  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.
