Traffic regulation in the urban transportation network

In this paper, we consider a real-time regulation problem of the traffic within a disturbed urban transportation network. From a given timetable, we aim to find a new schedule of various buses after detection of a disturbance at a given time. The main objective is to find a solution maximizing the level of service for all passengers by minimising their waiting times at stops and theirs transit times in connecting nodes. This problem was already studied with evolutionary approaches and multi-agents techniques without analyzing or identifying its type before. In this paper, we prove that the problem has an optimal solution in the case of illimited buses capacities and we propose a formulation which allows its resolution without requiring the use of metaheuristics. Numerical experiments demonstrates the effectiveness of the theoretical formulation comparing it with evolutionary approaches.