COOPERATIVE EFFECTS IN CLOSED QUEUING NETWORKS

An aggregated network of a reservation and a renewal is considered. Its elements after a failure at working places pass through a network of repair nodes and then return to a block of working places. If a number of elements n tends to infinity we obtain a law of zero and one for a probability that all working places are occupied by elements. If this limit equals zero then we prove a tendency by a probability of a ratio between a number of occupied working places and n to b, 0<b<1, and a problem of b optimization is solved.

Keywords: closed queuing network, phase transition, route matrix.