction to a desired level based on real waiting conditions. Finally, initial location is given up and a closest available vacant location is chosen. 3.4. The principle for changing of waiting location The waiting location changing principle is inspired by Schelling’s segregation model [20], which gives a fundamental assumption that an individual decides to change his/her waiting location as soon as the ratio of neighboring people who entered the scope where they shouldn’t be there exceeds an tolerant threshold. In the original segregation model, there are two kinds of agents and each agent chooses to move or to stay according to his/her neighborhood configuration. A satisfied agent is one that is surrounded by at least t percent of agents that are like itself. This threshold t is one that will apply to all agents in the model, even though in reality everyone might have a different threshold they are satisfied with. The behaviors of an individual are affected by the social and physical features of the surrounding environment. Pedestrians being in crowded environment have high tolerant threshold because of difficulty in maintaining personal space requirements. So the location changing behavior at crowded subway platform is likely to be rarer than that at less dense environments. The choice of waiting position belongs at a tactical level in the model hierarchy, so the preferred waiting positions are assigned before performing a simulation. We defined the concept of uncomfortable to quantify influence of the social characteristics of the surrounding environment, it was derived from that of ‘satisfaction’ of Schelling’s segregation model, what is Si

Si =

Nv f −

j,k

Nikj

Nv f

(6)

where Nvf represents the number of pedestrians appeared in the visual field of pedestrian i and Nikj represents the number of pedestrians appeared in the distance they should be there. For instance, the value of Nikj is equal to 1 if a friend appears in the personal distance, and 0 otherwise.



Nikj =

1 dikj ∈ dck , j = 1, 2, · · · , Jk , k = 1, 2, 3, 4 0 dikj ∈ / dck

(7)

4 where k=1 Jk = Nv f . The individual-dependent tolerance threshold η of uncomfortable varies in different environments. According to the field observation at subway platform, the changing of waiting locations is not frequent. At the crowded subway platform, the threshold is set to 20% empirically. A waiting pedestrian walks a suitable way to the next waiting location and keeps waiting for a train until the value exceeds the tolerant threshold. The expected microscopic behavior occurred in this process can be produced by adopting the fuzzy logic based model [38]. We followed a assumption used in [10] that the desired speed increases linearly with the distance to the next destination (waiting location) until it reaches the normal desired speed at a distance d from the destination. The desired walking direction points to the destination. Finally, the waiting pedestrians reach the destination and their desired speeds returns to zero.



Vd =

d pd  d

Vn

Vn ·

d pd d

d pd < d

(8)

where dpd denotes the distance between current location to the next destination, and Vn denotes the normal desired speed. d is a constant and it can be chosen by considering the motion of a free pedestrian in the proximity of its desired position. 3.5. Effects of varied environments on pedestrian’s perception The behaviors (activities) of a person are usually determined by individual’s characteristics, cultural norms, subjective evaluations of space, and the environment that he/she exists in [21]. For the same person, the environment is regarded as deterministic factor in making decision for individual’s behaviors. The physical environment represents the conditions that affect the behavior of people and the development of things and it is not static over time. Pedestrians’ cognition and perception of things also change with time and environments. For example, the public demand for personal space continues to reduce in a proactive or passive manner, with increasing crowd density in public space. The personal distance of 0.6 m is seen as acceptable in low density space but of 0.2 m in high density space. Individual’s perception on spatial social distance may be re-formed by reducing expectation to a relatively low level. From our field observations at subway stations, we found that the environmental change including train arrival and density variety are main distinction of environments, and these stimuli have significant influences on pedestrian’s perception on expected personal distance. The perceive value of distance is reduced as the train arrival and it also reduces with the growing density of pedestrians, and vise versa. These factors are also taken into account in the modeling and simulations. f The distance d p is represented by the two linguistic fuzzy sets {Near, Far}. We assumed that their membership functions follow a trapezoid model based on our experience and knowledge. The original membership functions were shown in black

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149

Fig. 13. Contrast of membership functions for the distance d pf .

Fig. 14. Scale coefficient κ .

lines of Fig. 13. The expression of trapezoidal membership functions is simplified into its parameter form [x1 , x2 , x3 , x4 ]. Under the influence of stimuli, the membership functions are changed into the κ · [x1 , x2 , x3 , x4 ], as shown in red dotted lines of Fig. 13, where κ is a scale coefficient. It is used to quantify the influences of environmental change on pedestrian’s perception on expected personal distance. More specifically, the scale coefficient has negative exponential relation to the density when the density of waiting zones is larger than their capacities. Small increase will lead to great changes in the scale coefficient. When the train has arrived at the station, the impact of train arrival is considered. Otherwise, its impact is negligible. The step function was presented to describe its relationship. The scale coefficient κ is defined as follows:

  sgn(ρ − ρ ∗ ) + 1 sgn(t − t ∗ ) + 1 ∗ κ = 1 − ( τ · ( 1 − e ( ρ −ρ ) ) · + (1 − τ ) · 2

2

(9)

where sgn( · ) represents a sign function, t∗ and ρ ∗ represent a point in time that a train is arriving and capacity of a waiting zone, respectively. The parameters of t and ρ correspond to the time-base of train interval and crowd density, respectively. When ρ ∗ < ρ and t < t∗ , then sgn(ρ − ρ ∗ ) = sgn(t − t ∗ ) = −1 and κ = 1. The horizon of crowd density is set to [0, 5] p/m2 . The value of capacity belongs to the interval of [1.08, 2.17] p/m2 [Sebastian 2015]. We have selected the median value 1.625 p/m2 as the value of ρ ∗ . And τ ∈ [0, 1] is a weight coefficient, defining the influence of stimuli on the perception for distance. The influence of train arrival on distance is larger than that of density variety according to the results of field observations at Xidan subway station (Fig. 18). So, we have empirically set τ as 0.35. We assume that the train interval is 300 s and the dwell time is 40 s. The relationship between the scale coefficient κ and crowd density ρ and train operational time t is shown in Fig. 14.

