Traffic control using graph-theory

In this paper the design of a controller for a traffic crossing is presented by means of an example. The controller to be developed has to minimise the waiting time of the public transportation while maintaining the individual traffic flow as well as possible. First, the model of the chosen traffic crossing is derived. Then, using a combination of ‘Dynamic Programming’ and ‘Branch and Bound’ the control algorithm is presented. A visualisation of the algorithm is given by means of graphs, complexity issues are investigated, and computational refinements proposed. Simulation results are shown at the end. The actual implementation of the control algorithm for the example shown is under way and carried out in co-operation with the Transportation Authority of the city of Zurich. The work presented here is part of a bigger project. The overall goal is to provide the traffic engineer with a tool for designing ‘intelligent’ controllers for traffic lights.