Microscopic pedestrian simulation model combined with a tactical model for route choice behaviour

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Abstract

This study proposes a microscopic pedestrian simulation model for evaluating pedestrian flow. Recently, several pedestrian models have been proposed to evaluate pedestrian flow in crowded situations for the purpose of designing facilities. However, current pedestrian simulation models do not explain the negotiation process of collision avoidance between pedestrians, which can be important for representing pedestrian behaviour in congested situations. This study builds a microscopic model of pedestrian behaviour using a two-player game and assuming that pedestrians anticipate movements of other pedestrians so as to avoid colliding with them. A macroscopic tactical model is also proposed to determine a macroscopic path to a given destination. The results of the simulation model are compared with experimental data and observed data in a railway station. Several characteristics of pedestrian flows such as traffic volume and travel time in multidirectional flows, temporal–spatial collision avoidance behaviour and density distribution in the railway station are reproduced in the simulation.

Introduction

This study proposes a pedestrian simulation model for evaluating pedestrian flow. An important aspect of planning pedestrian facilities where many pedestrians visit, such as busy stations and event venues, is to maintain a certain level of services (LOS). Providing a sufficient LOS in crowded places is necessary to avoid two situations: (1) significant travel time delays and (2) accidents resulting from crowds-many fatalities have occurred in crowded situations.

Pedestrian simulation modelling is considered to be a powerful tool for evaluating pedestrian flows in facilities. Conventional models can be classified as macroscopic and microscopic models. Macroscopic models evaluate flow using fundamental diagrams (Hughes, 2002, Huang et al., 2009). However, pedestrian flows are multidirectional and they cannot be explained by a single flow-density relationship. The experimental data analyses (Lam et al., 1995, Daamen and Hoogendoorn, 2003) imply that pedestrian flow cannot be expressed by a unique fundamental diagram because of the complicated characteristics of multidirectional flow. However, general fundamental diagrams for pedestrian flow have not yet been completed in previous studies. Alternatively, microscopic simulations have advantages when evaluating pedestrian flow in more general situations by representing individual pedestrian behaviour.

Microscopic models can be divided based on spatial representation. A cell-based spatial representation such as a cellular automaton is one such methodology (for example, Blue and Adler, 2000, Kirchner et al., 2004). These studies discussed different conflict avoidance rules between pedestrians. As these studies deal with spaces as discretised cells, there are some drawbacks when representing multidirectional flow, especially for diagonal movements. Thus, several continuous space representations have been proposed. One of the well-known microscopic models using continuous spatial representation explains obstacle avoidance by a repulsive power (Helbing and Mornar, 1995, Teknomo, 2006). These models considered a pedestrian as a particle whose movement is decided by the repulsive power between pedestrians. Hoogendoorn (2004) proposed a model that represents the decision making process of pedestrian movement so that pedestrians can maximise their utility by determining direction and speed. Antonini et al., 2006, Robin et al., 2009 proposed discrete choice models to determine direction and speed of pedestrians at each time interval. The utility depends on desired direction and speed, positions and moving directions of other pedestrians and so on. However, these previous models do not sufficiently consider anticipatory behaviour in the decision making process, especially when pedestrians negotiate each other to avoid collisions. To overcome this drawback, Asano et al. (2009) proposed a microscopic movement model that employs a multi-player game theory to describe the decision making process of pedestrians trying to minimise their travel times while avoiding collisions. This study adopts the model proposed by Asano et al. to implement a pedestrian simulation.

The microscopic model proposed by Asano et al. (2009) only considers pedestrians’ reactions and movements that are needed to avoid other pedestrians. Models describing such microscopic behaviour are referred to as ‘operational models’ (Hoogendoorn et al., 2000). To build a pedestrian simulation, it is necessary to overlap a model that describes pedestrians’ route choices to their destinations in a wide area such as a whole station facility. Models describing behaviour in more macroscopic situations than operational models are often referred to as ‘tactical models’. For example, a decision made by a pedestrian to make a detour to avoid a congested area should be modelled by a tactical model, whereas his/her decision to avoid collision with another pedestrian should be modelled by an operational model.

This study proposes a microscopic pedestrian simulation consisting of an operational model and a tactical model. An operational model, which describes pedestrians’ avoidance behaviour, is modelled as a two-player game, which is a simplified version of the model in Asano et al. (2009), in order to reduce the calculation cost. In addition, a tactical model that describes pedestrians’ route choices is proposed in this study. The tactical model considers congestion in the whole study area to determine a desired direction for each pedestrian, and the result will be passed onto the operational model. Then, these two models are integrated to implement a pedestrian simulation. The simulation is evaluated with empirical data from an experiment and observation data in a railway station.

Section snippets

Model framework

The model consists of two modules: an operational model and a tactical model (see Fig. 1). The origin and destination of each pedestrian are given in this paper.

The tactical model finds the shortest path from a current position to an exogenously-given destination with consideration for macroscopic conditions, such as the density of pedestrians in the areas where pedestrians will pass through and expected travel times to the destination through each alternative route. The tactical model

Assumptions

This operational model determines pedestrians’ applicable direction and speed at a certain moment, considering their given desired speed and direction as well as possible conflicts to other pedestrians within a specific future time period. The desired direction, noted as φd, is determined in the tactical model as explained in the next section. The desired speed is given explicitly to each pedestrian as a certain probabilistic distribution.

The model assumes that pedestrians detect positions and

Network settings for route choice

The tactical model searches macroscopic routes that minimise travel costs from origins of pedestrians to their destinations. These origins and destinations are exogenously given. Multiple destinations can be also set to one pedestrian, e.g. one of several exits can be taken by a pedestrian in the case of an evacuation. The macroscopic route provides the desired direction of each pedestrian so as to decide speed and direction in the operational model.

This model simplifies the network structure

Outline of validations

The proposed model is validated empirically with data sets obtained by an experiment and an observation. This paper explains the verification and validation using these two data sets.

At first, the verification of the operational model was conducted using the experimental data. The experiment was conducted to analyse microscopic pedestrian behaviour in multidirectional flows under several different conditions, e.g. different flow settings and crossing angles (Asano et al., 2007).

The data taken

Conclusions

This paper proposed a pedestrian simulation model that describes the anticipatory behaviour of pedestrians and their macroscopic route choice. The model consists of an operational model and a tactical model. The operational model considers anticipation behaviour between two pedestrians. The ‘giving way’ behaviour is incorporated by a two-player game. The verification of the model by comparing experimental data implies macroscopic characteristics of pedestrian behaviour, especially speed and

Acknowledgements

This research is funded by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. The data in the railway station is provided by the Research and Development Center of JR East Group, Prof. Ryosuke Shibasaki and Dr. Katsuyuki Nakamura. We also thank Dr. Agachai Sumalee for his valuable advice.

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