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

Bara Kim; Jeongsim Kim

doi:10.1016/j.spl.2017.10.007

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

Bara Kim, Jeongsim Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider a batch arrival M^X∕G∕1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard M^X∕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 language	English
Pages (from-to)	54-62
Number of pages	9
Journal	Statistics and Probability Letters
Volume	134
DOIs	https://doi.org/10.1016/j.spl.2017.10.007
Publication status	Published - 2018 Mar 1

Keywords

Girsanov-type change of measure
Impatient customers
Loss probability

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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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.",

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