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.

最大压力 (MP) 控制是为数不多的经证明可以最大化网络吞吐量或最大限度地稳定网络的交通信号控制器之一。根据目前公布的理论结果，如果所有交叉口都配备 MP 控制以满足所有可稳定的需求，则可以稳定网络。然而，预算限制可能不允许在所有交叉路口安装 MP 控制。以前的工作在证明稳定性属性时没有考虑有限数量的 MP 控制交叉口。因此，尚不清楚是否仍可以通过有限部署 MP 控制来稳定网络。本文使用 Lyapunov 漂移技术证明，即使部署有限，MP 控制也可以在可行的需求范围内稳定网络。然后我们提出了一个优化公式，以在给定有限预算的情况下找到安装 MP 控制的最佳交叉点。我们还提出了一种贪婪的高效算法来解决该优化问题，并证明该算法可以最优地解决问题。然后介绍了使用称为 AVDTA 的内部定制模拟器在奥斯汀市中心网络上进行模拟的数值结果。从优化问题中获得的不同部署量的理论最大可服务需求的变化似乎在大多数时候与模拟结果相匹配。我们发现，就可服务的稳定需求而言，MP 控制的有限部署几乎总是比 MP 控制的随机部署表现更好。观察到平均总队列长度和链路密度随着 MP 控制数量的增加而减少，这表明网络性能更好。安装 MP 控制装置后，每辆车的平均行驶时间也有所减少，这表明旅行者将如何从更多的 MP 控制装置中受益。