Mixed backpressure policy for path based traffic signal control

Inspired by the feature of maximum throughput in backpressure scheme, we propose a mixed backpressure index for network-wide urban traffic signal control. This index is essentially a multi-objective function incorporating the pressure defined in BP scheme and road occupancy of every path embedded with the path based store-and-forward model. With this index, the one-step mixed backpressure control is developed to optimize the network-wide signal timing plans every time step and proved to inherit the property of stability of backpressure scheme. In order to overcome the erratic switching among stages in the backpressure scheme, we further extend one-step mixed backpressure control to multi-step by applying model predictive control methodology, where in each control cycle the green time of each stage is constrained to be consecutive. Both the one-step and multi-step mixed backpressure control are equivalently formulated as mixed integer linear programming problem for computational efficiency. The results of numerical study on a calibrated network of Caohejing District in Shanghai indicate that the mixed backpressure index based methods provide better performance in terms of delay time as well as maximum queue length than other throughput-optimal methods. Additionally, they allow for relative fairness of delay time associated with paths with appropriate parameter design.

Caohejing District in Shanghai

Fig.1 Average delay per vehicle over simulation time as a function of traffic load degree under different control methods

Fig.2 Average delay time of each path under different control methods at moderate loads