A concept of optimal control at a bottleneck with symmetric volume of traffic

An analysis of the optimal control of traffic lights at a bottleneck with symmetric volume of traffic is supplied, based on the minimization of the asymptotic expectation of the queue length (of vehicles). The process of queue lengths considered depends on an unknown starting distribution. By a fixed point theorem it is shown that the asymptotic expectation of the queue length, which turns out to be the expectation of the ergodic distribution, is invariant under alterations of the starting distribution, a result important not only for the correctness of the definition of the optimization concept but also for its numerical realization.