A mathematical model for the fixed-time traffic control problem

The paper deals with the fixed-time traffic control problem, which consists of finding a periodic schedule for the signals controlling the vehicular traffic in a system of intersections. A traffic model is used which allows for constraints on green durations, conflicts and coordinations. The resulting mathematical model is formulated as an extension of the feasible differential problem of network flow theory over a special graph associated with the intersection system. The fixed-time traffic control problem is proved to be NP-complete in general. A specialized algorithm is proposed for its solution; moreover an alternative solution method based on mixed-integer linear programming is given. Finally, a real example is modelled and solved.