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February 2004 Stability and instability of a two-station queueing network
J. G. Dai, John J. Hasenbein, John H. Vande Vate
Ann. Appl. Probab. 14(1): 326-377 (February 2004). DOI: 10.1214/aoap/1075828055

Abstract

This article proves that the stability region of a two-station, five-class reentrant queueing network, operating under a nonpreemptive static buffer priority service policy, depends on the distributions of the interarrival and service times. In particular, our result shows that conditions on the mean interarrival and service times are not enough to determine the stability of a queueing network under a particular policy. We prove that when all distributions are exponential, the network is unstable in the sense that, with probability 1, the total number of jobs in the network goes to infinity with time. We show that the same network with all interarrival and service times being deterministic is stable. When all distributions are uniform with a given range, our simulation studies show that the stability of the network depends on the width of the uniform distribution. Finally, we show that the same network, with deterministic interarrival and service times, is unstable when it is operated under the preemptive version of the static buffer priority service policy. Thus, our examples also demonstrate that the stability region depends on the preemption mechanism used.

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J. G. Dai. John J. Hasenbein. John H. Vande Vate. "Stability and instability of a two-station queueing network." Ann. Appl. Probab. 14 (1) 326 - 377, February 2004. https://doi.org/10.1214/aoap/1075828055

Information

Published: February 2004
First available in Project Euclid: 3 February 2004

zbMATH: 1070.90020
MathSciNet: MR2023024
Digital Object Identifier: 10.1214/aoap/1075828055

Subjects:
Primary: 90B15
Secondary: 37D45 , 60K20

Keywords: fluid model , large deviations estimate , Multiclass queueing network , push start , reentrant line , stability , virtual station

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 1 • February 2004
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