article

The tightness in the ergodic analysis of regenerative queueing processes

Author:

Evsei MorozovAuthors Info & Claims

Queueing Systems: Theory and Applications, Volume 27, Issue 1/2

Pages 179 - 203

https://doi.org/10.1023/A:1019114131583

Published: 14 December 1997 Publication History

Abstract

The tightness of some queueing stochastic processes is proved and its role in an ergodic analysis is considered. It is proved that the residual service time process in an open Jackson-type network is tight. The same problem is solved for a closed network, where the basic discrete time process is embedded at the service completion epochs. An extention of Kiefer and Wolfowitz's key lemma to a nonhomogeneous multiserver queue with an arbitrary initial state is obtained. These results are applied to get the ergodic theorems for the basic regenerative network processes.

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Cited By

Morozov EMorozova T(2020)The Remaining Busy Time in a Retrial System with Unreliable ServersDistributed Computer and Communication Networks10.1007/978-3-030-66471-8_42(555-566)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-66471-8_42
Morozov ERumyantsev ADey SDeepak T(2019)Performance analysis and stability of multiclass orbit queue with constant retrial rates and balkingPerformance Evaluation10.1016/j.peva.2019.102005134:COnline publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1016/j.peva.2019.102005
Morozov EMaltseva MSteyaert B(2018)Verification of the Stability of a Two-Server Queueing System With Static PriorityProceedings of the 22st Conference of Open Innovations Association FRUCT10.5555/3266365.3266388(166-172)Online publication date: 21-May-2018
https://dl.acm.org/doi/10.5555/3266365.3266388
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Published In

cover image Queueing Systems: Theory and Applications

Queueing Systems: Theory and Applications Volume 27, Issue 1/2

1997

199 pages

ISSN:0257-0130

Issue’s Table of Contents

Copyright © Copyright © 1997 Kluwer Academic Publishers.

Publisher

J. C. Baltzer AG, Science Publishers

United States

Publication History

Published: 14 December 1997

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Cited By

Morozov EMorozova T(2020)The Remaining Busy Time in a Retrial System with Unreliable ServersDistributed Computer and Communication Networks10.1007/978-3-030-66471-8_42(555-566)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-66471-8_42
Morozov ERumyantsev ADey SDeepak T(2019)Performance analysis and stability of multiclass orbit queue with constant retrial rates and balkingPerformance Evaluation10.1016/j.peva.2019.102005134:COnline publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1016/j.peva.2019.102005
Morozov EMaltseva MSteyaert B(2018)Verification of the Stability of a Two-Server Queueing System With Static PriorityProceedings of the 22st Conference of Open Innovations Association FRUCT10.5555/3266365.3266388(166-172)Online publication date: 21-May-2018
https://dl.acm.org/doi/10.5555/3266365.3266388
Morozov EPhung-Duc T(2017)Stability analysis of a multiclass retrial system with classical retrial policyPerformance Evaluation10.1016/j.peva.2017.03.003112:C(15-26)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1016/j.peva.2017.03.003
Avrachenkov KMorozov ESteyaert B(2016)Sufficient stability conditions for multi-class constant retrial rate systemsQueueing Systems: Theory and Applications10.1007/s11134-015-9463-982:1-2(149-171)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1007/s11134-015-9463-9
Morozov EDelgado R(2009)Stability analysis of regenerative queueing systemsAutomation and Remote Control10.1134/S000511790912006670:12(1977-1991)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.1134/S0005117909120066
Morozov E(2007)A multiserver retrial queueQueueing Systems: Theory and Applications10.1007/s11134-007-9024-y56:3-4(157-168)Online publication date: 1-Aug-2007
https://dl.acm.org/doi/10.1007/s11134-007-9024-y
Morozov E(2004)Weak Regeneration in Modeling of Queueing ProcessesQueueing Systems: Theory and Applications10.1023/B:QUES.0000027988.38058.8d46:3/4(295-315)Online publication date: 1-Mar-2004
https://dl.acm.org/doi/10.1023/B%3AQUES.0000027988.38058.8d
Morozov E(2002)Stability of Jackson Type Network OutputQueueing Systems: Theory and Applications10.1023/A:101503750203840:4(383-406)Online publication date: 1-May-2002
https://dl.acm.org/doi/10.1023/A%3A1015037502038

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