A rate balance principle and its application to queueing models

B. Oz, I.J.B.F. Adan, M. Haviv

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
66 Downloads (Pure)

Abstract

We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth-and-death-like transitions, for which it is shown that for any state n, the rate of two consecutive transitions from n- 1 to n+ 1 coincides with the corresponding rate from n+ 1 to n- 1. We demonstrate how useful this observation is by deriving well-known, as well as new, results for non-memoryless queues with state-dependent arrival and service processes. We also use the rate balance principle to derive new results for a state-dependent queue with batch arrivals, which is a model with non-birth-and-death-like transitions.

Original languageEnglish
Pages (from-to)95-111
Number of pages17
JournalQueueing Systems
Volume87
Issue number1-2
DOIs
Publication statusPublished - 1 Oct 2017

Keywords

  • Batch arrivals
  • Birth–death process
  • Conditional distribution
  • G/M/1
  • M/G/1
  • Rate balance
  • Residual lifetime

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