On the tra c equations for batch routing queueing networks andstochastic Petri
نویسندگان
چکیده
The traac 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 traac equations are therefore of great importance. This note provides a necessary and suucient condition on the structure of the network for a solution of the traac 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 suucient for the existence of a solution for the traac equations for batch routing queueing networks and stochastic Petri nets.
منابع مشابه
On the tra c equations for batch routing queueing networks and stochastic Petri nets
The tra c 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 tra c equations are therefore of great importance. This note provides a necessary and su cien...
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