150

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160 Table 4 The statistic of frequency and degree of membership for fuzzy variables ‘Close’ and ‘Far’. Freq. and Deg. are short for frequency and degree of membership, respectively. ‘Close’

Group

Freq.

Deg.

Freq.

Deg.

218 204 127 68 37 24 9 4 2 1

1 0.936 0.583 0.312 0.170 0.110 0.041 0.018 0.009 0.005

0 14 56 148 179 200 211 218 218 218

0 0.064 0.257 0.679 0.821 0.917 0.968 1 1 1

0 ∼ 0.1 0.1 ∼ 0.2 0.2 ∼ 0.3 0.3 ∼ 0.4 0.4 ∼ 0.5 0.5 ∼ 0.6 0.6 ∼ 0.7 0.7 ∼ 0.8 0.8 ∼ 0.9 0.9 ∼ 1.0

Degree of membership

‘Far’

Close 1 0.8 0.6 0.4 0.2 0

0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

‘Close’

1.0 ∼ 1.1 1.1 ∼ 1.2 1.2 ∼ 1.3 1.3 ∼ 1.4 1.4 ∼ 1.5 1.5 ∼ 1.6 1.6 ∼ 1.7 1.7 ∼ 1.8 1.8 ∼ 1.9 1.9 ∼ 2.0

Degree of membership

Group

‘Far’

Freq.

Deg.

Freq.

Deg.

1 0 0 0 0 0 0 0 0 0

0.005 0 0 0 0 0 0 0 0 0

218 218 218 218 218 218 218 218 218 218

1 1 1 1 1 1 1 1 1 1

Far 1 0.8 0.6 0.4 0.2 0

0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

f

f

Distance dp [m]

Distance dp [m]

Fig. 15. Histograms representation of membership functions for fuzzy sets ‘Close’ and ‘Far’. The red lines represent the best fitted curves with trapezoid model. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 5 Regression analysis for fuzzy sets ‘Close’ and ‘Far’ with different types of models. Type

Trapezoid

Fuzzy set R2

‘Close’ 0.859

Sigmoid ‘Far’ 0.898

‘Close’ 0.414

Exponential ‘Far’ 0.983

‘Close’ 0.885

‘Far’ 0.318

4. Simulation experiments and results analysis 4.1. Parameter estimation We estimated the parameters and types of fuzzy variables (including antecedents and consequents) defined in the model by adopting a F statistical method. The universe of discourse of fuzzy variable and the number of fuzzy sets used to cover the universe of discourse are determined by the combination of empirical and experimental data and human experience f and knowledge. Take the distance d p for an example. It was represented by the two linguistic fuzzy sets {Close, Far}. The universe of discourses of fuzzy variables were all set to the interval of [0,2], and it was divided into 20 group. The statistic of frequency and degree of membership for fuzzy variables ‘Close’ and ‘Far’ are shown in Table. 4. Histograms representation of membership functions is shown in Fig. 15. The type of model and unknown parameters of the fuzzy sets ‘Close’ and ‘Far’ shown in Fig. 13 were estimated by using a regression method. For ease of calculation, typical membership function models are used to approximate the real data. We attempted to adopt three types of model, i.e., trapezoid, sigmoid and exponential model. The regression analysis for fuzzy variables ‘Close’ and ‘Far’ with these models are shown in Table. 5. The mean value of R2 of trapezoid model is larger than that of other two models. So, we chosen the trapezoid model as the membership function of fuzzy variables (red lines in the Fig. 15). For other variables, the same strategy was adopted to estimate the parameters. The heuristic rules used in fuzzy logic model were extracted from human experience and knowledge rather than selected arbitrarily. Based on the estimated membership functions, the fuzzy logic based model was applied to predict pedestrian waiting behaviors at subway platform. To illustrate and validate our model, we performed next the simulations on the subway platform scenario. 4.2. Validation of the model After parameter estimation, computer simulations were performed to validate the proposed fuzzy logic based model by comparing the simulation results with the collected data from field observations.

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160

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180 s

Fig. 16. Snapshots of pedestrian waiting behavior in (a) queuing mode, (b) clustering mode, and (c) scattering mode.

