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^*

^*Corresponding author for this work

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

3 Citations (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

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

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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10.1016/j.spl.2017.10.007

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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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AU - Kim, Jeongsim

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AB - 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.

KW - Girsanov-type change of measure

KW - Impatient customers

KW - Loss probability

UR - https://www.scopus.com/pages/publications/85034592459

U2 - 10.1016/j.spl.2017.10.007

DO - 10.1016/j.spl.2017.10.007

M3 - Article

AN - SCOPUS:85034592459

SN - 0167-7152

VL - 134

SP - 54

EP - 62

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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