Performance, Throughput Properties, and Optimal Location Evaluation for Max-pressure Control

Abstract

Max pressure (MP) signal timing is an actuated decentralized signal control policy. Rigorous mathematical studies have proven stability or bounded total vehicle queues over a long period for all feasible demands. Those studies also established the theoretical benefits of different MP policies. However, the theoretical studies make some assumptions about traffic properties that may not represent reality, the effects of which are not explored much in the literature under realistic traffic conditions. The first portion of this study focuses on examining how different variations of MP control perform in realistic scenarios and finding the most practical policy among those for implementation in real roads. Microsimulation models of seven intersections from two corridors, County Road (CR) 30 and CR 109 from Hennepin County, Minnesota were created. Real life demand and current signal timing data provided by Hennepin County, Minnesota were used to make the simulations as close to reality as possible. Then, the performance comparisons of current actuated-coordinated (AC) signal control with an acyclic MP and two variations of cyclic MP policies are shown. The performance of different control policies in terms of delay, throughput, worst lane delay and number of phase changes are also presented. How different parameters affect performance of the MP policies is also presented. We found that better performance can be achieved with cyclic max pressure policy by allowing phase skipping when no vehicles are waiting. Findings from this study also suggest that most of the claimed performance benefits can still be achieved in real life traffic conditions even with the simplified assumptions made in the theoretical models. In most cases, MP control policies outperformed current signal control. The second portion of this study covers deployment strategies of MP control under limited budget and the associated stability properties. 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 thesis proves that even with a limited deployment, MP control can stabilize a network within feasible demand. Then, an optimization formulation to find the optimal intersections to install MP control given a limited budget is presented. We also present an efficient greedy 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 mostly match with simulation results. 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.