Optimal control of oversaturated signals is one of the major concerns of traffic engineering practice today. Although some control strategies have been proposed in the past, due to their limitations they have not been used in practice. One of their major deficiencies is that the effects of queue length constraints on the signal operation have been inadequately investigated. Thus, the optimal control strategy with state variable constraints is studied in this paper. The optimal policy minimizing intersection delay subject to queue length constraints is to switch the signals as soon as the queues are at their limits so that the input and output flows are balanced. Cycle length can remain constant if only one queue length constraint is imposed but it must be free to vary if constraints are imposed on more than one queue. The conditions under which the problem is impossible are stated. A numerical solution method is proposed for determining the optimal control for the case in which the intersection demand is predictable for the entire control period.
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