ON CLOSED SUPPORT T-INVARIANTS AND THE TRAFFIC EQUATIONS

The traffic equations are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product fo rm queueing networks. Conditions characterising the structure of the n etwork that guarantees the existence of a solution for the traffic equ ations 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 netwo rks and stochastic Petri nets.