A pedestrian hopping model and traffic light scheduling for pedestrian-vehicle mixed-flow networks

This paper presents a pedestrian hopping model and a traffic signal scheduling strategy with consideration of both pedestrians and vehicles in the urban traffic system. Firstly, a novel mathematical model consisting of several logic constraints is proposed to describe the pedestrian flow in the urban traffic network and its dynamics are captured by the hopping rule, which depicts the changing capacity of each time interval from one waiting zone to another. Based on the hopping mechanism, the pedestrian traffic light scheduling problems are formulated by two different performance standards: pedestrian delay and pedestrian unhappiness. Then the mathematical technique and the meta-heuristic approach are both adopted to solve the scheduling problem: Mixed integer linear programming (MILP) formulation for pedestrian delay model and discrete harmony search algorithm (DHS) for both pedestrian delay model and unhappiness model. Secondly, a mathematical model about the vehicle traffic network, which captures drivers psychological responses to the traffic light signals, is introduced. Thirdly, a traffic light scheduling strategy to minimize the trade-off of the delays between pedestrians and vehicles is proposed. Finally, we translate this traffic signal scheduling problem for both pedestrians and vehicles into a MILP problem which can be solved by several existing tools, e.g., GUROBI. Numerical simulation results are provided to illustrate the effectiveness of our real-time traffic light scheduling for pedestrian movement and the potential impact to the vehicle traffic flows by the pedestrian movement.