At first, we performed a case simulation at a waiting zone of subway platform with size of 4 m∗ 4 m, as shown in Fig. 16, which was taken from the up direction of the platform of Xidan subway station. There is a screen door with width of 2 m on the middle of upper wall. The left and right sides of the selected waiting zone are connected with other waiting zones. The arriving process of pedestrians was considered to be continuous and steady which can be assumed to follow a Poisson distribution. It is also commonly assumed that the speed of pedestrian obeys a normal distribution with the mean value of 1.34 m/s and standard deviation of 0.26 m/s. For simplicity, the radius of waiting pedestrian is set to unified r p = 0.25 m. The simulation time is set to 3 min, which is the mean period from a train leaving the platform to the next train entering and stopping at the platform. Pedestrians are generated from the bottom of the waiting zone, following a Poisson distribution with a rate of 8.0 p/min. Once pedestrians entered into the waiting zone, they move towards a suitable waiting position. This case simulation was performed to validate the behaviors of waiting pedestrian under different waiting modes by comparing the results with the observed behaviors. The software used to implement the simulation of waiting passengers is the MATLAB 2018a. Snapshots of pedestrian waiting behaviors in three queuing modes at different time steps: 10, 50, 90, 130 and 180 s are shown in Fig. 16. The snapshots of simulation process of waiting pedestrians under the queuing mode are shown in Fig. 16(a). Pedestrians always line up to form queues in front of the screen doors along the marking lines on platforms. At the beginning of the simulation, pedestrians maintain a large distance with front pedestrian and the queues keep loose. The distance headway between two adjacent pedestrians is decreased with the increment of the number of waiting pedestrians (density). After the train arrived, a wave-like propagation phenomenon of the gap between the successors is observed. Finally, the queues are further compressed. In Fig. 16(b), we performed the simulation of waiting pedestrians under the clustering mode. The phenomenon of the first half of the simulation is similar with that in Fig. 16(a). As the increment of the number of waiting pedestrians, they are spontaneously gathering together in boarding regions along the marking lines. A clogging phenomenon was observed in front of each screen door. Similarly, the gathered pedestrians are compressed once a train was arrived. Fig. 16(c) displays the snapshots of waiting pedestrians under the scattering mode. The pedestrian chosen an

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Fig. 17. Snapshots of waiting pedestrians and alighting pedestrians at different time steps: 30, 120, 210, 300 s after start of the simulation. The blue dots and red dots represent the waiting pedestrians and arriving pedestrians, respectively. (a) Pedestrians disembark a train; (b) Pedestrians move to the platform and alighting pedestrians leave the platform; (c) Pedestrians wait at the waiting zones; (d) A train arrives and the queue/clogging of waiting pedestrians are compressed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

arbitrary location within a waiting zone as the standing position rather than followed the guidance of marking lines. The irregularity of waiting behaviors is shown in simulations. We also found that the pedestrians kept bigger distance with their neighbors than these pedestrians waiting in other two modes when the density is low. The waiting positions changed more frequently than other two modes. Similarly, the waiting crowd is compressed when the density increases or a train arrives. To further validate the proposed model, the predicted waiting behaviors are compared with that observed from field observations. The simulations are performed at the real scenario of Xidan subway platform with a realistic density/flow of waiting pedestrians and walking pedestrians. The collected data at tactical level such as waiting modes, distribution of waiting pedestrians and waiting time was regarded as input data of the scenario. The percentages of three waiting modes and distribution of waiting pedestrians on the waiting zones are in accordance with the observed data (see Fig. 6 and Fig. 4 respectively). These settings were predetermined in simulations with the same values of field observations. The simulation was started from the leaving of last train and ended with the stopping of next train (a duration of 300 s). We assumed that none of the waiting pedestrians who should be left by last train were stranded in platform due to objective situations, subjective wishes or other possible causes such as overcrowded train compartments. Two trains arrive with 320 pedestrians from two directions, which have to alight the trains and go through and leave the platform. The arrive rate of waiting pedestrians follows a Poisson distribution with a rate of 80 p/min. They enter the platform from two entrances. The numbers of pedestrians entering the subway platform from middle and right entrances occupy the 65% and 35% of pedestrian flows, respectively. The percentages of three waiting modes as well as the waiting modes for each waiting zone are specified in advance. The snapshots of waiting pedestrians and alighting pedestrians at different time steps: 30, 120, 210, 300 s after start of the simulation are shown in Fig. 17. The simulation results are in accordance with that collected from field observation at subway platform. Then, we also performed simulations to collect data about two critical states, i.e., distance headway and movement speed, which reflect the fundamental characteristics of waiting pedestrians interacting with neighbors and environments, and contrast them with the data collected from field observations. We performed several simulations similar to the one mentioned above to further validate the proposed models. The adjustment of the number of waiting pedestrians was made. The global density of waiting pedestrians at the platform was varied from low (less than 0.3 p/m2 ) to high (more than 1.2 p/m2 ), and the maximum of local density reached 5 p/m2 . The distance headway is an important index in evaluation of pedestrian waiting model. We defined the distance headway dij,k as the Euclidean distance (L2 ) between the decision maker and his/her front pedestrian, which is given by

di j,k =



(xik − x jk )2 + (yik − y jk )2 − 2r p

(10)

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160

Before

After

1000

1000 Field observation Simulation

750 500

Frequency

Frequency

153

250 0

Field observation Simulation

750 500 250 0

12

12 0.35

Data source

1.15 0.75 Distance [m]

1.95

1.55

0.35 Data source

1.15 0.75 Distance [m]

1.55

1.95

(a) Low density Before

After 1000 Field observation Simulation

750 500

Frequency

Frequency

1000

250 0

Field observation Simulation

750 500 250 0

12

12 0.35

Data source

1.15 0.75 Distance [m]

