Abstract: Bandwidth-based traffic signal coordination plays a crucial role in improving the efficiency of vehicles within urban traffic networks. It is widely adopted in the field of arterial and network traffic signal control. However, traditional bandwidth-based network control methods mostly focus on optimizing coordination variables, such as offsets and phase sequences, after the coordinated paths are determined. This neglects the simultaneous optimization of path selection and coordination variables, resulting in limited coordination effectiveness and challenges in catering to the varied control requirements of different coordination paths. To address these issues, this paper focuses on the concurrent optimization of path selection and bandwidth-based coordination within an unclosed traffic network. The coordination path is taken as a decision variable and optimized concurrently with offsets and phase sequences. The choice sets for coordination paths and coordination path pairs are determined through an analysis of the inflow and outflow relationships of traffic movements between adjacent intersections. The optimization objective is to maximize the sum of weighted bandwidth. To capture the spatial and temporal constraints involving bandwidth, coordinated path pairs, offsets, phase sequences, travel time, and red and green time, a time- space diagram is employed. In addition, binary variables are introduced to formulate optimization constraints for the coordination path pairs. The simultaneous optimization of path selection and bandwidth-based coordination is formulated as a mixed-integer nonlinear programming problem. The results of a numerical example demonstrate that, when compared to the traditional bandwidth- based model that focuses on coordinating through paths, the proposed model automatically selects key coordination paths with higher traffic volumes in the traffic network. Consequently, the sum of weighted bandwidths generated by this model at the network level increases by 14.16% , and the sum of weighted bandwidths on four arterials sees improvements of 17.26%, 20.68%, -0.29%, and 39.19%, respectively.

Key words: urban traffic, optimization of coordination paths, time-space diagram, unclosed traffic network, bandwidth-based traffic signal coordination

摘要： 绿波协调控制可显著提升城市路网中车辆的通行效率，已被广泛应用于干道和区域交通信号控制领域。然而，传统路网绿波控制方法多是在协调路径确定后优化相位差和相序等协调变量，忽视了路径选择与协调变量的同步优化，协调效果有限，难以满足不同协调路径的差异化控制需求。针对此问题，本文以非闭合路网为研究对象，将协调路径视为决策变量，与相位差和相序协同优化，提出一种适于非闭合交通路网的路径选择与绿波协调同步优化方法。通过分析相邻交叉口之间车流的流入和流出关系，确定其协调路径与协调路径对备选集合。以绿波带宽加权和最大为优化目标，利用时距图刻画绿波带宽、协调路径对、相位差、相序、行驶时间和红绿灯时间之间的时空约束关系，同时，引入二元变量建立协调路径对优选约束条件，构建路径选择与绿波协调同步优化的混合整数非线性规划模型。算例结果表明：相比于传统面向直行路径的绿波协调控制模型，所提模型能够自动识别路网中大流量的关键协调路径，在路网层面生成的权重绿波带宽总和提高了 14.16%，在 4 条干道 层 面 生 成 的 权 重 绿 波 带 宽 总 和 分别提高了17.26%，20.68%，-0.29%和39.19%。

关键词: 城市交通, 协调路径优选, 时距图, 非闭合路网, 绿波信号协调