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

TL;DR

This paper develops heavy-traffic limit models for fixed-cycle traffic-light queues, enabling accurate performance approximations and optimal green time allocations in congested traffic conditions.

Contribution

It introduces a novel heavy-traffic limit framework for fixed-cycle traffic-light queues and applies it to optimize green time division among conflicting streams.

Findings

Heavy-traffic limits accurately approximate queue behavior in congested conditions.

Optimization based on heavy-traffic approximations yields near-optimal traffic signal plans.

The framework applies to vehicle-actuated strategies, broadening its applicability.

Abstract

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. The same type of limiting result can be established for several vehicle-actuated strategies which adds to the general applicability of the framework presented in this paper.