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February, 1994 Stability of Generalized Jackson Networks
S. P. Meyn, D. Down
Ann. Appl. Probab. 4(1): 124-148 (February, 1994). DOI: 10.1214/aoap/1177005203


In this paper we study open generalized Jackson networks with general arrival streams and general service time distributions. Assuming that the arrival rate does not exceed the network capacity and that the service times possess conditionally bounded second moments, we deduce stability of the network by bounding the expected waiting time for a customer entering the network. For Markovian networks we obtain convergence of the total work in the system, as well as the mean queue size and mean customer delay, to a unique finite steady state value.


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S. P. Meyn. D. Down. "Stability of Generalized Jackson Networks." Ann. Appl. Probab. 4 (1) 124 - 148, February, 1994.


Published: February, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0807.68015
MathSciNet: MR1258176
Digital Object Identifier: 10.1214/aoap/1177005203

Primary: 68M20
Secondary: 60J10

Keywords: general state space Markov processes , Harris recurrence , Queueing networks

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.4 • No. 1 • February, 1994
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