Queueing Networks with Several Demand Types, Immediate Service, and Node Bypassing by Demands

We consider open networks with several demand types. Demands arrive at a node with probability depending on the node state and demand type and displace the demands being served. The displaced demands are queued at the same node or are moved instantly to another node according to a route matrix or leave the system. It is proved that the stationary distribution depends only on the mean service time and not on the type of its distribution.