Modeling and simulation on interaction between pedestrians and a vehicle in a channel
Authors: Zhang Ji  , Wei Yan-Fang  , Dong Li-Yun  ,   1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;,   2. College of Physical Science and Technology, Yulin Normal University, Yulin 537000, China;,   3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China
Published: December 2020

The mixed traffic flow composed of pedestrians and vehicles shows distinct features that a single kind of traffic flow does not have. In this paper, the motion of a vehicle is described by the finer deterministic Nagel-Schreckenberg model, while the motion of pedestrians is mimicked by the lattice gas model with taking the floor field into account. Then the interaction between a certain vehicle and pedestrians in a narrow channel is investigated in two cases, i.e., pedestrians move in the same as or opposite to the direction of vehicle. The direction of the pedestrian movement is determined by the floor field, and the vehicle (and its influential area), regarded as a movable obstacle, and thus causing the floor field to change. Because of the timely change of vehicle speed and the size of impact area, the floor field must be calculated at each time step. Through numerical simulation, the fundamental diagram for pedestrian flow under the typical parameters is obtained together with the average speed of the vehicle as a function of pedestrian density. It is found that there are two critical densities, i.e., <i>ρ</i><sub>1</sub> and <i>ρ</i><sub>2</sub>. When <i>ρ</i><sub>1</sub> ≤ <i>ρ</i> ≤ <i>ρ</i><sub>2</sub>, the fundamental diagrams in the two cases are significantly different. This is due to the reverse movement of pedestrian and vehicle, the congestion ahead of the vehicle makes the average speed of pedestrians significantly lowered. In this case, the flux of pedestrians is a linear function of pedestrian density, and its slope indicates the speed at which pedestrian congestion propagates upstream. It can also represent the speed of the moving bottleneck formed by the vehicle. The slope mainly depends on the width of the vehicle and the anticipation time of pedestrians. When <i>ρ</i> < <i>ρ</i><sub>1</sub> and <i>ρ</i> > <i>ρ</i><sub>2</sub>, there is no obvious difference between the two cases. We further investigate the effect of three parameters, i.e., the anticipation time of pedestrians, the width and the speed limit of the vehicle. When pedestrians have the same direction as the vehicle, these parameters only have negligible effects. However, in the case that pedestrians move oppositely to the vehicle, the width of the vehicle influences the mixed traffic significantly. When the width of the vehicle is small, even in rather high pedestrian density, the vehicle can move forward. In addition, larger anticipation time of pedestrians is helpful in improving the speed of vehicle, while the effect of the speed limit of vehicle is relatively small. The spatial distribution of pedestrians and the vehicle and the short time average speed of the vehicle are also provided to reveal more information about both pedestrians and the vehicle.