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Abstract-A simplified isolated controlled vehicular traffic intersection with two movements is considered. A discreteevent max-plus model is proposed to formulate an optimization problem for the green-red switching sequence. In the case when the criterion is a strictly increasing, linear function of the queue lengths, the problem becomes a linear programming (LP) problem. Also, in this case, the steady-state control problem can be solved analytically. A sufficient and necessary condition for steady-state control is derived, and the structure of optimal steady-state traffic control is revealed. Our condition is the same as the necessary condition in [5] for both queue lengths to be non-increasing at an isolated intersection.

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