defined as one minimizing the total delay from time zero to infinity, discounted with an exponential weight factor. Traffic is treated as a continuous fluid with constant arrival rates and constant departure rates during the green phase of the traffic light. Optimal policies are found as functions of arbitrary queue lengths and light phase at time zero. A control algorithm proposed by Dunne and Potts, switch the light as soon as a queue vanishes, is shown to be optimal in the above sense for some initial states. However, if initial queues are very large, and departure rates are unequal for the 2 traffic streams, the optimal policy will involve 1 or more policy modifications in which the light is switched to the lane of higher flow before the queue in the other lane vanishes. If, conversely, the initial queues are very small, the optimal policy may include 1 or more modifications in which the light is kept green for a certain length of time after a queue vanishes.
Samenvatting