Study of the behavioral mechanism of self-organized pedestrian counter flow

Abstract

Pedestrian flow, whether uni-directional bi-directional or multi-directional, may trigger serious disasters such as stampedes resulting in trampling of people. People may be injured or even killed in these disasters. As a result, the effect of building facilities on comfort and safety of pedestrians movement becomes one of the important concerns of building designers and facilities managers. Factors affecting the level of service relate closely to pedestrian flow pattern. Previous studies indicate that self-organized patterns emerging in pedestrian counter flows may affect the flow rate and velocity of crowds. However, the studies rarely discuss the inter-personal interaction among pedestrians. In this study, we first performed well-controlled experiments to capture the moving characteristics of pedestrians in a corridor. Pedestrians’ moving trajectories were first extracted with digital image processing and were then mapped into real space coordinates by adopting a direct linear transformation approach. Moving characteristics of single pedestrians, and interaction between pedestrians and the corridor, as well as interaction between pair pedestrians were analyzed. It was found that when walking in the corridor, the average relaxation time of typical Chinese pedestrians was about 0.71s, and the maximum mean velocity of free walking was about 1.51m/s. Meanwhile, these pedestrians also kept a suitable distance from the wall to avoid potential collisions. When walking too close to the wall, the pedestrian had a tendency to walk away. This phenomenon was then expressed as an exponential decay force function. When one pedestrian tried to evade another pedestrian standing still in the corridor, the interaction between them showed a non-isotropic feature. The experimental results indicated that the participants preferred to walk with right preference more significantly. We further quantified the interaction among pedestrians, and found that the force from those who located on the right-forward direction did not change much while the force from those who located on the left-forward direction did vary with increase of distance. Interaction among pedestrians in a single file uni-directional flow show that the moving pedestrian is affected by the direct predecessor most but is barely affected by others. Based on the experimental findings, two models were established, namely, a metric distance based model and a k-Nearest-Neighbor (kNN) counterflow model, which could be used to investigate the fundamental interaction affecting pedestrian counter flow. The basic update schemes of these two models were the same with a cellular automaton (CA) random walker model, which is called the basic model hereafter. Pedestrians moving in a long channel will evolve into left moving pedestrians and right moving pedestrians. These pedestrians interact with each other in different forms in different models. In the metric distance based model, the direction choosing behavior of an individual is influenced by all those who are at a small metric distance and come from the opposite direction, while in the kNN counterflow model, the direction choosing behavior of an individual is influenced by the distribution of a fixed number of k-Nearest neighbors coming from the opposite direction. The self-organized lane formation was captured and factors affecting the number of lanes formed in the channel were investigated. Results implied that with varying of density, the lane formation pattern varies substantially in the case of metric distance based model while it is nearly the same in the kNN counterflow model, which matches field observations. This means that the kNN interaction plays a more fundamental role in the emergence of collective pedestrian phenomena. The correlations among mean velocity, occupancy and total entrance density at the boundaries of the counter flow system were also studied. Reasons for lane formation in CA models were theoretically investigated on the basis of the game theory. Reasons for velocity enhancement and flow improvement are also discussed. The kNN counterflow model was further validated by comparing lane formation pattern and the fundamental diagram with real pedestrian counter flow. The results indicated that the kNN interaction enhances the mean velocity in the free flow phase by providing more efficient traffic conditions, and is able to quantify features such as segregation and phase transition in high density pedestrian traffic situations. Considering factors such as pedestrians’ locations are out of alignment in reality, we further modified the kNN model into a multi-grids kNN model to mimic pedestrian flow. Dynamics of the multi-grids kNN model were studied to detail traffic characteristics of pedestrian counter flow. With these insights into the behavioral mechanism of pedestrian counter flow, we illustrate in the present study areas of crowd control by providing an example of improving traffic situation for pedestrian counter flow in a long corridor, in respect of a series of layout designs. To facilitate application, we further embed the kNN counterflow model into a Geographic Information System (GIS) platform and try to derive a fundamental diagram, as well as a real-time level-of-service map, so as to evaluate levels of services of pedestrian traffic facilities and efficiencies of different crowd control methods. Keywords: pedestrian flow, controlled experiments, cellular automaton model, pedestrian interaction, crowd control, optimal design, GIS