Model

Xiao Y, Gao ZY*, Qu YC, Li XG. A pedestrian flow model considering the impact of local density: Voronoi diagram based heuristics approach. Transportation Research Part C-Emerging Technologies. 2016;68:566-80. | 

Abstract: Local density, which is an indicator for comfortable moving of a pedestrian, is rarely considered in traditional force based and heuristics based pedestrian flow models. However, comfortable moving is surely a demand of pedestrian in normal situations. Recently, Voronoi diagram had been successfully adopted to obtain the local density of a pedestrian in empirical studies. In this paper, Voronoi diagram is introduced into the heuristics based pedestrian flow model. It provides not only local density but also other information for determining moving velocity and direction. Those information include personal space, safe distance, neighbors, and three elementary characteristics directions. Several typical scenarios are set up to verify the proposed model. The simulation results show that the velocity-density relations and capacities of bottleneck are consistent with the empirical data, and many self-organization phenomena, i.e., arching phenomenon and lane formation, are also reproduced. The pedestrians are likely to be homogeneously distributed when they are sensitive to local density, otherwise pedestrians are nonuniformly distributed and the stop-and-go waves are likely to be reproduced. Such results indicate that the Voronoi diagram is a promising tool in modeling pedestrian dynamics.

Xiao Y, Chraibi M, Qu YC, Tordeux A, Gao ZY*. Investigation of Voronoi diagram based direction choices using uni- and bi-directional trajectory data. Physical Review E. 2018;97(5):052127.| 

Abstract: In a crowd, individuals make different motion choices such as “moving to destination”, “following another pedestrian”, and “making a detour”. For the sake of convenience, the three direction choices are respectively called destination direction, following direction and detour direction in this paper. Here, it is found that the featured direction choices could be inspired by the shape characteristics of Voronoi diagram. To be specific, in the Voronoi cell of a pedestrian, the direction to a Voronoi node is regarded as a potential “detour” direction, and the direction perpendicular to a Voronoi link is regarded as a potential “following” direction. A pedestrian generally owns several alternative Voronoi nodes and Voronoi links in a Voronoi cell, and the optimal detour and following direction are determined by considering related factors such as deviation. Plus the destination direction which is directly pointing to the destination, the three basic direction choices are defined in a Voronoi cell. In order to evaluate the Voronoi diagram based basic directions, the empirical trajectory data in both uni- and bi-directional flow experiments are extracted. A time series method considering the step frequency is used to reduce the original trajectories’ swaying phenomena which might disturb the recognition of actual forward direction. The deviations between the empirical velocity direction and the basic directions are investigated, and each velocity direction is classified into a basic direction or regarded as an inexplicable direction according to the deviations. The analysis results show that each basic direction could be a potential direction choice for a pedestrian. The combination of the three basic directions could cover most empirical velocity direction choices in both uni- and bi-directional flow experiments.

Qu YC, Xiao Y, Wu JJ*, Tang T, Gao ZY. Modeling detour behavior of pedestrian dynamics under different conditions. Physica A. 2018;492:1153-67. |

Abstract: Pedestrian simulation approach has been widely used to reveal the human behavior and evaluate the performance of crowd evacuation. In the existing pedestrian simulation models, the social force model is capable of predicting many collective phenomena. Detour behavior occurs in many cases, and the important behavior is a dominate factor of the crowd evacuation efficiency. However, limited attention has been attracted for analyzing and modeling the characteristics of detour behavior. In this paper, a modified social force model integrated by Voronoi diagram is proposed to calculate the detour direction and preferred velocity. Besides, with the consideration of locations and velocities of neighbor pedestrians, a Logit-based choice model is built to describe the detour direction choice. The proposed model is applied to analyze pedestrian dynamics in a corridor scenario with either unidirectional or bidirectional flow, and a building scenario in real-world. Simulation results show that the modified social force model including detour behavior could reduce the frequency of collision and deadlock, increase the average speed of the crowd, and predict more practical crowd dynamics with detour behavior. This model can also be potentially applied to understand the pedestrian dynamics and design emergent management strategies for crowd evacuations. 

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