Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Abstract

Setting traffic light signals is a classical topic in traffic engineering, and important in heavytraffic 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.

Heavy-traffic single-server queues and the transform method

“…Boxma and Cohen apply the transform method to an extended form of Pollaczek's integral (3) to identify the heavy-traffic limit. Other studies that apply this transform method for heavytraffic analysis are [21,22] on the GI/G/s queue and [5,4] on the fixed-cycle traffic-light queue, a variation of the GI/G/1 queue.…”