The Annals of Applied Probability

Stability of Generalized Jackson Networks

S. P. Meyn and D. Down

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 1 (1994), 124-148.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005203

Digital Object Identifier
doi:10.1214/aoap/1177005203

Mathematical Reviews number (MathSciNet)
MR1258176

Zentralblatt MATH identifier
0807.68015

JSTOR
links.jstor.org

Subjects
Primary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Queueing networks Harris recurrence general state space Markov processes

Citation

Meyn, S. P.; Down, D. Stability of Generalized Jackson Networks. Ann. Appl. Probab. 4 (1994), no. 1, 124--148. doi:10.1214/aoap/1177005203. https://projecteuclid.org/euclid.aoap/1177005203


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