Title: Kinetic Monte Carlo Simulations of Traffic and Pedestrian Flows

Speaker：Sun Yi 
Time：2018年5月16日 10:00-11:00
Location：Center for Mathematical Sciences, Room 813
Abstract：

We employ an efficient list-based kinetic Monte Carlo (KMC) method to study 1D and 2D traffic flow models and 2D pedestrian flow models based on the exclusion principle and Arrhenius microscopic dynamics. 1) The traffic flow model implements stochastic rules for cars' movement based on the configuration of the traffic ahead of each car. In particular, we compare two different look-ahead rules: one is based on the distance from the car under consideration to the car in front of it, the other one is based on the density of cars ahead. The 1D numerical results of these two rules suggest different coarse-grained macroscopic limits in the form of integro-differential Burgers equations. The 2D results of both rules exhibit a sharp phase transition from freely flowing to fully jammed, as a function of initial density of cars. However, the look-ahead rule based on the density of the traffic produces more realistic results. 2)  The pedestrian flow model implements stochastic rules for pedestrians' movements based on the configuration of the surrounding conditions of each pedestrian. The rules can reflect the pedestrians' decisions of action such as moving forward, stopping to wait, lane switching, back stepping, etc. The simulation results of both two-way and four-way flows exhibit a state transition from freely flowing to fully jammed, as a function of initial density of pedestrians. At different states the relationships of density-flow and density-velocity are different from each other.