Procedia Computer Science Volume 66, 2015, Pages 372–381 YSC 2015. 4th International Young Scientists Conference on Computational Science
Optimization-based Calibration for Micro-level Agentbased Simulation of Pedestrian Behavior in Public Spaces Daniil Voloshin, Dmitriy Rybokonenko and Vladislav Karbovskii 1 ITMO University, Saint-Petersburg, Russia
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Abstract Pedestrian and crowd models have been on a rise over the past few decades which has been marked by emergence of a multitude of approaches and their implementations. However, determining and proving whether particular models reproduce the intended process adequately is still a complex task. Not only do researchers aim to assure that proposed algorithms correlate with the real-world mechanisms of collective behavior, but seek ways to adjust the crucial parameters of the model that vary between the cases to the observations and experimental results. Following this line of thought, we have calibrated our pedestrian simulator through rather frugal optimization of parameters with genetic algorithms to the data derived from the analysis of the real-world reference data. We present the results of such optimization along with the description of the case studied and the overall process of data collection. The paper is concluded with a discussion of the results of the calibration, observations made throughout the research and perspectives for further studies. Keywords: agent-based modeling, crowd simulation, optimization, calibration, transport, public spaces, genetic algorithm
1 Introduction Calibration is one of the key issues in the field of pedestrian simulation. Despite the advances in the domain and emergence of the supportive infrastructure for the reference data collection and further adjustment to the documented behavior of actual pedestrians, the balance between the robustness and generalization of approaches is still yet to achieve. In this paper a solution is proposed based on the optimization of parameters of the pedestrian model to the values estimated throughout the study of the empirical data using genetic algorithms.
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doi:10.1016/j.procs.2015.11.043
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The rest of this paper is divided into 4 sections. First, in Section 2 we come up with the discussion of the state-of-the-art solutions that are of relevance for the problem proposed for the investigation in the present paper. In Section 3, we proceed onto the methods that were used for data collection and analysis in the research, with a brief discussion of the case under investigation. Primary results and observations that were made during the scrutiny of the evidences gathered are charted in Section 4. In Section 5 conclusions are drawn along with the discussion of further research that we consider having looked into the issue presented.
2 Related works Pedestrian behavior modelling is relatively new field in transportation modelling, yet represents comprehensive and reliable instrument for transportation studies. In general, pedestrian flow simulation on transport can be divided into 2 groups. The first group is composed of models aimed at simulation of pedestrian behavior under abnormal conditions. By such conditions scholars consider either emergency situations, or cases when travel demand increases dramatically (e.g. as in public meetings, mass celebrations, religious events etc.). With respect to emergency environment, the bulk of research is focused on the evacuation behavior from congested facilities. The models of increased travel demand are aimed at realistic simulations of passengers’ circulations and crowd dynamics. Thus, for instance, Lei et al [1] examine relationships between such parameters as occupant density, presence of classified as a so-called queuing model, which describes pedestrian movement from one point to another, either uni- or multidirectional, while queues start to emerge when pedestrian traffic demand exceeds capacities of exit/entry points [2]. The second group is composed of models aimed at assessment and further optimization of transport facilities. An extensive body of research is concerned of pedestrian behavior in subway areas located in front of and after the payment area (ticket offices). Thus, Liao and Liu [3] propose a microscopic simulation of passengers behavior in the so-called “nonpayment” area, simulating queue choice, passengers movement and path navigation. Implementing Anylogic simulation software, Yang [4] assesses the impact of pedestrians arrival rate and the number of operating ticket offices on the length of the queue in order to introduce optimal strategies for queue minimization and ticket office utilization in peak and off-peak hours. Such kind of models inevitably comprise the elaboration of decision-making algorithms. Thus, Hoogendoorn et al [5] allocate decision-making to the tactical level of pedestrian behavior. Due to the fact that pedestrian behavior in transport is constrained by physical properties of the latter, route choice (queue choice) is performed through the finite number of alternatives and thus, is predominantly assessed by means of discrete choice theory [6]. Thus, agents are supposed to choose route (queue, gate etc.) that minimizes expected disutility, composed of walking time to the gate and expected waiting time [7]. Today there is a demand for the effective tools and methodologies for assessment of