Extension of the loss probability formula to an overloaded queue with impatient customers

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticle

Abstract

We consider a batch arrival MX∕G∕1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard MX∕G∕1 queue with no impatience. But this expression is only applicable when the offered load ρ is less than 1. We give a formula for the loss probability applicable for any values of ρ>0, by proving that the loss probability is analytic in ρ on (0,∞) through a Girsanov-type change of measure.

Original languageEnglish
Pages (from-to)54-62
Number of pages9
JournalStatistics and Probability Letters
Volume134
DOIs
Publication statusPublished - 2018 Mar 1

Fingerprint

Loss Probability
Queue
Customers
Batch Arrivals
Change of Measure
Waiting Time Distribution
Stationary Distribution

Keywords

  • Girsanov-type change of measure
  • Impatient customers
  • Loss probability

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Extension of the loss probability formula to an overloaded queue with impatient customers. / Kim, Bara; Kim, Jeongsim.

In: Statistics and Probability Letters, Vol. 134, 01.03.2018, p. 54-62.

Research output: Contribution to journalArticle

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