Paper:

# Network-Wide Optimization of Traffic Signals Using Mixed Integer Programming

## Md. Abdus Samad Kamal^{*1}, Jun-ichi Imura^{*2}, Tomohisa Hayakawa^{*2},

Akira Ohata^{*3}, and Kazuyuki Aihara^{*4}

^{*1}Japan Science and Technology Agency and Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

^{*2}Department of Mechanical and Environmental informatics, Tokyo Institute of Technology, 2-12-1-W8-1 Ookayam, Meguro-ku, Tokyo 152-8552, Japan

^{*3}Toyota Motors Corporation, Sizuoka 410-1107, Japan

^{*4}Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

In this paper a network-wide traffic signal control scheme in a model predictive control framework using mixed integer programming is presented. A concise model of traffic is proposed to describe a signalized road network considering conservation of traffic. In the model, the traffic of two sections that belong to a traffic signal group of a junction are represented by a single continuous variable. Therefore, the number of variables required to describe traffic in the network becomes half compared with the models that describe section wise traffic flows. The traffic signal at the junction is represented by a binary variable to express a signal state either green or red. The proposed model is transformed into a mixed logical dynamical system to describe the traffic flows in a finite horizon, and traffic signals are optimized using mixed integer linear programming (MILP) for a given performance index. The scheme simultaneously optimizes all traffic signals in a network in the context of model predictive control by successively extending or terminating a green or red signal of each junction. Consequently, traffic signal patterns with the optimal free parameters, i.e., the cycle times, the split times and the offsets, are realized. Use of the proposed concise traffic model significantly reduces the computation time of the scheme without compromising the performance as it is evaluated on a small road network and compared with a previously proposed scheme.

*J. Robot. Mechatron.*, Vol.26, No.5, pp. 607-615, 2014.

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