The PH/PH/1 multi-threshold queue

Niek Baër; Richard J. Boucherie; Jan-Kees van Ommeren

doi:10.1007/978-3-319-08219-6_7

The PH/PH/1 multi-threshold queue

Niek Baër, Richard J. Boucherie, Jan-Kees van Ommeren

Stochastic Operations Research

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

3 Citations (Scopus)

10 Downloads (Pure)

Abstract

We consider a PH/PH/1 queue in which a threshold policy determines the stage of the system. The arrival and service processes follow a Phase-Type (PH) distribution depending on the stage of the system. Each stage has both a lower and an upper threshold at which the stage of the system changes, and a new stage is chosen according to a prescribed distribution. The PH/PH/1 multi-threshold queue is a Quasi-Birth-and-Death process with a tri-diagonal block structured boundary state which we model as a Level Dependent Quasi-Birth-and-Death process. An efficient algorithm is presented to obtain the stationary queue length vectors using Matrix Analytic methods.

Original language	English
Title of host publication	Analytical and Stochastic Modeling Techniques and Applications
Subtitle of host publication	21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings
Editors	Bruno Sericola, Miklós Telek, Gábor Horváth
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	95-109
Number of pages	15
ISBN (Electronic)	978-3-319-08219-6
ISBN (Print)	978-3-319-08218-9
DOIs	https://doi.org/10.1007/978-3-319-08219-6_7
Publication status	Published - 2014
Event	21st International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2014 - Budapest, Hungary Duration: 30 Jun 2014 → 2 Jul 2014 Conference number: 21

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer International Publishing
Volume	8499
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	21st International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2014
Abbreviated title	ASMTA
Country/Territory	Hungary
City	Budapest
Period	30/06/14 → 2/07/14

Keywords

EWI-24982
$PH/PH/1$ queue
Multiple thresholds
Tri-diagonal block structured boundary state
METIS-305985
PH/PH/1 queue
IR-91594
Matrix Analytic Methods
Quasi-birth-and-death process

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10.1007/978-3-319-08219-6_7

Cite this

Baër, N., Boucherie, R. J., & van Ommeren, J.-K. (2014). The PH/PH/1 multi-threshold queue. In B. Sericola, M. Telek, & G. Horváth (Eds.), Analytical and Stochastic Modeling Techniques and Applications: 21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings (pp. 95-109). (Lecture Notes in Computer Science; Vol. 8499). Springer. https://doi.org/10.1007/978-3-319-08219-6_7

Baër, Niek ; Boucherie, Richard J. ; van Ommeren, Jan-Kees. / The PH/PH/1 multi-threshold queue. Analytical and Stochastic Modeling Techniques and Applications: 21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings. editor / Bruno Sericola ; Miklós Telek ; Gábor Horváth. Cham, Switzerland : Springer, 2014. pp. 95-109 (Lecture Notes in Computer Science).

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abstract = "We consider a PH/PH/1 queue in which a threshold policy determines the stage of the system. The arrival and service processes follow a Phase-Type (PH) distribution depending on the stage of the system. Each stage has both a lower and an upper threshold at which the stage of the system changes, and a new stage is chosen according to a prescribed distribution. The PH/PH/1 multi-threshold queue is a Quasi-Birth-and-Death process with a tri-diagonal block structured boundary state which we model as a Level Dependent Quasi-Birth-and-Death process. An efficient algorithm is presented to obtain the stationary queue length vectors using Matrix Analytic methods.",

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Baër, N, Boucherie, RJ & van Ommeren, J-K 2014, The PH/PH/1 multi-threshold queue. in B Sericola, M Telek & G Horváth (eds), Analytical and Stochastic Modeling Techniques and Applications: 21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings. Lecture Notes in Computer Science, vol. 8499, Springer, Cham, Switzerland, pp. 95-109, 21st International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2014, Budapest, Hungary, 30/06/14. https://doi.org/10.1007/978-3-319-08219-6_7

The PH/PH/1 multi-threshold queue. / Baër, Niek; Boucherie, Richard J.; van Ommeren, Jan-Kees.
Analytical and Stochastic Modeling Techniques and Applications: 21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings. ed. / Bruno Sericola; Miklós Telek; Gábor Horváth. Cham, Switzerland: Springer, 2014. p. 95-109 (Lecture Notes in Computer Science; Vol. 8499).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Baër N, Boucherie RJ, van Ommeren JK. The PH/PH/1 multi-threshold queue. In Sericola B, Telek M, Horváth G, editors, Analytical and Stochastic Modeling Techniques and Applications: 21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings. Cham, Switzerland: Springer. 2014. p. 95-109. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-08219-6_7

The PH/PH/1 multi-threshold queue

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Keywords

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