A joint moments based analysis of networks of MAP/MAP/1 queues

András Horváth, Gábor Horváth, M. Telek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of inter-node traffic. Utilising recent results on Markov arrival processes (MAPs), we apply a given number of joint moments of the consecutive inter-event times to describe the inter-node traffic. This traffic description is compact (uses far less parameters than the alternative methods) and flexible (allows an easy reduction of the complexity of the model, which increases in each analysis step). Numerical examples demonstrate the accuracy and the computational complexity of the proposed approximate analysis method.

Original languageEnglish
Title of host publicationProceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008
Pages125-134
Number of pages10
DOIs
Publication statusPublished - 2008
Event5th International Conference on the Quantitative Evaluation of Systems, QEST 2008 - St. Malo, France
Duration: Sep 14 2008Sep 17 2008

Other

Other5th International Conference on the Quantitative Evaluation of Systems, QEST 2008
CountryFrance
CitySt. Malo
Period9/14/089/17/08

Fingerprint

Queueing networks
Markov processes
Decomposition
Electric network analysis
Numerical analysis
Computational complexity

Keywords

  • Joint moment
  • MAP/MAP/1 queue
  • Markov arrival process
  • Matrix-geometric method
  • Queueing network

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Hardware and Architecture
  • Control and Systems Engineering

Cite this

Horváth, A., Horváth, G., & Telek, M. (2008). A joint moments based analysis of networks of MAP/MAP/1 queues. In Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008 (pp. 125-134). [4634965] https://doi.org/10.1109/QEST.2008.26

A joint moments based analysis of networks of MAP/MAP/1 queues. / Horváth, András; Horváth, Gábor; Telek, M.

Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008. 2008. p. 125-134 4634965.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Horváth, A, Horváth, G & Telek, M 2008, A joint moments based analysis of networks of MAP/MAP/1 queues. in Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008., 4634965, pp. 125-134, 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008, St. Malo, France, 9/14/08. https://doi.org/10.1109/QEST.2008.26
Horváth A, Horváth G, Telek M. A joint moments based analysis of networks of MAP/MAP/1 queues. In Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008. 2008. p. 125-134. 4634965 https://doi.org/10.1109/QEST.2008.26
Horváth, András ; Horváth, Gábor ; Telek, M. / A joint moments based analysis of networks of MAP/MAP/1 queues. Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008. 2008. pp. 125-134
@inproceedings{687aef07fa7e4233913bdfef1e1b898d,
title = "A joint moments based analysis of networks of MAP/MAP/1 queues",
abstract = "The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of inter-node traffic. Utilising recent results on Markov arrival processes (MAPs), we apply a given number of joint moments of the consecutive inter-event times to describe the inter-node traffic. This traffic description is compact (uses far less parameters than the alternative methods) and flexible (allows an easy reduction of the complexity of the model, which increases in each analysis step). Numerical examples demonstrate the accuracy and the computational complexity of the proposed approximate analysis method.",
keywords = "Joint moment, MAP/MAP/1 queue, Markov arrival process, Matrix-geometric method, Queueing network",
author = "Andr{\'a}s Horv{\'a}th and G{\'a}bor Horv{\'a}th and M. Telek",
year = "2008",
doi = "10.1109/QEST.2008.26",
language = "English",
isbn = "9780769533605",
pages = "125--134",
booktitle = "Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008",

}

TY - GEN

T1 - A joint moments based analysis of networks of MAP/MAP/1 queues

AU - Horváth, András

AU - Horváth, Gábor

AU - Telek, M.

PY - 2008

Y1 - 2008

N2 - The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of inter-node traffic. Utilising recent results on Markov arrival processes (MAPs), we apply a given number of joint moments of the consecutive inter-event times to describe the inter-node traffic. This traffic description is compact (uses far less parameters than the alternative methods) and flexible (allows an easy reduction of the complexity of the model, which increases in each analysis step). Numerical examples demonstrate the accuracy and the computational complexity of the proposed approximate analysis method.

AB - The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of inter-node traffic. Utilising recent results on Markov arrival processes (MAPs), we apply a given number of joint moments of the consecutive inter-event times to describe the inter-node traffic. This traffic description is compact (uses far less parameters than the alternative methods) and flexible (allows an easy reduction of the complexity of the model, which increases in each analysis step). Numerical examples demonstrate the accuracy and the computational complexity of the proposed approximate analysis method.

KW - Joint moment

KW - MAP/MAP/1 queue

KW - Markov arrival process

KW - Matrix-geometric method

KW - Queueing network

UR - http://www.scopus.com/inward/record.url?scp=56649116053&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56649116053&partnerID=8YFLogxK

U2 - 10.1109/QEST.2008.26

DO - 10.1109/QEST.2008.26

M3 - Conference contribution

SN - 9780769533605

SP - 125

EP - 134

BT - Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008

ER -