1.95

1.55

0.35 Data source

1.15 0.75 Distance [m]

1.55

1.95

(b) Middle density Before

After 1000 Field observation Simulation

750 500

Frequency

Frequency

1000

250 0

Field observation Simulation

750 500 250 0

12

12 0.35

Data source

1.15 0.75 Distance [m]

1.55

1.95

0.35 Data source

1.15 0.75 Distance [m]

1.55

1.95

(c) High density Fig. 18. Distance headway distributions of model simulations and field observations before and after arriving of a train at different density levels.

where (xik , yik ) and (xjk , yjk ) represent the coordinates of the decision maker Pi and the front pedestrian Pj in time k, respectively. The validation was performed by comparing the results of model-based simulations, and dataset collected from field observations. The distance distributions of model simulations and field observations before and after arriving of a train at various density levels are shown in Fig. 18. Histograms of the distance headway are shown in Fig. 18. One can see that the results of model simulations shows a similar changing trend with the data collected from field observations. The greater distance headway seems to be more frequent when the density is low. Over 85% of data belongs to the distance headway interval ranging from 0 up to 0.3 m and the remaining belongs to the interval of [0.3 m 2 m]. As it is also observed in Fig. 18, the distance headway decreased with the increment of density of waiting pedestrians at waiting zones as well as the arriving of train. The arriving of train compresses the waiting pedestrians and decreases the distance headway under the condition of same density level, and its effects on the distance is reduced with the increasing of density. The platform does not allow for much larger distance headway due to the limited available space. Waiting pedestrians move forward a little bit because of the compression of waiting space and/or increment of expectation for boarding the train, leading to a smaller interpersonal distance to the pedestrian standing in front. Fig. 19 shows the probability density distribution histogram of the simulation data and the observation data at the same ambient conditions, i.e., density level and time period. The goodness of fit between model simulations and field observations is reported in Table. 6, where

MSE =

n 1 ( fsimulation (dk ) − fdata (dk ))2 n k=1

(11)

154

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160

Before Probability density

Probability density

Before 6 Field observation Simulation

4 2 0 12

1.15 0.75 Distance [m]

0.35 Data source

1.55

6 Field observation Simulation

4 2 0 12

1.95

0.35 Data source

Probability density

Probability density

Field observation Simulation

2 0 12 1.15 0.75 Distance [m]

0.35 Data source

1.55

Field observation Simulation

4 2 0 12 0.35

Data source

Field observation Simulation

2 0 12 1.15 0.75 Distance [m]

Data source

1.15 0.75 Distance [m]

1.55

1.95

Before Probability density

Probability density

Before

0.35

1.95

6

1.95

6 4

1.55

After

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1.15 0.75 Distance [m]

1.55

6 Field observation Simulation

4 2 0 12

1.95

0.35 Data source

1.15 0.75 Distance [m]

1.55

1.95

Fig. 19. Comparison of probability density between model simulations and field observations. Table 6 Goodness of fit between model simulations and field observations, where LD, MD and HD denote low density, middle density and high density, respectively.

MAE =

Condition

LD, t < t∗

LD, t > t∗

MD, t < t∗

MD, t > t∗

HD, t < t∗

HD, t > t∗

MSE MAE

3.68e−03 2.71e−02

7.15e−03 3.78e−02

5.62e−03 3.35e−02

8.22e−03 4.05e−02

1.72e−02 5.87e−02

1.13e−02 4.75e−02

n 1 | fsimulation (dk ) − fdata (dk )| n

(12)

k=1

where MSE and MAE are the abbreviation of Mean Square Error and Mean Absolute Error, respectively. n = 20 and dk is the median value of the kth distance interval. The value fsimulation (dk ) and fdata (dk ))2 are the probability density of simulation data and observed data, respectively. It is worth noting that the match between two datasets is satisfactory and the MSE and MAE between them are acceptable. The speed is a reflection on dynamical characteristics of waiting pedestrians. The speed of a waiting pedestrian at time k is approximated using finite differences:



vik =

xik t

2

 +

yik t

2

where xik = xi,k − xi,k−1 , yik = yi,k − yi,k−1 , and t = tk − tk−1 .

(13)

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2000

800 400

1600

Field observation Simulation

1200

Frequency

1200

2000

1600

Field observation Simulation

Frequency

Frequency

1600

800 400

0

800 400

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0 1 2

0.45

1.65 1.05 Speed [m/s]

1 2

2.85

2.25

Field observation Simulation

1200

0 1 2

155

0.45

Data source

(a) Low density

1.65 1.05 Speed [m/s]

2.85

2.25

0.45

Data source

1.65 1.05 Speed [m/s]

2.25

2.85

(c) High density

(b) Middle density

Field observation Simulation

2 1 0 1

Field observation Simulation

2 1 0 1

2

Data source

3

0.45

1.65 1.05 Speed [m/s]

2.25

2.85

Probability density

3

Probability density

Probability density

Fig. 20. Speed distributions of model simulations and field observations at different density levels.