pedestrian simulation and algorithms that has been formulated long before the actual emergence of the plausible solutions. Under different notations, model assessment is an essential section of any pedestrian simulation/modelling-related academic work that is out. However, only recently academics in the field have started to devote their articles thoroughly to the topic of calibration [8] [9] [10] of models. For instance, Rudloff [10] – proposes a rather extensive comparative analysis of various calibration approaches and results of their validation, which is, however, performed using the simulated data, whereas in this paper a focus is cast on the calibration of the pedestrian model using empirical observations. With respect to the mechanism of calibration/validation, two key approaches dominate the literature in the field – automated calibration [11] and manual evaluation, performed by experts [12]. The former is less time and participation-consuming but rather demanding on the technical side and requires certain level of expertise in the use of sensors or video tracking mechanisms and software. Calibration techniques vary in the nature and characteristics of the reference data: it can be either
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collected through real-world or experimental observations [13] [14] or derived through the use of the virtual reality or telepresence systems [15]. The choice of instruments for data collection in each of the cases is specific. Compared to virtual, synthetic and experimental data (offering a wide range of tools – from infrared sensors to automated tracking mechanisms), real-world pedestrian behavior is almost exclusively accessed with the use of video tracking. In the same time, the latter is a rather demanding technique – it is strongly dependent from the possibility of mounting the recording device in a manner that would guarantee the best viewing angles, which is sometimes not achievable in public spaces and some transport facilities as the one described in this paper. Taking into account the fact that various pedestrian models operate on different levels and thus process different parameters, one of the key issues in the field of calibration is the parameter estimation and optimization [16]. In this respect, two broad approaches are identifiable – comparison of the simulation output to higher-level metrics [11] gathered from the empirical data (flux, evacuation times, fundamental diagrams) and estimation of the deviation of the virtual agents’ individual trajectories [8] from the routes formed by real-world pedestrians. The latter methodology is found to be more suitable for the cases where the researcher is capable of acquiring precise data with minor errors, which skews the range of suitable datasets towards the experimental side. Though there is yet no predominant methodology for pedestrian model parameter optimization, evolutionary algorithms became widely used in recent years [17] [18] [19] – since they are easy to implement, efficient and are adjustable to great numbers of tasks, which makes them a decent match for force-based models.
3 Methods 3.1 Optimization-based framework Since this research is aimed at adjusting the already-existing pedestrian model to the real-world data, a framework for solving this type of problems has been developed. Refer to Fig. 1 for the scheme of the framework and its adaptation to the calibration of the model to the data acquired for the metro station entrance crowd case. For a more elaborated discussion of the modules and procedures, see sections 3.2 – 3.4.
Figure 1 Structure and implementation of optimization-based framework
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3.2 Description of the case In order to calibrate the model to the data from a relevant real-world process, an object that consistently attracts great numbers of people, who, in their aggregate, have a potential of forming a crowd of a reasonable density. Such a facility has been found in the center of St. Petersburg – the Vasileostrovskaya metro station. On average, it serves two million passengers monthly. Being the busiest station of the line, it is widely known for producing severe congestions at peak hours. In order to organize the pedestrian inflow and minimize the risk of stampede on the street side, in 2011 it was supported with a fenced winding passageway – the design frequently used for the check-in ques in the airports. However, this only partially relieved the issue – the density of the crowd at the station entrance is still relatively high. Station terminal has five doors forming three entrances, separated with two fences. What is crucial for the case considered, in the peak hours station doors are partially closed (see Fig. 2 (a) for the scheme of the entrance doors, where red rectangles mark blocked doors (d1, d5), green – open doors (d2-d4), yellow marks (E1-E4) – composition of entrances separated by fences) in order to control the number of people in the station hallway and thus prevent stampedes in front of the inner gates. Station faces an open square with various obstacles located on it (see Fig. 2 (b)) – kiosks, garden fences, street illumination pillars etc. Two of the entrances operating at the peak hour are accessed through fenced passageways preceded by the staircase – a straight one and the winding one. The third entrance is only used in peak hours for letting physically challenged people and those with small children, and is left open in the off-peak periods.
