Throughput properties and optimal locations for limited deployment of Max-pressure controls

Max-pressure (MP) control is one of the few traffic signal controllers proven to maximize network throughput or maximally stabilize the network. According to the theoretical results published so far, it can stabilize a network if all intersections are equipped with MP control for all stabilizable demands. However, budget constraints may not allow the installation of MP control on all intersections. Previous work did not consider a limited number of MP controlled intersections while proving the stability properties. Therefore, it is not clear whether a network can still be stabilized with a limited deployment of MP control. Using Lyapunov drift techniques this paper proves that even with a limited deployment, MP control can stabilize a network within feasible demand. Then we present an optimization formulation to find the optimal intersections to install MP control given a limited budget. We also present a greedy efficient algorithm to solve that optimization problem and prove that the algorithm solves the problem to optimality. Numerical results from simulations conducted on the downtown Austin network using an in-house custom simulator called AVDTA are then presented. The change in theoretical maximum servable demands for different amounts of deployments obtained from the optimization problem seemed to match with simulation results most of the times. We found that limited deployment of MP control almost always performed better than random deployment of MP control in terms of servable stable demand. Average total queue length and link density were observed to decrease as the number of MP controls increased which indicates better network performance. Average travel times per vehicle also decreased with installations of MP controls which shows how the travelers would benefit from more MP controls.