The static property of a perturbed multiclass closed queueing network and decomposition

Queueing 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. The paper defines 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. It shows that a multiclass closed queueing network may be indecomposable even if every customer cannot reach every server in the network. A necessary and sufficient condition for a multiclass network to be indecomposable is given. The results clearly display the dynamic feature of queueing networks.