A simulation model for pedestrian flow through walkways with corners

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Abstract

In this paper, a microscopic pedestrian model is developed for simulating pedestrian flow through walkways with not only perpendicular corners. These developments mainly include the determination of desired direction of pedestrians in the walkways, the action of pedestrians encountering walls around corner, and the generation of pedestrians in the walkways at the initial time of each simulation. Using the developed model, the effects, which the walkway corner and pedestrian preference to inside routes have on the pedestrian queue, trajectory and flow-density relation, are investigated by numerical simulations. Simulation results indicate that, under certain conditions, increasing the turning degree of corner has negative impact on the pedestrian queues; the effects of the pedestrian preference to inside routes on the pedestrian queues and flows are not still positive; the flow-density relation of pedestrian flow through walkways with corners, compared with that of pedestrian flow through bottleneck, is more complex, and in different region partition in the walkways, different relation of flow to initial density can be shown.

Introduction

Recently, many researchers and authorities have shown great interests in pedestrian flow problems, and the behavior and property of pedestrian flow in different scenarios have been investigated through mathematical models and computer simulations. For example, Lee and Lam [15] presented a pedestrian simulation model for signalized crosswalks in Hong Kong. Xu and Song [25] simulated an evacuation process of a four-story building by an improved multi-grid model. Qiu and Hu [20] proposed a unified framework for modeling the structure aspect of different groups in pedestrian crowds. Oğuz et al. [19] proposed a framework to simulate and visualize pedestrian crowds during outdoors emergency situations. These models and simulations play important roles in shedding light and gaining insight on pedestrian problems, and help make decisions for engineering in maintaining public facilities’ level of service and assuring pedestrian safety in public facilities during crowd accidents.

One of the critical factors affecting the behavior and property of pedestrian flow in walkways is the geometry and layout of those walkways. In fact, the design and layout of walkways are not as regular as those of roadways and are more complex, in that those walkways may have several openings, uncertain boundary or internal obstacles, and support the movement in several directions. Thus, diversiform flow patterns exist in walkways and need be studied. For instance, Helbing et al. [10] simulated the pedestrian flow in a walkway with triangular pieces in the middle by the social force model and found that if the walkway contains a widening, the flow of pedestrians will drop. Blue and Adler [1] presented the use of cellular automata simulation for modeling bi-directional pedestrian walkways. Tajima and Nagatani [23] investigated the pedestrian flow in a T-shaped channel, where the branch flow joins the main flow at the junction, under the open boundary condition. Helbing et al. [9] showed the simulation results of stripe formation in two intersecting pedestrian flows using the social force model. Guo et al. [8] proposed a microscopic pedestrian simulation model to investigate intersecting pedestrian flows with different angles. Nagatani [18] presented a cellular automaton model for simulating bi-directional pedestrian flow on a footway with a soft boundary.

Corners exist in most walkways in public places for serving pedestrians. In the walkways in closed areas, such as meeting rooms, supermarkets and theatres, corners are right angles generally, and the corners of other degrees are rare. However, in the walkways in opening areas, such as plazas and parks, the corners of other degrees are often seen. Still [21] observed the effect of the corners is neither transient, nor negligible, it relates to the dynamics of crowds and the use of space, it has a relationship to the crowd density and speed, and it can dominate the crowd flow and behavior especially during emergency egress. Thus, in the design of the evacuation routes in either the enclosed buildings or open spaces, if the effect of the corners of different degrees on pedestrian flow is not considered, possible losses caused by the evacuation congestion in any emergent events, such as fire and terrorism attack, may occur. To avoid or alleviate these losses, the effect of the corners and the behavior of pedestrian flow in the walkways with corners should be carefully and thoroughly researched. To our knowledge, there are few studies that deal with this issue by either modeling method [16] or empirical or experimental method [21].

In this paper, the microscopic pedestrian model proposed in Refs. [6], [8] is further developed for simulating pedestrian flow through the walkways with the corners of different degrees. First, based on the simulation scenarios introduced, the desired directions of pedestrians in the walkways with corners are determined, the actions of pedestrians encountering walls around corner are formulated, and the generation of pedestrians in the walkways at the initial time of each simulation is ruled. Through numerical simulations, the developed model is then used to investigate the effects, which the corners of the walkways and the pedestrian preference to inside routes have on the pedestrian queue, trajectory and flow-density relation.

Section snippets

Simulation scenarios

For the sake of clarity, we present the proposed approach for specific simulation scenarios, and focus on these scenarios shown in Fig. 1. In sequent numerical simulations, we will show some phenomena of pedestrian flow in these scenarios. Scenario (a) involves a walkway with an inner corner θ at the middle position. The width and the inner length of the walkway are W and L, respectively. Pedestrians can enter the walkway by the entrance boundary and exit by the exit boundary. Scenarios (b)–(d)

Numerical simulations

Pedestrian movements in these scenarios in Fig. 1 are simulated by the developed model. The input data are as follows: the width of the walkways W = 3 m, the inner length or perimeters of the walkways L = 24 m, the time step Δt = 0.05 s, the free velocity κn = 1.3 m/s, the pedestrian radius rn = 0.25 m, the radius of pedestrians’ surrounding circular area Rn = 6rn, the deviation parameter λ = 20, and the intensity parameters τ = 0.2, ξ = 0.05, ɛ = 0.1 and μ = 0.1.

First, we investigate the effects of the corner θ in the

Conclusions

In this paper, a microscopic pedestrian model, proposed in Refs. [6], [8], has been developed to formulate the pedestrian flow in the walkways with corners of different degree. Due to the specific space representation and geometry of the walkways, both the formulae for determining the desired direction of pedestrians and the rule of generating pedestrian, applicable to the above scenarios, are proposed. In addition, the actions of pedestrians encountering corner wall is also formulated. The

Acknowledgements

We extend our sincere thanks to the anonymous referees for their constructive comments. The work described in this paper was jointly supported by Grants from the National Natural Science Foundation of China (71001047), the Natural Science Foundation of Inner Mongolia (2010BS1001), and the Program of Higher-level Talents of Inner Mongolia University (Z20090113).

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