Sample-path large deviations for generalized processor sharing queues with Gaussian inputs

M.R.H. Mandjes, Miranda van Uitert

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Abstract

In this paper we consider the generalized processor sharing (GPS) mechanism serving two traffic classes. These classes consist of a large number of independent identically distributed Gaussian flows with stationary increments. We are interested in the logarithmic asymptotics or exponential decay rates of the overflow probabilities. We first derive both an upper and a lower bound on the overflow probability. Scaling both the buffer sizes of the queues and the service rate with the number of sources, we apply Schilder’s sample-path large deviations theorem to calculate the logarithmic asymptotics of the upper and lower bound. We discuss in detail the conditions under which the upper and lower bound match. Finally we show that our results can be used to choose the values of the GPS weights. The results are illustrated by numerical examples.
Original languageUndefined
Pages (from-to)225-256
JournalPerformance evaluation
Volume61
Issue number2-3
DOIs
Publication statusPublished - 2005

Keywords

  • IR-77399
  • Differentiated services
  • Schilder’s theorem
  • Many-sources asymptotics
  • Gaussian traffic
  • Sample-path large deviations
  • Weight setting
  • Generalized processor sharing
  • Communication networks

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