随着车辆保有量的增加，城市交通拥堵现象越来越严重，带来了很多经济、社会、环境方面的问题。交叉口的信号配时策略是城市交通控制中的重要环节，也是解决城市拥堵问题的有效手段。本文针对孤立交叉口，研究信号配时策略，即如何配置绿信比以最小化车辆总延误。由于信号灯对车流的中断，交叉口附近的离开曲线通常呈现出非光滑的阶梯状特性，这使得总延误的计算十分复杂。本文利用较为光滑的分段线性函数近似复杂的离开曲线，从而把交叉口的动态特性建立成一个凸优化模型，即多阶段信号配时模型。由于交通流量和信号控制的实时性，本文递归地采用一个贪婪算法对车辆总延误进行在线优化，然后探讨了该递归贪婪算法的最优性。本文通过一个反例证明一般情况下该算法的最优性不成立，同时提出一个最优性的充分条件，并对该条件的充分性进行了证明。该条件的本质是对交叉口流量的随机性加以限制，假定交叉口的车流具有一定的稳定性：在某个周期饱和程度较强的车流在下个周期仍然饱和程度较强。该充分条件在实际中较容易满足。这表明本文采用的多阶段信号配时模型在实际中有着广泛的应用价值。最后，本文比较多阶段信号配时模型以及传统的最优控制模型的联系。本文选取了一个广受研究者青睐的简单而不失一般性的交通场景：由两条单行道汇成的交叉口。本文在这个简单场景下建立了多阶段信号配时模型以及最优控制模型，并比较了两者的解。本文指出，两种模型的解都呈现类似的bang-bang控制的特性，即在某个转折周期前后采取不同的配时策略。但是由于离散化的因素，两种模型的解不能完全重合，区别主要表现在转折周期附近。本文接下来分析了离散化的影响，并通过一个简单的梯度下降调整算法表明，在以上简单场景下最优控制模型的解可以在几步之内调整为多阶段信号配时模型的解。这样就建立了多阶段信号配时模型以及传统最优控制模型之间的联系，证明在一定条件和意义下两种模型之间的等价性。

This thesis studies the signal timing strategies for individual oversaturated intersections to minimize the total delay. Due to the interruption of traffic signals, the traffic near intersections always exhibit complex characteristics. As a result, the total delay function is generally non-linear and non-convex of the control variables, which makes it difficult to optimize.To tackle this problem, this dissertation considers a convex approximation of total delay by assuming linear departure curve in every single cycle and formulated the signal timing process into a discrete-time model -- multiple-cycle smoothed curve signal timing model. A recursive greedy algorithm is applied to solve this model in an online manner to deal with the real-time traffic demand. This dissertation further studied the global optimality of the algorithm. Firstly, a counterexample is proposed to show that the recursive greedy algorithm cannot guarantee the global optimality of multiple-cycle signal timing plan for all traffic senarios. Second, a simple sufficient global optimality condition is proposed and the optimality is proven. It is further shown that this condition will usually be satisfied in ordinary traffic scenarios. This indicates that the powerful smoothed curve signal timing model is useful in practices. This finding also provides a good starting point to further analyze the performance of oversaturated intersections.This dissertation also compares the discrete-time model with the conventional continuous-time dynamical models under a simple and typical scenario: isolated signalized intersection with only two one-way vehicle flows. First, both the discrete-time model and continuous-time model under this scenario. Second, the continuous-time and discrete-time solution are compared. Both the continuous-time and discrete-time solution exhibits a bang-bang characteristics, but they may not fully coincide in many situations. It is further shown that, in many cases, the continuous-time solution can be converted to the discrete-time solution within a few gradient descent adjustments. Finally, an algorithm is proposed to implement such conversion. These findings shed light on the connection between the continuous-time and discrete-time signal timing models.