On queues with service and interarrival times depending on waiting times

Onno J. Boxma, Maria Vlasiou

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)
1 Downloads (Pure)

Abstract

We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, B-A+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for $p=0$ it describes the waiting time of the server in an alternating service model. For all other values of $p$ this model describes a FCFS queue in which the service times and interarrival times depend linearly and randomly on the waiting times. We derive the distribution of $W$ when $A$ is generally distributed and $B$ follows a phase-type distribution, and when $A$ is exponentially distributed and $B$ deterministic.
Original languageEnglish
Pages (from-to)121-132
JournalQueueing systems
Volume56
DOIs
Publication statusPublished - 20 Mar 2007
Externally publishedYes

Keywords

  • math.PR
  • 60K25

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