Abstract: Traffic signals on urban arterials and in grid networks operate in coordinated systems to provide for smooth progression of major traffic movements. In the past decades, continued efforts have been made to the research and development of coordinated traffic signal control strategies. The models and systems that have been developed include both the off-line models such as TRANSYT and PASSER, and on-line systems such as SCOOT, SCATS, UTCS, and the latest RT-TRACS, which is a framework still under development. Despite the availability of so many models and systems, all of them have been designed by using heuristic algorithms to optimize the signal offset. On the other hand, most of existing theoretical methodologies for optimizing the signal offset are deterministic in nature, which ignore the stochastic variations o# vehicles. The lack of a sophisticated theoretical basis in the state-of-the-art for optimizing the signal offset has significantly limited the researcher’s ability to evaluating existing models and systems in an objective manner. This paper presents a stochastic process- based approach for determining the optimal offset of two adjacent traffic signals for one directional traffic flow, which minimizes the average total delay and/or average total number of stops. By using the probability theory and queuing theory, the proposed approach incorporates both platoon dispersions and the stochastic variations of the queue at the intersection. A computational algorithm for determining the optimal offset is presented. With a possible expansion of the proposed algorithm to more complicated scenarios, it has a high potential to be incorporated into existing models or systems for both evaluation and implementation purposes.

Key words: traffic signal, signal offset, signal coordination, platoon dispersion

摘要： 城市交通主干道及格状网络上的交通信号通常以协调的方式运作，目的是使主要的交通流能够顺畅地流动.过去几十年来，协调信号控制策略一直是研究热点，相关的模型系统也得以开发，包括离线模型如TRANSYT,PASSER，在线系统如SCOOT,SC ATS,UTCS,以及正在
开发中的RT-TRACS， 尽管有这么多的模型和系统,它们无一例外都是使用启发式算法来优化信号的位相差.而另一方面，现有的有关优化信号位相差的理论方法都是确定性的，通常忽略了车流的随机变动.由于缺乏能够决定最优位相差的成熟的理论基础，我们在对现有模型和系统作客观的评价时受到了很大的限制.本文提出了基于概率过程的单向交通流相邻交叉口信号间位相差优化理论方法，该方法的优化目标是使车流的总延误和总停车次数最小.利用概率论和排队论，该方法兼顾了车流离散和车队在交叉口的随机变化.最后，设计了该方法的实用算法并给出应用实例.该算法可以被扩展到更复杂的交通网络，而待到被内嵌到现有模型或系统中之后，既可用于评价，又可用于实施的目的.

关键词: 交通信号, 信号位相差, 信号协调, 车队离散