(a)
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Figure 2 Outline of the transport facility and the public space around it: (a) Scheme of the station entrance (b) Physical map of the station entrance and the square
3.3 Data collection and analysis Recording of the video footage has been planned for the time preceding the highest load of the station – 18.10 pm (MSK (UTC+3)) - it has been determined through the repetitive observations performed prior to the start of collection of empirical data. Thus, the 20min sample comprises the period before the peak, at it and right after. The footage has been recorded using the portable camera fixed on a monopod, located in two points capturing the larger parts of the entrance, fenced passageways leading to them and the square (see Fig. 3). The footage has been broke down into samples, each lasting 88 seconds. Subsequently, they have been divided into smaller parts, 15 seconds each, in order to distinguish between waves of pedestrians and minimize their potential effect on the measurements. The raw data analysis has been divided into two blocks – evaluation of the aggregate characteristics of the crowd and those of the individual
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Figure 3 Crowds at metro station entrance at peak hour - an excerpt from the video footage: (a) Straight passageway (b) Winding passageway
pedestrians. The primary feature of the crowds formed in the passageways is the number of people queuing inside the area, limited by the fence and those forming a crowd outside its limits. Another metric considered is the flow of pedestrians – namely, a number of people crossing a line at the beginning of the passageway chosen as a measuring point at a given period of time. The winding passageway has been additionally divided into three smaller compartments after the primary acquaintance with the data, in order to control for the unevenness of pedestrians density at certain areas (it can be partially explained by the fact that the staircase segment and the beginning of the que are separated with a longer “corridor” and are facing different directions). Disaggregate characteristics were tracked for each pedestrian separately. The sample has been comprised manually from all the pedestrians queueing outside the passageway border line. Each pedestrian features an angle variable that describes the direction that he/she comes from towards the crowd. Another metric is the number of people queuing in front of a given pedestrian – it is measured in average “bodyspaces” that separate a person from the start of the passageway. Position on a staircase is considered as well – a pedestrian is assigned to one of three (left/center/right) single person-wide ques with people arranged in a somewhat of a checkerboard pattern. As soon as all the pedestrians are marked at a certain time step and their features have been captured, the amount of time it takes for them to walk the passageway and reach the entrance to the station is recorded in order to evaluate the average speed of a passenger in a crowd in the setting described above.
3.4 Model The model that has been used in this research is based on the micro-level agent-based pedestrian simulation module of the PULSE framework [20]. Relocations of pedestrians are processed on two levels: path planning and collision avoidance (managed with our previous realization of the Social Force-inspired algorithm [21], current version is available at [22]). Path planning in the metro station entrance case is a simplified version of the activity-based navigation used in [23] – agents are generated at points that denote key routes that lead from the adjacent streets to the square in front of the station and move towards one of the station entrances. Paths of agents are mapped on the graph produced through Quad Tree rasterization
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Figure 4 Scheme of the modelled space
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(for the discussion of the realization of the method and its advantages, see [23]) based on the information about the generation point and the chosen exit. The inflow to the square before station, as it has been determined through the analysis of the video footages and direct observations, is limited to 5 major areas outlined in Fig. 4, where marks 1-5 denote agent generation points, 6 stands for Entrance 1 (straight passageway), 7 for Entrance 2 (winding passageway) and 8 for the station exit. For the collision avoidance of agents we have chosen the Social Force algorithm due to the plausible results [24] that it produces when simulating micro-level evacuation dynamics which are closely related to dynamics of passengers queuing for the entrance to the metro station chosen as a reference case herein. It has been developed by D. Helbing and Molnar and described in their seminal work [21]. For the description of modifications that were applied to the original design, see [23]. According to the genuine formalization, the systematic part of agent’s acceleration is calculated according to the following formulae: ܨԦఈ ሺݐሻ ൌ ܨԦఈ ሺݒԦఈ ǡ ݒఈ ݁Ԧఈ ሻ ܨԦఈఉ ሺ݁Ԧఈ ǡ ݎԦఈ െ ݎԦఉ ሻ ܨԦఈ ሺ݁Ԧఈ ǡ ݎԦఈ െ ݎԦఈ ሻ ఉ
The first component is the agent’s own acceleration, the second one is a mutual repulsion between agents and the third is mutual repulsion between the agents and the obstacles. In the framework of parameter optimization, individual acceleration has been left aside, whereas according to Helbing and Molnar, remaining components have two varying parameters: strength of interaction ܣand its range ܤ [16], namely: ܣ ǡ ܤ for mutual repulsion between agents and ܣ ǡ ܤ for mutual repulsion between agents and the obstacles.
