Transient properties of many-server queues and related QBDs

S Asmussen, Mats Pihlsgård

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)249-270
JournalQueueing Systems
Volume46
Issue number3-4
DOIs
Publication statusPublished - 2004

Subject classification (UKÄ)

  • Probability Theory and Statistics

Free 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

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