The problem of minimizing delay of a system of oversaturated intersections subject to queue length constraints is solved using optimal control theory. Turning movements, storage capacity and travel times between intersections are taken into consideration and it is shown that coordination of the signals, according to analytical relationships developed here, is necessary for optimal operation. It is also demonstrated that the entire congestion period must be divided into two intervals and that the optimal control in both intervals is determined by considering separate test functions. In each interval the optimal control is bang-bang if none of the queues reaches its upper or lower bound, and the switch-over points are at most three per intersection. The optimal control policy with queue length constraints requires, in general, utilization of variable cycle lengths and splits. Numerical determination of the optimal control policy is proposed based on the results presented here and a technique described previously (Michalopoulos and Stephanopoulos, 1977).
ASJC Scopus subject areas