Optimum Management of Urban Traffic Flow Based on a Stochastic Dynamic Model

In this paper, we use a recently developed dynamic model for urban traffic flow subject to practical constraint characteristics of intersections equipped with traffic light. We define an objective functional based on the analytical expressions for traffic throughput, congestion, and drivers’ waiting time at an intersection. Following this, an optimization problem is formulated and an algorithm is presented based on the principle of optimality due to Bellman. The solution, if implemented, is expected to improve throughput, reduce congestion, avoid traffic jams, and promote driver satisfaction. The system is simulated with a series of numerical experiments and the corresponding optimization problems are solved using the proposed algorithm. The optimal feedback control laws independent of initial state are acquired, and the optimal cost is found according to any given initial condition. It is believed that this dynamic model would be potentially applicable for the real-time adaptive traffic control system.