Field observation Simulation

2 1 0 1

2

Data source

3

0.45

1.65 1.05 Speed [m/s]

2.25

2.85

2

Data source

0.45

1.65 1.05 Speed [m/s]

2.25

2.85

Fig. 21. Comparison of probability density between model simulations and field observations. Table 7 Goodness of fit between model simulations and field observations. Condition

Low density

Middle density

High density

MSE MAE

3.36e−03 2.59e−02

2.28e−03 2.14e−02

5.35e−03 3.27e−02

The speed distributions of model simulations and field observations at various density levels are shown in Fig. 20. One can see that the results of model simulations shows a similar changing trend with the data collected from field observations under different density levels. The fluctuation of pedestrian’s speed under low density level is more frequently than that under high density level. The great majority of waiting pedestrians almost remain stationary (less than 0.3 m/s) in a standing position at most of the waiting time. The frequency of speed interval [0.3 m/s 0.6 m/s] is second only to interval of [0 0.3 m/s]. The speed value belonging to interval of [1.2 m/s 1.5 m/s], containing the value of desired speed, appears more frequently than the remaining values. A pedestrian enters into a waiting zone at the desired speed and the speed decreases as he/she approaches the preferred position. Once reached the preferred standing position, waiting pedestrians almost keep stationary until a train is arrived at the platform. But, pedestrians may walk forward a bit at a slow speed with the increment of density or arriving of a train during waiting process. Comparison of probability density between model simulations and field observations for distance are shown in Fig. 21. The goodness of fit between them is reported in Table. 7. We can see that the match between two datasets is satisfactory. The MSE and MAE between them are acceptable. 4.3. Effect of waiting pedestrians on dynamics of passing pedestrians From our field observations at subway stations we found that waiting pedestrians may hinder or block the motion of other pedestrians who want to pass through the waiting zone. Previous researches have shown that high density waiting (stationary/standing) pedestrians have significant influence on the movement of walking (passing) pedestrians. The results revealed that waiting pedestrians decreased the average velocity of passing pedestrians and increased the walking time and path length [3,10,33,34]. To quantify the effect of the presence of waiting pedestrians and their waiting modes on the walking time of passing pedestrians at subway platform, a simple and realistic simulation scenario was designed according to the real floor plan topology of island platform. The scenario consists of a straight corridor with size 20 m long and 4 m wide. There is a waiting zone with size 4 m × 4 m in the middle of corridor, as depicted in Fig. 22. Since the walking time of passing pedestrians is strongly influenced by the number of waiting pedestrians, the density of waiting pedestrians was also kept as a variable. 10, 20 and 40 waiting pedestrians in total with different waiting modes were generated respectively to populate the waiting zone in three simulations. Another group of 20 pedestrians who want to pass through waiting zone were generated in the left end of the corridor (the origin zone) following an uniform distribution with a mean rate of 4 s−1 . Their destination is located at the right end of the corridor, and the pedestrians always aim for the closest point of the destination. It is also assumed that the speed of passing pedestrians obeys a normal distribution with the mean value of 1.34 m/s and standard deviation of 0.26 m/s. The extension of walking time required to passing through the platform under different waiting modes is measured and compared to the scenario with no waiting pedestrians on the waiting zone.

156

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0

Destination

Origin

4

Waiting zone

8

12

20 (m)

Fig. 22. The geometry of the simulated scenario. The black zones correspond to the origin and destination of passing pedestrians. The waiting zones are marked with gray dotted square where pedestrians stand on and wait for a train.

Fig. 23. Effect of waiting pedestrians under different modes on the mean delay of walking pedestrians at various density levels. “N = 0” represents a reference a scenario without any waiting pedestrians. The errorbars represent the 95% confidence intervals of a estimation method, based on 50 repetitions of the simulations.

The effect of waiting pedestrians under different modes on the mean delay of passing pedestrians at various density levels is shown in Fig. 23. We define the delay of a pedestrian as the difference between its real walking time and the time it would have taken if he/she walks along the shortest route at the desired speed. The white bars of Fig. 23 show that waiting pedestrians have less influence on passing pedestrians under low density level regardless of which waiting mode is chosen. With the increment of density of waiting pedestrians, they bring more delay to the passing pedestrians and its influence on delay of passing pedestrians becomes even more apparent by contrasting with the reference scenario of “N = 0”. We can see that there are significant differences between the simulated delays of passing pedestrians under different waiting modes. The waiting pedestrians under the scattering mode causes an additional 21.44% and 10.78% delay compared to that under the queuing mode and the clustering mode in the 20 passing pedestrians simulations, respectively, when the density level of waiting pedestrians is high. Thus, the queuing mode is an efficient way to organize waiting pedestrians and it brings less delay to passing pedestrians comparing with other two modes. The behaviours of passing pedestrians are largely influenced by waiting pedestrians who are waiting on the waiting zones with scattering mode, since the passing pedestrians have to deviate considerably and frequently in order to avoid collision with standing ones. The simulation results also show that the dynamics of passing pedestrians are greatly affected by waiting pedestrians. We further quantified the effect of waiting pedestrians and their waiting modes on the dynamical characteristics of passing pedestrians, i.e., movement speed and turn angle. The variations of movement speed in the simulations with no waiting pedestrians and 40 waiting pedestrians under different waiting modes are shown in Fig. 24. Over 80% of speed data are in the interval of [1.2 m/s 1.5 m/s] when no waiting pedestrians are presented (“N = 0”). This value decreases significantly with the present of waiting pedestrians. The influence of the scattering mode on the movement of passing pedestrians is much deeper stronger than other two modes, which causes an additional 10.52% and 7.91% decrease, on average, compared to the queuing mode and the clustering mode in the 20 passing pedestrians simulations, respectively. The frequency of a speed value belonging to the interval of [0.3 m/s 1.2 m/s] has a remarkable increment. That is because the waiting pedestrians hinder/block the movement of passing pedestrians and force them to decrease their movement speeds and change the predetermined routes. The variations of turn angle in the simulations with no waiting pedestrians and 40 waiting pedestrians under different waiting modes are shown in Figs. 25. The turn angle is defined as the angle between two consecutive directions. The values of turn angle are concentrated in the interval of [−10◦ 10◦ ] when no waiting pedestrians are presented (“N = 0”). Most of passing pedestrians go straight to their destinations without unnecessary deviation. The walking pedestrians passing

