Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows

Bert Zwart, Sem Borst, Michel Mandjes

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18 Citations (Scopus)
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We consider a fluid queue fed by multiple On–Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant" subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a “minimally critical" set of On–Off flows with regularly varying On periods. In case the dominant set contains just a single On–Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On–Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reduced-load equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios.
Original languageEnglish
Pages (from-to)903-957
Number of pages55
JournalAnnals of applied probability
Issue number2
Publication statusPublished - 2004


  • MSC-90B22
  • reduced-load equivalence
  • MSC-60K25
  • MSC-60F10
  • EWI-17714
  • Fluid models
  • IR-70355
  • Heavy-tailed distributions
  • METIS-220817
  • Queueing Theory
  • Knapsack problem
  • Large deviations


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