Analysis of a single server queue interacting with a fluid reservoir

I.J.B.F. Adan, Erik A. van Doorn, J.A.C. Resing, Willem R.W. Scheinhardt

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)

Abstract

We consider a single-server queueing system with Poisson arrivals in which the speed of the server depends on whether an associated fluid reservoir is empty or not. Conversely, the rate of change of the content of the reservoir is determined by the state of the queueing system, since the reservoir fills during idle periods and depletes during busy periods of the server. Our interest focuses on the stationary joint distribution of the number of customers in the system and the content of the fluid reservoir, from which various performance measures such as the steady-state sojourn time distribution of a customer may be obtained. We study two variants of the system. For the first, in which the fluid reservoir is infinitely large, we present an exact analysis. The variant in which the fluid reservoir is finite, is analysed approximatively through a discretization technique. The system may serve as a mathematical model for a traffic regulation mechanism -- a two-level traffic shaper -- at the edge of an ATM network, regulating a very bursty source. We present some numerical results showing the effect of the mechanism.
Original languageUndefined
Pages (from-to)313-336
Number of pages22
JournalQueueing systems
Volume29
Issue number2-4
DOIs
Publication statusPublished - 1998

Keywords

  • Single-server queue
  • traffic regulator
  • METIS-140559
  • IR-62351
  • Fluid queue
  • EWI-12855

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