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160

1250

N=0 Queuing Clustering Scattering

1000 Frequency

157

750 500 250 0

1 2 3 4 2.55 2.85 1.95 2.25 1.65 1.35 0.75 1.05 0.15 0.45 Speed (m/s)

Data source

Fig. 24. Speed distribution of passing pedestrians. A total of 5712 data were collected from 20 repetitions of the simulations (5 for each scenario). The data collected from the scenarios of “N = 0”, “Queuing”, “Clustering”, and “Scattering” include 1424, 1426, 1430, and 1432 data elements, respectively.

1000 N=0 Queuing Clustering Scattering

Frequency

750 500 250 0

1 2 3 4

Data source

-80

-60

-40

0

-20

20

40

60

80

o

Angle ( ) Fig. 25. Turn angle distribution of passing pedestrians. A total of 4002 data were collected from 20 repetitions of the simulations (5 for each scenario). The data collected from the scenarios of “N = 0”, “Queuing”, “Clustering”, and “Scattering” include 998, 1005, 1002, and 997 data elements, respectively.

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through the waiting pedestrians deviate more considerably and frequently than that no standing pedestrians present. The scattering mode makes passing pedestrians turns more frequently than other two modes, which causes an additional 22.80% and 16.20% rotation compared to the queuing mode and the clustering mode in the 20 passing pedestrians simulations, respectively. The large rotations (|θ | ≥ 50◦ ) caused by the scattering mode are more frequent than other two modes. The waiting pedestrians bring more delay to the passing pedestrians and its influence on delay of passing pedestrians becomes even more apparent by contrasting with the reference scenario “N = 0” without waiting pedestrians. The present of waiting pedestrians forces passing pedestrians to deviate from planned routes. The scattering mode makes passing pedestrians have a greater chance of encountering waiting pedestrians in the crossing. Other two modes are relative orderly manner that waiting pedestrians are concentrated in certain region of a waiting zone, and it reduces the probability of hindering by waiting pedestrians as well as the delay, the variation of movement speed and the frequency of large rotation. 5. Discussion and conclusion In this paper we investigated the crowd behaviors at two major Beijing’s subway stations by analyzing the data of field observations and video recordings on these subway platforms. Three waiting modes of pedestrians at subway platform, i.e., queuing mode, clustering mode, and scattering mode, were found during the waiting process. The orderly waiting modes were occurred much more common than scattering mode because of the constraints of moral codes and/or cultural norms and the guidance of marking lines on the platform. The extension of fuzzy logic based models, incorporating with the behavioral heuristic rules, were proposed based on the waiting modes and behavioral characteristics of waiting pedestrians at subway platform. In addition, the effects of varied environments, including train arrival and density variety, on pedestrian’s perception were taken into account in modeling process. These models were validated and calibrated in various scenarios of a major Beijing subway station by contrasting the simulation results with data collected during the field observations and has proven to be capable of reappearing real-life waiting phenomena and pedestrian data. At first, the foundations of Information Science like ‘information theory’, ‘cognitive science’, and ‘soft computing’ were adopted to collect pedestrians’ data, perceive the behavior of waiting pedestrians, and support the development of waiting pedestrian’s model. In addition, the implementations and information technologies of ‘Fuzzy Logic and Approximate Reasoning’, ‘Expert and Decision Support Systems’, ‘Information and Knowledge’, and ‘Perceptions’ were also used to model and simulate pedestrian’s waiting behavior at subway platform. Consider the intrinsic limitations of humans’ cognitive abilities for distinguishing detail and storing information, pedestrian’s perceptions toward surrounding environments are usually represented by natural language, which are inherently vague and imprecise. Humans have outstanding ability of computing and reasoning with imprecise information instead of exactly numerical value, arriving at reasonable conclusions expressed as words from premises expressed in a natural language or having the form of mental perceptions. A fuzzy logic approach, compared with other methods, is highly robust in coping with the uncertainty and imprecision that are inherent in perception information. It also provides a scientific approach for the management of pervasive reality of fuzziness and vagueness in human cognition. In addition, fuzzy logic also has the ability to utilize human experience and knowledge and imitate human thought processes. For example, the near obstacle has a greater impact on the obstacle-avoiding behavior than the far. Using the fuzzy logic framework, the processes of pedestrian’s reasoning and decision making can be formulated by a set of simple and intuitive fuzzy rules, coupled with advantages of accessible input information and easily understandable output. Similarly, for the problems relate to modeling and simulation of pedestrian’s waiting behaviors, a fuzzy logic approach also has certain advantages over other approaches, such as its ability to use perceptual information, utilize human experience and knowledge and imitate human thought processes. So, it is a natural and suitable tool to model pedestrian dynamics. The proposed fuzzy logic model can take human experience and knowledge into full consideration in modeling processes, and associate the perceptual information obtained from environments with the decision making of pedestrian’s waiting behaviors. The environmental influences on pedestrian dynamics are evaluated quantitatively based on the obtained perceptual information. Finally, the fuzzy logic model is fully validated by simulations of waiting pedestrians, walking pedestrians and their interactions at subway platform. The basic data of subway platform were recorded. Through observation and data collection, we found three waiting modes and the proportion of selected modes under different density conditions at the real subway platform. The distribution of waiting passengers on the waiting zone was also revealed, which presents a saddle-shape along the train operation direction under any density level. More pedestrians were willing to choose waiting zones close to the entrances of the platform, which may make it difficult for subsequent passengers to pass through this area and lead to congestion. The time for passengers to get on and off the train is prolonged. Simulations were performed to evaluate and quantify the effects of waiting pedestrians and their modes on dynamics of passing pedestrians, i.e., delay time, walking speed and turn angle by using proposed models. The waiting pedestrians under the scattering mode causes an additional 21.44% and 10.78% delay compared to that under the queuing mode and the clustering mode in the 20 passing pedestrians simulations, respectively, when the density level of waiting pedestrians is high. It also causes the frequent rotation and speed decrease of waiting passengers. The scattering mode makes passing pedestrians have a greater chance of encountering waiting pedestrians in the crossing. We found that orderly waiting mode and even distribution of waiting passengers are conducive to improving operational efficiency of subway platform and reducing congestion caused by high passenger density. For the manager of subway station, they should try to avoid the condition that large numbers of passengers waiting or staying too long at entrances of the

