Closed Queueing Network with Changing Number of Request Classes at Nodes

A closed queueing network with multiserver nodes that provide service for requests of different types, where each node may have its own number of request types, and with several finite sources with their own transition matrices is considered. Generating times at the sources and servicing times at the nodes are exponentially distributed. In the considered class of service disciplines at the nodes, a discipline is found for which the stationary probability distribution of the network states has a multiplicative form. The uniqueness of such a discipline in the considered class is proved. A particular case of this discipline is the one where the choice of a request to be serviced is equiprobable and does not depend on either the number of the request in a queue or its type.