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

A multiclass closed queueing network is viewed as a dynamic system. It is considered that 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. An indecomposable network is defined 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 is shown that a multiclass closed queueing network may be undecomposable 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. It is concluded that the results clearly display the dynamic feature of queueing networks