A criterion for the occurrence or non-occurrence of a traffic collapse at a bottleneck

For a bottleneck controlled by traffic lights with a stochastic volume of traffic a criterion for the occurrence or non-occurrence of a traffic collapse is formulated. This criterion is based on the expectation of the asymptotic queue length of vehicles. Its boundedness implies together with a theorem of Prohorov the relative compactness of the corresponding sequence of distributions, which is used in a subsequent papaer to prove ergodicity of the queueing process by a fixed point theorem.