article

A tandem retrial queueing system with two Markovian flows and reservation of channels

Authors:

Valentina Klimenok,

Olga TaraminAuthors Info & Claims

Computers and Operations Research, Volume 37, Issue 7

Pages 1238 - 1246

https://doi.org/10.1016/j.cor.2009.03.030

Published: 01 July 2010 Publication History

Abstract

We consider a tandem queueing system with single-server first station and multi-server second station. The input flow at Station 1 is described by the BMAP (batch Markovian arrival process). Customers from this flow are considered as non-priority customers. Customers of an arriving group, which meet a busy server, go to the orbit of infinite size. From the orbit, they try their luck in exponentially distributed random time. Service times at Station 1 are independent identically distributed random variables having an arbitrary distribution. After service at Station 1 a non-priority customer proceeds to Station 2. The service time by a server of Station 2 is exponentially distributed. Besides customers proceeding from Station 1, an additional MAP flow of priority customers arrives at Station 2 directly, not entering Station 1. If a priority customer meets a free server upon arrival, it starts service immediately. Else, it leaves the system forever. It is assumed that a few servers of Station 2 are reserved to serve the priority customers only. We calculate the stationary distribution and the main performance measures of the system. The problem of optimal design is numerically investigated.

References

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Cited By

Nazarov APaul SPhung-Duc TMorozova M(2022)Analysis of Tandem Retrial Queue with Common Orbit and MMPP Incoming FlowDistributed Computer and Communication Networks: Control, Computation, Communications10.1007/978-3-031-23207-7_21(270-283)Online publication date: 26-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-23207-7_21
Vishnevskii VDudin A(2017)Queueing systems with correlated arrival flows and their applications to modeling telecommunication networksAutomation and Remote Control10.1134/S000511791708001X78:8(1361-1403)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1134/S000511791708001X
Kim CKlimenok VDudin A(2016)Priority tandem queueing system with retrials and reservation of channels as a model of call centerComputers and Industrial Engineering10.1016/j.cie.2016.03.01296:C(61-71)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1016/j.cie.2016.03.012
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A tandem retrial queueing system with two Markovian flows and reservation of channels
1. Computing methodologies
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Published In

cover image Computers and Operations Research

Computers and Operations Research Volume 37, Issue 7

July, 2010

203 pages

ISSN:0305-0548

Issue’s Table of Contents

Copyright © Elsevier Ltd © 2009.

Publisher

Elsevier Science Ltd.

United Kingdom

Publication History

Published: 01 July 2010

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Cited By

Nazarov APaul SPhung-Duc TMorozova M(2022)Analysis of Tandem Retrial Queue with Common Orbit and MMPP Incoming FlowDistributed Computer and Communication Networks: Control, Computation, Communications10.1007/978-3-031-23207-7_21(270-283)Online publication date: 26-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-23207-7_21
Vishnevskii VDudin A(2017)Queueing systems with correlated arrival flows and their applications to modeling telecommunication networksAutomation and Remote Control10.1134/S000511791708001X78:8(1361-1403)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1134/S000511791708001X
Kim CKlimenok VDudin A(2016)Priority tandem queueing system with retrials and reservation of channels as a model of call centerComputers and Industrial Engineering10.1016/j.cie.2016.03.01296:C(61-71)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1016/j.cie.2016.03.012
Klimenok VSavko R(2015)Tandem system with retrials and impatient customersAutomation and Remote Control10.1134/S000511791508005676:8(1387-1399)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1134/S0005117915080056
Dudin AManzo RPiscopo R(2015)Single server retrial queue with group admission of customersComputers and Operations Research10.1016/j.cor.2015.03.00861:C(89-99)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.cor.2015.03.008
Dudin SDudina O(2013)Help desk center operating model as a two-phase queueing systemProblems of Information Transmission10.1134/S003294601301006749:1(58-72)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1134/S0032946013010067
Dudin AKim CKlimenok VTaramin OWang JYue W(2010)A dual tandem queueing system with a finite intermediate buffer and cross trafficProceedings of the 5th International Conference on Queueing Theory and Network Applications10.1145/1837856.1837872(102-109)Online publication date: 24-Jul-2010
https://dl.acm.org/doi/10.1145/1837856.1837872

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