In: Journal of Applied Probability, Vol. 35, No. 2, pages 473-481. 1998.
Abstract: The traffic equations are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterizing the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note shows that the new condition stating that each transition is covered by a minimal closed support T-invariant, is necessary and sufficient for the existence of a solution for the traffic equations for batch routing queueing networks and stochastic Petri nets.
Keywords: closed support T-invariants, performance analysis, queueing networks, stochastic Petri nets, traffic equations.