A Markov Jump Approach to Modeling and Analysis of Pedestrian Dynamics

The key issue of establishing a pedestrian dynamics model is to select the direction and magnitude of the pedestrian velocity. In this paper, an improved Markov jump model based on the heuristic method is proposed to simulate the dynamic behavior of the pedestrians. According to the speed of the pedestrian, the pace is divided into four states, and the next step of the state is only determined by the current state and state transition matrix. According to the characteristics of decision-making in the pedestrian motion, a heuristic method is referenced, which is based on the pedestrian visual field, and the pedestrian will select the moving direction according to the proposed method. The validity of the model is verified by constantly modifying the parameters and components, which achieves the fundamental flow-density or velocity-density diagram and gets the reappearance of the self-organization phenomena, such as “arching and clogging” and “lane formation.” The simulation results show that the fundamental diagrams are qualitatively consistent with the field data in the cited works.