Traffic in Connecting Networks When Existing Calls are Rearranged

Each state of the network realizes a given assignment of inlets to outlets, a specification of who is to talk to whom. There is a natural map 7 that takes the set S of states into the set A of assignments. The equilibrium probabilities of the process xt on S we use as a traffic model are complicated and unknown functions of the offered load. But it turns out that, because of the policy of rearranging whenever necessary, y(xt) is also a Markov process, and one whose state probabilities are easy to calculate. We give explicit analytical formulas for the equilibrium probability of a given assignment of inlets to outlets, for the probability of n calls in progress. For networks that are one-sided (inlets = outlets) or twosided (inlets n outlets =