The PH/PH/1 multi-threshold queue

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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.
Original languageEnglish
Title of host publicationAnalytical and Stochastic Modeling Techniques and Applications
Subtitle of host publication21st International Conference, ASMTA 2014, Budapest, Hungary, June 30 – July 2, 2014. Proceedings
EditorsBruno Sericola, Miklós Telek, Gábor Horváth
Place of PublicationCham, Switzerland
PublisherSpringer
Pages95-109
Number of pages15
ISBN (Electronic)978-3-319-08219-6
ISBN (Print)978-3-319-08218-9
DOIs
Publication statusPublished - 2014
Event21st International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2014 - Budapest, Hungary
Duration: 30 Jun 20142 Jul 2014
Conference number: 21

Publication series

NameLecture Notes in Computer Science
PublisherSpringer International Publishing
Volume8499
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Conference on Analytical and Stochastic Modeling Techniques and Applications, ASMTA 2014
Abbreviated titleASMTA
CountryHungary
CityBudapest
Period30/06/142/07/14

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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

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). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-08219-6_7