The moving behavior of a large object in the crowds in a narrow channel

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Abstract

In this paper, the interaction between the large object and the pedestrians in the narrow channel is studied. The pedestrians are modelled by the lattice gas model and they are regarded as biased random walkers. The dependence of the average speed of the large object on the density of the pedestrians, the size of the large object, and the position of the large object is investigated. The simulations show that with the increase of the pedestrian density, the average speed of the large object either decreases or remains constant. It is found that when the large object is moving opposite to the pedestrians, generally it will move fast in the middle of the channel. However, if it moves in the same direction as the pedestrians, then it will move fast when it is along the wall.

Introduction

Recently, self-driven many-particle systems have attracted the interest of many physicists [1], [2], [3], [4], [5], [6]. In the system, these driving force is not of external origin but is associated with each single particle and self-produced. Self-driven “particles” are a paradigm of many active or living systems, in which they are a simplified and abstract representation of the most important dynamic behavior of cells, animals, and humans. Typical examples of self-driven systems are vehicular flow, pedestrian flow, and so on.

Vehicular flow theory has a history of about 80 years. It includes the empirical and theoretical study and modelling of vehicle traffic. The empirical observations in the last few decades show that traffic flow can be classified into free flow and different kinds of congested flow. The possibility of phase transitions between the different traffic states causes complex spatio-temporal phenomena in traffic, e.g., metastable states, hysteresis, capacity drops, and so on. In order to study the properties of vehicle traffic, many traffic flow models have, therefore, been proposed and investigated.

Pedestrian crowds have been empirically studied for more than four decades now. Current research focuses on the microsimulation of pedestrian crowds. There have been many recent models of pedestrian traffic dynamics. These include the social force model [7], microsimulation models [8], cellular automaton models [9], emergency and evacuation models [10], and artificial-intelligence-based models [11]. The scientific interest concerns self-organization phenomena, noise-induced ordering, and collective phenomena in panic situations such as “freezing by heating” [12], the “faster-is-slow effect” [13], and herding behavior [13].

Nevertheless, there was little effort in modelling and simulating the interaction between different modes of transport. This would be particularly relevant for Asian traffic conditions, where traffic is characterized by low speed and a mixture of vehicles, pedestrians, and bicycles.

In this paper, a preliminary work has been done in this field. We consider the situation in a narrow channel. In the channel besides the pedestrians, there are bicycles, tricycles, barrows, and so on. For simplicity, the bicycles, tricycles, barrows are assumed to be large objects comparing with the pedestrians. Moreover, it is supposed to move at most one site per timestep (see Section 2). The pedestrian is assumed to be a biased random walker. We study the moving behavior of the large object in the crowd.

The paper is organized as follows. In Section 2, the simulation model is presented. In Section 3, the simulation are carried out and two subcases (the vehicle goes the opposite direction to and the same direction as the pedestrians) are analyzed. In Section 4, the conclusion is given.

Section snippets

Model

The model is defined on the square lattice of W×L sites, where W is the width of the channel and L is the length of the channel. The particles (walkers) go to the right and the large object goes either to the left (case 1) or to the right (case 2). Each site contains only a single walker. The walker is inhibited from overlapping on the site. The excluded-volume effect is taken into account. The large object occupies W1×L1 sites, where W1 is its width and L1 is its length. When the walker

Case 1

In this section, we carry out the simulations. Firstly, we consider case 1, i.e., the large object moves to the left. In the simulations, the parameters are W=10, L=100, L1=6, D=0.5. First, we consider the situation that the large object is in the middle of the channel. In Fig. 3, we show the average speed of the large object against ρ, the density of the walkers. One can see that (except W1=1) for small ρ, the large object can move with positive speed. With the increase of ρ, the average speed

Conclusion

In this paper, the interaction between the large object and the pedestrians in the narrow channel is studied. The pedestrians are modelled by the lattice gas model and they are regarded as biased random walkers. Here, we assume that the large object cannot move laterally and can move at most one site per timestep.

The dependence of the average speed on the density of the pedestrians, the size of the large object, and the position of the large object is investigated. The simulations show that

Acknowledgements

We acknowledge the support from the National Natural Science Foundation in China (NNSFC) with Grant nos. 10272101 and 10404025 and the Alexander Von Humboldt Foundation.

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