定时控制分析
Analysis of Fixed-Time Control
摘要：
将信号交叉口网络建模为排队网络。交叉口由固定时间（FT）控制进行调节，所有交叉口都具有相同的周期长度或周期$T$。车辆从网络外部以确定的周期性流到达入口链路，也具有周期$T$，在交叉口以固定比例转弯，并最终离开网络。车辆在每个路段行驶的时间是固定的，在路段的尽头，它们会加入一个队列。在每个交叉路口都有一个单独的队列。队列的存储容量是无限的，因此不会发生溢出。网络在时间$t$的状态是所有队列长度的矢量$x(t)$，以及沿链路行驶的车辆的位置。状态按照延迟-微分方程演化。假设网络是稳定的，即$x(t)$是有界的。则（1）存在唯一的周期轨迹$x^*(t)$，周期为$T$ ;（2）每个轨迹都收敛到这个周期轨迹;（3）如果车辆不遵循环路，则收敛发生在有限时间内。周期性轨迹决定了整个网络的性能。
英文摘要：
A network of signalized intersections is modeled as a queuing network. The intersections are regulated by fixed-time (FT) controls, all with the same cycle length or period, $T$. Vehicles arrive from outside the network at entry links in a deterministic periodic stream, also with period $T$, make turns at intersections in fixed proportions, and eventually leave the network. Vehicles take a fixed time to travel along each link, and at the end of the link they join a queue. There is a separate queue at each intersection for each movement. The storage capacity of the queues is infinite, so there is no spill back. The state of the network at time $t$ is the vector $x(t)$ of all queue lengths, together with the position of vehicles traveling along the links. The state evolves according to a delay-differential equation. Suppose the network is stable, that is, $x(t)$ is bounded. Then (1) there exists a unique periodic trajectory $x^*(t)$, with period $T$; (2) every trajectory converges to this periodic trajectory; (3) if vehicles do not follow loops, the convergence occurs in finite time. The periodic trajectory determines the performance of the entire network.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
