Finite queues at the limit of saturation

Miklós Telek, Miklós Vécsei

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

3 Citations (Scopus)

Abstract

A wide range of real life systems are modeled by queueing systems with finite capacity buffers. There are well established numerical procedures for the analysis of these queueing models when the load islower or higher than the system capacity, but these numerical methods become unstable as the loadgets close to the system capacity. We present simple modifications of the standard computational methodswhich remain numerically stable at saturation as well. We consider two specific Markov models: finite quasi birth death (QBD) processand finite Markov fluid queue (MFQ). The first one describes the behavior of queueing systems with discretebuffer content, while the second one describes the behavior of queueing systems with continuous buffer content. The stationary solution of a finite QBD process is a combination of two matrix geometric serieswhile the stationary fluid density of a finite MFQ is a combination of two matrix exponential functions. Apart of this there are several further similarities between the discrete and continuous buffer modelsat saturation. The proposed solution method exploits the similarities of the models.

Original languageEnglish
Title of host publicationProceedings - 2012 9th International Conference on Quantitative Evaluation of Systems, QEST 2012
Pages33-42
Number of pages10
DOIs
Publication statusPublished - Dec 13 2012
Event2012 9th International Conference on Quantitative Evaluation of Systems, QEST 2012 - London, United Kingdom
Duration: Sep 17 2012Sep 20 2012

Publication series

NameProceedings - 2012 9th International Conference on Quantitative Evaluation of Systems, QEST 2012

Other

Other2012 9th International Conference on Quantitative Evaluation of Systems, QEST 2012
CountryUnited Kingdom
CityLondon
Period9/17/129/20/12

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Keywords

  • Markov fluid model
  • finite quasi birth death processes
  • matrix analytic methods
  • matrix geometric solution

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Telek, M., & Vécsei, M. (2012). Finite queues at the limit of saturation. In Proceedings - 2012 9th International Conference on Quantitative Evaluation of Systems, QEST 2012 (pp. 33-42). [6354631] (Proceedings - 2012 9th International Conference on Quantitative Evaluation of Systems, QEST 2012). https://doi.org/10.1109/QEST.2012.20