A Mathematical Programming Model and a Firefly-Based Heuristic for Real-Time Traffic Signal Scheduling With Physical Constraints

Traffic congestion is one of the challenges that face urban cities’ planners. It affects the environment as it increases the emissions of CO2 and affects the logistics systems as it may increase the travel time of different vehicles. Scheduling traffic signals is one of the ways to solve this problem. In the urban traffic signal scheduling problem, it is desired to get the optimum schedule for each considered traffic signal to maximize or minimize a specific objective function(s); these schedules determine the active and inactive traffic phases during each cycle time. In this paper, a mathematical programming model for solving the urban traffic signal scheduling problem is presented, the proposed mathematical model captures the physical constraints of the problem. Furthermore, a firefly-based rolling horizon approach is proposed to solve the problem. Both methods are used to solve a traffic-responsive system, which is considered the future of traffic control systems. The performance of both methods has been simulated using the SUMO traffic simulator to verify the solutions. The performance of the solutions was measured using the average queue length of the roads, the average waiting time, and the average travel time. The proposed methods have been applied to a real case study, and the results were remarkable.