AN M/M/1 Queue in random environment with disasters

Noam Paz, Uri Yechiali

Research output: Contribution to journalArticlepeer-review

Abstract

We study a M/M/1 queue in a multi-phase random environment, where the system occasionally suffers a disastrous failure, causing all present jobs to be lost. The system then moves to a repair phase. As soon as the system is repaired, it moves to phase i with probability qi ≥ 0. We use two methods of analysis to study the probabilistic behavior of the system in steady state: (i) via probability generating functions, and (ii) via matrix geometric approach. Due to the special structure of the Markov process describing the disaster model, both methods lead to explicit results, which are related to each other. We derive various performance measures such as mean queue sizes, mean waiting times, and fraction of lost customers. Two special cases are further discussed.

Original languageEnglish
Article number1450016
JournalAsia-Pacific Journal of Operational Research
Volume31
Issue number3
DOIs
StatePublished - Jun 2014

Keywords

  • M/M/1 queue
  • disasters
  • generating functions
  • lost customers
  • matrix geometric
  • random environment

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