Traffic Signal Control in an MPC Framework Using Mixed Integer Programming

Abstract

This paper presents network wide traffic signal control in a model predictive control framework using mixed integer programming. A concise model of traffic is proposed to describe the traffic flows in a signalized road network. In the model, the traffic signal at a junction is represented by a binary variable to express a signal state either green or red, and the traffic of two sections that belong to a traffic signal group at the junction are represented by a continuous variable. Therefore, less number of variables are required to describe traffic in the network than any model that describes each section traffic individually. The traffic signal control framework using the proposed traffic model is evaluated on a small road network that experiences varying traffic flows over time. The framework simultaneously generates all traffic signals in the network by turning them flexibly to red and green that optimize the traffic flows in the context of model predictive control. Successive generations of red and green signals at all junctions create traffic signal patterns with optimal free parameters, i.e., the cycle times, the split times and the offsets, depending on the traffic flow conditions in the network. Use of the concise traffic model reduces the computation time of mixed integer programming significantly.