Pedestrian-vehicle interference at a signalized crossing based on detailed microscopic traffic flow models

Interference between pedestrians and motor vehicles at signalized intersections not only leads the traffic to delay and traffic efficiency to decrease, but also induces traffic crashes to happen frequently. In this paper, a microscopic discrete model for traffic flow is adopted to study the mutual interference mechanism between pedestrians and vehicles at signalized intersection. The vehicular traffic flow model is based on the refined NaSch model, and traffic lights are introduced to consider the driver anticipating in traffic signal switching. Based on the multi-step lattice gas model, the pedestrian flow model considers the fact that the pedestrians' speed increases gradually during pedestrian cross-street green time. Both models reflect real features of movement of vehicles (pedestrians) in daily life. When the traffic light signal switches, the vehicles (pedestrians) staying in the conflict area result in the delay of pedestrians (vehicles). It is assumed that pedestrians and vehicles cannot coexist in the conflict area at the same time. In the simulation, the periodic boundary condition is applied to the lane, and the open boundary condition is applied to the crosswalk. The arrival rate of pedestrian is assumed to satisfy the Poisson distribution. Both the fundamental diagram of vehicular traffic flow and the pedestrian waiting time are calculated, and the phase diagram revealing the global nature of the presented model is obtained accordingly. The quantitative characteristics of vehicle (pedestrian) delay time caused by pedestrians (vehicles) staying in the conflict area are given as well. Simulation results show that there is a critical split. When the split is less than the critical value, three kinds of traffic phases, i.e., free flow phase, saturated flow phase, and jamming flow phase, appear with the increase of density. When the split is larger than the critical value, four kinds of traffic phases, i.e., free flow phase, coexisting phase, saturated flow phase, and jamming flow phase are distinguished. The delay caused by the mutual interference between pedestrians and motor vehicles is closely related to the state of vehicle flow and the state of pedestrian flow. When the arrival rate of pedestrians is quite large and the split is large enough, these pedestrians in the waiting area cannot be emptied once in a single pedestrian cross-street cycle. The qualitative and quantitative characteristics of mutual interference between pedestrians and vehicles are discussed in more detail. The setting of a reasonable split not only ensures the efficiency of traffic flow, but also reduces the waiting time of pedestrians to cross the street.