Blocking Probabilities for Connecting Networks Allowing Rearrangements

We consider connecting networks in which we allow existing calls to be rearranged (rerouted) to accommodate a new call. This capability exists, for example, in the network of the recently proposed automatic main distribution frame [2,3,4] (where the need for switching live calls does not arise). For pract~cal reasons, we are particularly interested in networks in which we allow a fixed small number, say t, of calls to be rearranged. The probability that a (random) new call is still blocked even allowing t-l rearrangements is defined as the tth_ trial-blocking probability. When t is unlimited, then the network is said to allow total rearranging. If a network can accommodate any new call under total rearranging, it is said to be rearrangeable. In this paper, we propose a model for computing the tth_ trial-blocking probability recursively for the multi-stage Clos network. The computational complexity of this model is discussed and approximations suggested. We also give various modifications of this model to fit particular net works and possible extensions to more general networks. Finally, some simulation results and computer implementations of this model are mentioned.