Perimeter control for urban traffic system based on macroscopic fundamental diagram

In this paper, we study the application of perimeter flow control by simulation of cellular automaton model on urban traffic system. We find that the relation of traffic flow and vehicle density (Macroscopic Fundamental Diagram, MFD) will have different shapes for the core area and the peripheral area. The MFD shows free-flow state, saturate flow state and congestion state. But the magnitude of maximal flow and the position for congestion transition are different for the whole system and the core area. We suggest to realize the perimeter control strategy by assigning a special prohibiting phase to the perimeter traffic lights for the roads entering the core area. The strategy is controlled by two critical densities ρ1 and ρ2, which are determined by the MFD of the core area. Simulations show that both the average arrival rate and the average flow will be greatly improved with the perimeter flow control strategy. In addition, the perimeter flow control strategy can increase the critical density of traffic congestion. The probability of system-wide gridlock will decrease, and the system can perform well under both close and open boundary conditions. All the results indicate that the perimeter flow control strategy can effectively improve the performance of the traffic system.