Analytical investigation on the minimum traffic delay at a two-phase intersection considering the dynamical evolution process of queues

TL;DR

This paper analytically investigates the minimum traffic delay at a two-phase intersection by examining the queue evolution process, deriving optimal signal timings, and revealing conditions where extra green time is necessary.

Contribution

It introduces an analytical method to determine minimum traffic delay considering queue dynamics and identifies when additional green time is required for optimal traffic flow.

Findings

Minimum delay occurs when at least one constraint is active.

Two scenarios for optimal signal timing are identified.

Extra green time may be needed for one phase under certain conditions.

Abstract

This paper has studied the minimum traffic delay at a two-phase intersection, taking into account the dynamical evolution process of queues. The feature of delay function has been studied, which indicates that the minimum traffic delay must be achieved when equality holds in at least one of the two constraints. We have derived the minimum delay as well as the corresponding traffic signal period, which shows that two situations are classified. Under certain circumstance, extra green time is needed for one phase while otherwise no extra green time should be assigned in both phases. Our work indicates that although the clearing policies were shown in many experiments to be optimal at isolated intersections, it is sometimes not the case.