On queues with service and interarrival times depending on waiting times

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19 Citations (Scopus)

Abstract

We consider an extension of the standard G/G/1 queue, described by the equation , where P[Y=1]=p and 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: Theory and Applications
Volume56
Issue number3-4
DOIs
Publication statusPublished - 2007

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