Performance evaluation of weighted fair queuing system using matrix geometric method

Amina Al-Sawaai, Irfan Awan, Rod Fretwell

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

2 Citations (Scopus)

Abstract

This paper analyses a multiple class single server M/M/1/K queue with finite capacity under weighted fair queuing (WFQ) discipline. The Poisson process has been used to model the multiple classes of arrival streams. The service times have exponential distribution. We assume each class is assigned a virtual queue and incoming jobs enter the virtual queue related to their class and served in FIFO order.We model our system as a two dimensional Markov chain and use the matrix-geometric method to solve its stationary probabilities. This paper presents a matrix geometric solution to the M/M/1/K queue with finite buffer under (WFQ) service. In addition, the paper shows the state transition diagram of the Markov chain and presents the state balance equations, from which the stationary queue length distribution and other measures of interest can be obtained. Numerical experiments corroborating the theoretical results are also offered.

Original languageEnglish
Title of host publicationNETWORKING 2009 - 8th International IFIP-TC 6 Networking Conference, Proceedings
Pages66-78
Number of pages13
Volume5550 LNCS
DOIs
Publication statusPublished - 2009
Event8th International IFIP-TC 6 Networking Conference, NETWORKING 2009 - Aachen, Germany
Duration: May 11 2009May 15 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5550 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th International IFIP-TC 6 Networking Conference, NETWORKING 2009
CountryGermany
CityAachen
Period5/11/095/15/09

Fingerprint

Matrix-geometric Method
Queuing System
Markov processes
Queue
Performance Evaluation
Queuing
Markov chain
Matrix-geometric Solution
Servers
Queue Length Distribution
Finite Buffer
Finite Capacity
Single Server
Balance Equations
State Equation
State Transition
Stationary Distribution
Exponential distribution
Poisson process
Diagram

Keywords

  • First inter first out (FIFO)
  • Markov chain
  • Weighted fair queuing (WFQ)

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Al-Sawaai, A., Awan, I., & Fretwell, R. (2009). Performance evaluation of weighted fair queuing system using matrix geometric method. In NETWORKING 2009 - 8th International IFIP-TC 6 Networking Conference, Proceedings (Vol. 5550 LNCS, pp. 66-78). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5550 LNCS). https://doi.org/10.1007/978-3-642-01399-7_6

Performance evaluation of weighted fair queuing system using matrix geometric method. / Al-Sawaai, Amina; Awan, Irfan; Fretwell, Rod.

NETWORKING 2009 - 8th International IFIP-TC 6 Networking Conference, Proceedings. Vol. 5550 LNCS 2009. p. 66-78 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5550 LNCS).

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

Al-Sawaai, A, Awan, I & Fretwell, R 2009, Performance evaluation of weighted fair queuing system using matrix geometric method. in NETWORKING 2009 - 8th International IFIP-TC 6 Networking Conference, Proceedings. vol. 5550 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5550 LNCS, pp. 66-78, 8th International IFIP-TC 6 Networking Conference, NETWORKING 2009, Aachen, Germany, 5/11/09. https://doi.org/10.1007/978-3-642-01399-7_6
Al-Sawaai A, Awan I, Fretwell R. Performance evaluation of weighted fair queuing system using matrix geometric method. In NETWORKING 2009 - 8th International IFIP-TC 6 Networking Conference, Proceedings. Vol. 5550 LNCS. 2009. p. 66-78. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-01399-7_6
Al-Sawaai, Amina ; Awan, Irfan ; Fretwell, Rod. / Performance evaluation of weighted fair queuing system using matrix geometric method. NETWORKING 2009 - 8th International IFIP-TC 6 Networking Conference, Proceedings. Vol. 5550 LNCS 2009. pp. 66-78 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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