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Loss rate asymptotics in a GI/G/1 queue with finite buffer

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Author

Summary, in English

We consider the stationary loss rate l(K) of a GI/G/1 queue with finite buffer of size K. Let X-n = U-n - T-n, n >= 1 where U-n is the service time, T-n is the interarrival time and let rho be the traffic intensity. We derive sharp asymptotics for the loss rate as K -> infinity, in the cases (i): rho > 1, and (ii): rho < 1 and X-n non-lattice with light tails. We also look at another reflection, related to Moran's dam model. As an example, we look at the PH/PH/1 case, where we show how to compute the asymptotic loss rate as well as the exact one and illustrate our results numerically.

Publishing year

2005

Language

English

Pages

913-931

Publication/Series

Stochastic Models

Volume

21

Issue

4

Document type

Journal article

Publisher

Taylor & Francis

Topic

  • Probability Theory and Statistics

Keywords

  • random walk
  • phase-type distribution
  • Lundberg's inequality
  • Lundberg equation
  • asymptotics
  • Cramer-Lundberg approximation
  • stationary loss rate
  • reflection

Status

Published

ISBN/ISSN/Other

  • ISSN: 1532-6349