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platform. Managers can also make passengers choose to wait at zones far away from the entrance by setting fences. In addition, guides and broadcast should be equipped at the subway platform during the rush hours. Passengers may choose to wait at the zones far away from the entrance, which reduces the probability of congestion and passenger travel time. At the same time, passengers can be guided to choose the orderly waiting mode like queuing and clustering, so as to reduce the hindrance of waiting passengers to passing passengers and alighting passengers. Although the proposed models performed well in reproducing the behaviors of waiting pedestrians under different modes, some details are still needed to be discussed. In this paper, the transitions between three waiting modes are not taken into account in simulations. However, mode transitions always exist in reality. As part of the future work, the formation and transition of waiting modes under the intervention of guiders will be investigated and its effect on the operational efficiency of subway stations will be evacuated quantitatively. Declaration of Interest Statement The authors declare that there is no conflict of interests regarding this paper. Acknowledgments The authors would also like to thank Xiaoxia Yang, Qianling Wang, Jiemin Zhang, Yang Yang, Jing Chen, Wei Li, Chengjie Wei, Qi Meng, et al. in Beijing Jiaotong University, as well as Yanjun Zhang and Huai Zhan in Beijing MTR Corporation Limited for the field data collection and video record at the subway stations. This work is supported the Fundamental Research Funds for Central Universities under Grant 2019JBM079. References [1] G. Acampora, P. Foggia, A. Saggese, M. Vento, A hierarchical neuro-fuzzy architecture for human behavior analysis, Inf. Sci. 310 (2015) 130–148. [2] X. Chen, H. Li, J. Miao, S. Jiang, X. Jiang, A multiagent-based model for pedestrian simulation in subway stations, Simul. Modell. Pract. Theory 71 (2017) 134–148. [3] M. Davidich, F. Geiss, H.G. Mayer, A. Pfaffinger, C. Royer, Waiting zones for realistic modelling of pedestrian dynamics: a case study using two major german railway stations as examples, Transp. Res. Part C 37 (2013) 210–222. [4] GB50157-2003, Code for Design of Metro, China National Standard, 2013. [5] E.T. Hall, The Hidden Dimension, Doubleday & Co, 1966. [6] D. Helbing, L. Buzna, A. Johansson, T. Werner, Self-organized pedestrian crowd dynamics: experiments, simulations, and design solutions, Transp. Sci. 39 (1) (2005) 1–24. [7] S.P. Hoogendoorn, P.H. Bovy, W. Daamen, Microscopic pedestrian wayfinding and dynamics modelling, Pedestr. Evacuation Dyn. (2002) 123–154. [8] B. Hu, N. Xia, Cusp catastrophe model for sudden changes in a person’s behavior, Inf. Sci. 294 (2015) 489–512. [9] C. Jiang, F. Yuan, W.K. Chow, Effect of varying two key parameters in simulating evacuation for subway stations in china, Saf. Sci. 48 (4) (2010) 445–451. [10] F. Johansson, A. Peterson, A. Tapani, Waiting pedestrians in the social force model, Physica A 419 (2015) 95–107. [11] K.M. Kim, S.-P. Hong, S.-J. Ko, D. Kim, Does crowding affect the path choice of metro passengers? Transp. Res. Part A 77 (2015) 292–304. [12] A. Kirchner, A. Schadschneider, Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics, Physica A 312 (1–2) (2002) 260–276. [13] G. Köster, B. Zönnchen, A queuing model based on social attitudes, in: Traffic and Granular Flow’15, Springer, 2016, pp. 193–200. [14] S. Li, L. Yang, Z. Gao, K. Li, Robust train regulation for metro lines with stochastic passenger arrival flow, Inf. Sci. 373 (2016) 287–307. [15] X. Li, T. Chen, L. Pan, S. Shen, H. Yuan, Lattice gas simulation and experiment study of evacuation dynamics, Physica A 387 (22) (2008) 5457–5465. [16] Y. Li, X. Wang, S. Sun, X. Ma, G. Lu, Forecasting short-term subway passenger flow under special events scenarios using multiscale radial basis function networks, Transp. Res. Part C 77 (2017) 306–328. [17] H. Liu, B. Liu, H. Zhang, L. Li, X. Qin, G. Zhang, Crowd evacuation simulation approach based on navigation knowledge and two-layer control mechanism, Inf. Sci. 436 (2018) 247–267. [18] L. Mann, Queue culture: the waiting line as a social system, Am. J. Sociol. (1969) 340–354. [19] P. Pettersson, Passenger Waiting Strategies on Railway Platforms-Effects of Information and Platform Facilities-Case Study: Sweden and Japan, Royal Institute of Technology, Stockholm, Sweden, 2011. [20] T.C. Schelling, Micromotives and Macrobehavior, WW Norton & Company, 2006. [21] M.J. Seitz, S. Seer, S. Klettner, O. Handel, G. Köster, How do we wait? Fundamentals, characteristics, and modeling implications, in: Traffic and Granular Flows ’15, 2015, pp. 1–8. [22] S. Seriani, R. Fernandez, Pedestrian traffic management of boarding and alighting in metro stations, Transp. Res. Part C 53 (2015) 76–92. [23] C. Shi, M. Zhong, X. Nong, L. He, J. Shi, G. Feng, Modeling and safety strategy of passenger evacuation in a metro station in china, Saf. Sci. 50 (5) (2012) 1319–1332. [24] S. Srikukenthiran, D. Fisher, A. Shalaby, D. King, Pedestrian route choice of vertical facilities in subway stations, Transp. Res. Rec. (2351) (2013) 115–123. [25] L. Sun, S. Hao, Q. Gong, S. Qiu, Y. Chen, Pedestrian roundabout improvement strategy in subway stations, in: Proceedings of the Institution of Civil Engineers-Transport, Thomas Telford Ltd, 2017, pp. 1–10. [26] L. Sun, W. Luo, L. Yao, S. Qiu, J. Rong, A comparative study of funnel shape bottlenecks in subway stations, Transp. Res. Part A 98 (2017) 14–27. [27] L. Tan, M. Hu, H. Lin, Agent-based simulation of building evacuation: combining human behavior with predictable spatial accessibility in a fire emergency, Inf. Sci. 295 (2015) 53–66. [28] K. Teknomo, Microscopic pedestrian flow characteristics: development of an image processing data collection and simulation model, Tohoku University, Sendai, Japan, 2002. [29] J. Wu, S. Ma, Division method for waiting areas on island platforms at metro stations, J. Transp. Eng. 139 (4) (2012) 339–349. [30] X. Xu, J. Liu, H. Li, J. Hu, Analysis of subway station capacity with the use of queueing theory, Transp. Res. Part C 38 (2014) 28–43. [31] X. Xue, S. Wang, G. Bin, Z. Hou, A computational experiment-based evaluation method for context-aware services in complicated environment, Inf. Sci. 373 (2016) 269–286. [32] X. Yang, H. Dong, X. Yao, Passenger distribution modelling at the subway platform based on ant colony optimization algorithm, Simul. Modell. Pract. Theory 77 (2017) 228–244. [33] S. Yi, H. Li, X. Wang, Pedestrian behavior modeling from stationary crowds with applications to intelligent surveillance, IEEE Trans. Image Process. 25 (9) (2016) 4354–4368.

