The traffic equations are a set of linear equations, which are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note provides a necessary and sufficient condition on the structure of the network for solution of the traffic equations to exist. The basis of this structural characterisation is the equivalence between batch routing queueing networks and stochastic Petri nets at the level of the underlying stochastic process. Based on new and known results for stochastic Petri nets, 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 queuening networks and stochastic Petri nets.
On the Traffic Equations for Batch Routing Queueing Networks and Stochastic Petri Nets
SERENO, Matteo
1994-01-01
Abstract
The traffic equations are a set of linear equations, which are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note provides a necessary and sufficient condition on the structure of the network for solution of the traffic equations to exist. The basis of this structural characterisation is the equivalence between batch routing queueing networks and stochastic Petri nets at the level of the underlying stochastic process. Based on new and known results for stochastic Petri nets, 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 queuening networks and stochastic Petri nets.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.