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. This PH/PH/1 multi-threshold queue is modelled 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 languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages15
Publication statusPublished - Sep 2013

Publication series

NameMemorandum
PublisherUniversity of Twente, Department of Applied Mathematics
No.2011
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • EWI-23624
  • PH/PH/1 queue
  • Multiple thresholds
  • Level dependent quasi-birth-and-death process
  • IR-87098
  • METIS-297796
  • Matrix Analytic Methods

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