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Ergodicity of a Jackson network by batch arrivals

Published online by Cambridge University Press:  14 July 2016

A. A. Borovkov*
Affiliation:
Russian Academy of Sciences
R. Schassberger*
Affiliation:
Technical University of Braunschweig
*
Postal address: Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia 630090.
∗∗ Postal address: Institut für Mathematische Stochastik, Technical University of Braunschweig, Postfach 3329, D-38106 Braunschweig, Germany.

Abstract

The Jackson network under study receives batch arrivals at i.i.d. intervals and features Markovian routing and exponentially distributed service times. The system is shown to be stable, in the sense of not being overloaded, if and only if, for each node, the total arrival rate of external and internal customers is less than the service rate. The method of proof is of more general interest.

MSC classification

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1994 

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