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

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 at least one of the two constraint inequalities take the equal sign. 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 extra green time should be assigned to neither phase. 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.