M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis

Mehmet Akif Yazici; Tuan Phung-Duc

doi:10.1007/978-3-030-59854-9_12

M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis

Mehmet Akif Yazici^*, Tuan Phung-Duc

^*Corresponding author for this work

Informatics Institute

University of Tsukuba

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

1 Citation (Scopus)

Abstract

We propose an analytical method for an M/M/1 vacation queue with workload dependent service rates. We obtain the distribution of the workload in the system, and consider a power-saving and performance trade-off problem. Numerical experiments reveal that square root service rate function has lower cost than that of linear and quadratic service functions under certain scenarios.

Original language	English
Title of host publication	Quantitative Evaluation of Systems - 17th International Conference, QEST 2020, Proceedings
Editors	Marco Gribaudo, David N. Jansen, Anne Remke
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	148-152
Number of pages	5
ISBN (Print)	9783030598532
DOIs	https://doi.org/10.1007/978-3-030-59854-9_12
Publication status	Published - 2020
Event	17th International Conference on Quantitative Evaluation Systems, QEST 2020 - Vienna, Austria Duration: 31 Aug 2020 → 3 Sept 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12289 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Quantitative Evaluation Systems, QEST 2020
Country/Territory	Austria
City	Vienna
Period	31/08/20 → 3/09/20

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Keywords

Data center
Fluid model
Power-saving
Vacation queue
Variable service rate

Access to Document

10.1007/978-3-030-59854-9_12

Cite this

Yazici, M. A., & Phung-Duc, T. (2020). M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis. In M. Gribaudo, D. N. Jansen, & A. Remke (Eds.), Quantitative Evaluation of Systems - 17th International Conference, QEST 2020, Proceedings (pp. 148-152). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12289 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-59854-9_12

Yazici, Mehmet Akif ; Phung-Duc, Tuan. / M/M/1 Vacation Queue with Multiple Thresholds : A Fluid Analysis. Quantitative Evaluation of Systems - 17th International Conference, QEST 2020, Proceedings. editor / Marco Gribaudo ; David N. Jansen ; Anne Remke. Springer Science and Business Media Deutschland GmbH, 2020. pp. 148-152 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We propose an analytical method for an M/M/1 vacation queue with workload dependent service rates. We obtain the distribution of the workload in the system, and consider a power-saving and performance trade-off problem. Numerical experiments reveal that square root service rate function has lower cost than that of linear and quadratic service functions under certain scenarios.",

keywords = "Data center, Fluid model, Power-saving, Vacation queue, Variable service rate",

author = "Yazici, {Mehmet Akif} and Tuan Phung-Duc",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 17th International Conference on Quantitative Evaluation Systems, QEST 2020 ; Conference date: 31-08-2020 Through 03-09-2020",

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doi = "10.1007/978-3-030-59854-9_12",

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Yazici, MA & Phung-Duc, T 2020, M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis. in M Gribaudo, DN Jansen & A Remke (eds), Quantitative Evaluation of Systems - 17th International Conference, QEST 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12289 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 148-152, 17th International Conference on Quantitative Evaluation Systems, QEST 2020, Vienna, Austria, 31/08/20. https://doi.org/10.1007/978-3-030-59854-9_12

M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis. / Yazici, Mehmet Akif; Phung-Duc, Tuan.
Quantitative Evaluation of Systems - 17th International Conference, QEST 2020, Proceedings. ed. / Marco Gribaudo; David N. Jansen; Anne Remke. Springer Science and Business Media Deutschland GmbH, 2020. p. 148-152 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12289 LNCS).

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

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AB - We propose an analytical method for an M/M/1 vacation queue with workload dependent service rates. We obtain the distribution of the workload in the system, and consider a power-saving and performance trade-off problem. Numerical experiments reveal that square root service rate function has lower cost than that of linear and quadratic service functions under certain scenarios.

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Yazici MA, Phung-Duc T. M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis. In Gribaudo M, Jansen DN, Remke A, editors, Quantitative Evaluation of Systems - 17th International Conference, QEST 2020, Proceedings. Springer Science and Business Media Deutschland GmbH. 2020. p. 148-152. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-59854-9_12

M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis

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