Convergence analysis on control for traffic signals in urban road network

This paper presents an analysis on the convergence to a steady state for the traffic dynamics in a network of signalized intersections. The links carrying the traffic from one intersection to another in the network are partitioned into a series of cells whose dynamics is modelled as a nonlinear cell transmission model. A microscopic convergence analysis is presented for the network where the traffic lights at the intersections are controlled by pre-timed control in which the average flow rate along each link is assumed to be known accurately. A macroscopic convergence analysis is applied to the traffic network where the traffic lights are controlled by coordinated model predictive control. In coordinated model predictive control, each local agent optimizes the switching times of traffic light at one intersection online with sampled local traffic state around this intersection and exchanged information from neighbouring intersections. A unique periodic function for the microscopic steady state is proved to exist under pre-timed control while a unique macroscopic steady state is achieved under coordinated model predictive control for the traffic lights. This paper validates by simulations that the ability of coordinated model predictive control to stabilize the traffic demand is not worse than pre-timed control even though the average flow rate along each link is not assumed to be known and further no explicit cycle time for the traffic light is suggested. Moreover, the incurred delay from the steady state is lower on the average under coordinated model predictive control compared to pre-timed control.