4 Results The calculations have been performed 20 times for the population consisting of 50 individuals (individual is represented by a vector of parameters ܣ ǡ ܤ ǡ ܣ ǡ ܤ ) throughout 50 generations. The average time for a calculation of a single individual is approximately 1 minute considering the overhead and the peak count of agents is 350. The calculation unit used in the experiments is the one with the following characteristics: CPU: Intel Xeon CPU E7-2830, Processor Base Frequency: 2.13 GHz, Max Turbo Frequency: 2.4 GHz, Number of cores: 8, Number of threads: 16, RAM: 128 Gb, OS: MS Windows Server 2012 R2 Datacenter. The results presented in Fig. 5-6 are averaged for 20 experiments carried out. Fitness values take into account such characteristics as agent counts, number of overlaps between agents and obstacles, overlaps between agents, flow rate, passage time. Summarizing the results of optimization of three parameters of the pedestrian model, it has been found that pedestrian count and passage time characteristics of the model do not adjust as well as it has been expected. At the same time, throughout
(c) (a) (b) Figure 5 Genetic algorithm optimization results for straight and winding passageways: (a) Passageway pedestrian counts, (b) Flow, (c) Passage times
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generations, values for the flow characteristic of the model steadily approach the levels exhibited by the crowd observed in the reference case (Fig. 5 (b)). This can be partially explained by the simplified model of entrance door throughput that has been set up according to the capacity exhibited by the entrance doors in the reference case. As Fig. 6 illustrates, overlaps between the agents tend to decrease with new generations, since they are dependent from the characteristics of the force of interaction between the agents and obstacles. Reaching the high values, agents can not make it through the narrow passageways or their movement is significantly hindered, at low values obstacles do not generate significant repulsive force which results in agents penetrating the walls.
5 Discussion and conclusion From the analysis of the test results it became apparent that fitness values are decreasing throughout the experiments which may be interpreted as a plausible outcome. Concerning the macro-level parameters, it has been found that the average flux Figure 6 Genetic algorithm characteristics (number of pedestrians crossing the que optimization results for overlaps: borderline) are gradually approaching the values estimated in the (a) Between agents, (b) Between process of assessment of video data. One of the interesting points agents and obstacles has been made in relation to the speed characteristics of agents – throughout generations these values change slightly. Moreover, certain issues that have been experienced when adjusting the values for passage time and pedestrian counts in the passageways that we believe, can be eliminated by the use of more complicated models of the entrance capacity. For example, the simulator of the entrance hall crowd and ques can be used for regulating the excess or insufficient flow of pedestrians at the entrance to the station – which is regarded herein as one of the subjects for future studies. Errors, however, are not eliminated due to the complex configuration of the modelled space – on one hand, there is an open space and sufficiently narrow corridors. On the other hand – narrow corridors aggregate dense crowds. Agents are forced to generate significant impact upon each other in order to avoid overlaps, though this pressure is required to be limited to an extent that does not hinder the movement in the narrow passageways. That is as well true for the walls that are expected not to “clamp” agents together while not allowing them to fluctuate freely. Furthermore, it can be inferred that minor flow rates and low values of the passageway pedestrian counts in the early generations result from the extreme values that forces are set to when modelling large numbers of agents, some of which merely do not reach the passageway. In the course of the primary visual analysis of the video materials it became obvious that we are dealing with a curious case: it was noted that passengers approaching the station entrance preferred the longer winding passageway over the shorter one (roughly three times more frequently). Even those pedestrians who have been classified as having lower walking speeds (e.g. elderly persons, people walking in pairs etc.) made predominantly the same choice. It has been noted as well that people walking in pairs form rather sustainable dyads. In the winding passageway case it affected their turning behavior. In the straight passageway case, contrary to expectations, even in the dense crowds these dyads did not change their outlines (e.g. pedestrians did not change their formation from handto-hand for leader-follower. In the research summarized in this paper, we have focused on the
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atomized pedestrians. Being aware of the possible effects that small groups can have upon the behavior of the individual and the crowd, we have decided to exclude them from the focus in favor of future studies. Thus, we are looking forward to testing the assumptions that arose during the analysis of the metro station crowd. Data collection took place prior to the conservation of the station in 2015 due to the planned restoration works planned for 11 months in advance. By that time, taking into account numerous factors (reduction of the number of operating doors, construction of an extra entrance hall, new terminal of a different line’s station being put into operation) that have a potential to come into effect, the transport situation in the nearest proximity to the station is expected to alter. Having that considered, we are looking forward to collecting additional data and calibrate our model against it.
Acknowledgements Theoretical studies in this paper are financially supported by Ministry of Education and Science of the Russian Federation, grant proposal #2015-14-588-0003-4183. Experimental research in this paper is financially supported by The Russian Scientific Foundation, Agreement #14-21-00137 (15.08.2014).
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