160

M. Zhou, H. Dong and F.-Y. Wang et al. / Information Sciences 504 (2019) 136–160

[34] S. Yi, X. Wang, C. Lu, J. Jia, H. Li, l _0 Regularized stationary-time estimation for crowd analysis, IEEE transactions on pattern analysis and machine intelligence 39 (5) (2016) 981–994. [35] Q. Zhang, B. Han, D. Li, Modeling and simulation of passenger alighting and boarding movement in Beijing metro stations, Transp. Res. Part C 16 (5) (2008) 635–649. [36] X. Zheng, H. Li, L. Meng, X. Xu, X. Chen, Improved social force model based on exit selection for microscopic pedestrian simulation in subway station, J. Cent. South Univ. 22 (11) (2015) 4490–4497. [37] X. Zheng, H. Li, L. Meng, X. Xu, Y. Yang, Simulating queuing behaviour of pedestrians in subway stations, in: Proceedings of the Institution of Civil Engineers-Transport, Thomas Telford Ltd, 2017, pp. 1–8. [38] M. Zhou, H. Dong, F.-Y. Wang, Q. Wang, X. Yang, Modeling and simulation of pedestrian dynamical behavior based on a fuzzy logic approach, Inf. Sci. 360 (2016) 112–130. [39] M. Zhou, H. Dong, D. Wen, X. Yao, X. Sun, Modeling of crowd evacuation with assailants via a fuzzy logic approach, IEEE Trans. Intell. Transp.Systems 17 (9) (2016) 2395–2407.