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Transient properties of many-server queues and related QBDs

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Author

Summary, in English

The time tau(n) of first passage from queue length x to queue lengthn > x in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.

Publishing year

2004

Language

English

Pages

249-270

Publication/Series

Queueing Systems

Volume

46

Issue

3-4

Document type

Journal article

Publisher

Springer

Topic

  • Probability Theory and Statistics

Keywords

  • Levy process
  • transform
  • Laplace
  • Kella-Whitt martingale
  • heterogeneous servers
  • passage problem
  • first
  • exponential martingale
  • birth-death process
  • buffer overflow
  • MMM/MMM/c queue
  • Markov additive process
  • optional stopping

Status

Published

ISBN/ISSN/Other

  • ISSN: 0257-0130