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On closed support T-Invariants and the traffic equations

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Richard J. Boucherie  and
Matteo Sereno
Richard J. Boucherie*
Affiliation:
Universiteit van Amsterdam
Matteo Sereno*
Affiliation:
Università di Torino
*
∗Postal address: Department of Econometrics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands. E-mail address: [email protected]
∗∗Postal address: Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149 Torino, Italy.
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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 characterising 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

Traffic equationsclosed support T-invariantqueueing networkPetri net

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 473 - 481
Copyright
Copyright © Applied Probability Trust 1998 

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