Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions.

设置红绿灯信号是交通工程中的经典课题，在绿灯时间变得稀少且不可避免地形成更长的队列的繁忙交通条件下非常重要。对于固定周期交通灯队列，一种用于具有循环信号的交通灯的基本排队模型，我们获得了捕获长期队列行为的繁忙交通限制。我们利用极限定理来获得繁忙交通中一个队列的精确性能近似值。我们还考虑了旨在优化多个冲突交通流之间绿灯时间划分的优化问题。我们表明，插入高流量近似值会导致易于处理的优化问题和接近最佳的信号规定。