The static property of perturbed queueing networks

Queuing networks can be viewed as dynamic systems. A small perturbation of an event will be propagated to other events as the system evolves. The evolution of a perturbation strongly depends on the system structure. We define an indecomposable network as a network in which a perturbation of an event at any server will, with probability one, be finally lost or propagated to all servers in the network. We show that a multi-class closed queuing network may be indecomposable even if every customer can not reach every server in the network. A necessary and sufficient condition for a multi-class network to be indecomposable is given. The results clearly display the dynamic feature of queuing networks.