This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation. © 2012 Hui Xiong et al.
Xiong, H., Yao, L., Tan, H., & Wang, W. (2012). Pedestrian walking behavior revealed through a random walk model. Discrete Dynamics in Nature and Society, 2012. https://doi.org/10.1155/2012/405907