  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.
