城市交通网络正系统模型与稳态信号控制

城市路网内车流分布不均衡为交通拥堵原因之一，且交通控制系统为典型正系统．为此，本文采用Compartment正系统对网络交通流演化建模，以网络均衡为控制目标，提出稳态信号控制方法．首先，建立网络交通流Compartment正系统模型，可描述具有任意控制结构网络的过饱和特征；进一步，给定网络车流输入，由非负矩阵理论可得网络存在唯一稳定平衡点，给出平衡点解析计算公式．由此，提出网络稳态信号控制律，为路段状态反馈控制律．最后，以北京市奥林匹克公园区域拓扑路网为例，在VISSIM软件中建立仿真环境，比较稳态信号控制方法与定时控制方法，仿真结果表明在高需求网络条件下，稳态信号控制方法可改善网络整体性能和缓解局部拥堵．

Positive System Model of Urban Traffic Networks and Steady-state Signal Control

One reason behind traffic congestion is the unbalanced distribution of vehicle flows in urban road networks. Meanwhile, traffic control systems comprise a typical class of positive systems. Therefore, the evolution of traffic flows in the network must be modeled by compartment positive systems. In this study, we propose the steady-state signal control approach to achieve the balance of the network as a control objective. First, we establish the compartment positive system model of network flows, which can describe the oversaturated features of the network with any control structures. For given vehicle inputs of the network, there exists a unique stable equilibrium of the network from nonnegative matrix theory; from this, we educe the analytic computation formula of the equilibrium. On the basis of this formula, we propose the steady-state signal control law of the network, which is the link-state-feedback control law. Finally, we chose the network located at the Olympic Park area in Beijing, and compared the steady-state signal control approach with the fixed-time signal control approach in a VISSIM simulation environment. The results show that the steady-state signal control approach can improve network performance and reduce local congestion under higher demand conditions of the network.