Optimal routing in connecting networks over finite time intervals

A telephone connecting network is given, and with full information at all times about its state, routing policies are sought which minimize the expected number of attempted calls denied service in some finite interval. In this paper, the search is pursued as a mathematical problem in the context of a standard traffic model in terms of optimal control theory and dynamic programming. Certain combinatorial properties of the network, earlier found to be the key to minimizing the loss, also turn out to be relevant here: they lead to policies which differ from optimal policies only in accepting all unblocked call attempts, and provide a “practical” solution of the problem posed. In many cases, the policies found vindicate heuristic policies earlier conjectured to be optimal.