Physica A: Statistical Mechanics and its Applications
Pattern formation and jamming transition in pedestrian counter flow
Introduction
Recently, traffic and pedestrian flows have attracted considerable attention [1], [2], [3], [4]. Pedestrian flow is a kind of many-body system of strongly interacting persons. The pedestrian flow dynamics is closely connected with the traffic flow [5], [6]. To know the properties of pedestrian flow is important in our life. It is necessary to know the flow rate of pedestrian for rush hour and panic escape. It is also important to avoid the jammed state of pedestrians in the channel of the subway.
The typical pedestrian flows have been simulated by the use of a few models: the lattice-gas model of biased-random walkers [6], [7], [8], [9], the molecular dynamic model of active walkers [5], [10], [11], and the mean-field rate-equation model [12]. Henderson has conjectured that pedestrian crowds behave similarly to gases or fluids [13]. Helbing has shown that human trail formation is interpreted as self-organization effect due to nonlinear interactions among persons [5]. The escape panic [9], [10], [14], counter channel flow [6], [11], and bottleneck flow [12], [15] have been studied numerically. Muramatsu et al. have found that the jamming transition occurs in the pedestrian counter flow within a channel when the density is higher than the threshold [6]. Tajima et al. have shown that the clogging transition occurs in the unidirectional channel flow with a bottleneck if the density is higher than the threshold. The clogging transition is similar to that of the simple asymmetric exclusion model with a barrier [15], [16].
It has been observed that the pedestrians file away in the subway. The filing of pedestrian is interesting from the points of view of the pattern formation. How does the filing affect the jamming transition? Does the filing enhance the flow rate?
In this paper, we present the lattice gas models to mimic the filing formation of pedestrian flow. We extend the biased-random walker model to take into account the pedestrian state in the front. We study the pattern formation of pedestrian flow by following the front persons with the same direction or avoiding the front persons with the opposite direction. We investigate the dependence of the flow rate on the density. We show that the filing has little important effect on the jamming transition.
Section snippets
Model
We describe the extended lattice-gas model for the pedestrian counter flow in a channel. 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 lattice gas model has two components of particles. One component particle represents the walker going to the right and the other component particle represents the walker going to the left.
Fig. 1 shows the schematic illustration of the pedestrian counter flow within a channel.
Simulation result
We carry out the computer simulation for models A and B. Initially, there are no walkers within the channel. The right walkers are distributed randomly on the left boundary at probability p. The left walkers are also distributed randomly on the right boundary at the same probability p. All the walkers are numbered randomly from 1 to Nparticle, where Nparticle is the number of walkers existing within the channel, including the walkers on both boundaries. Following the rule in Section 2, the
Summary
We have presented the lattice gas models to mimic the filing formation of pedestrian counter flow. We have studied the pattern formation of pedestrian channel flow. We have shown that the pedestrian form in line and the two types of walkers file alternately at low density. We have found that the jamming transition occurs with increasing entrance density and the filing has little important effect on the jamming transition.
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