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

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

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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title = "Extension of the loss probability formula to an overloaded queue with impatient customers",

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.",

keywords = "Girsanov-type change of measure, Impatient customers, Loss probability",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: We are very grateful to professor Henk Tijms for providing us with the idea that inspired us to write this paper. B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831 ). J. Kim{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A4A01003813 ). Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

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doi = "10.1016/j.spl.2017.10.007",

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AU - Kim, Jeongsim

N1 - Funding Information: We are very grateful to professor Henk Tijms for providing us with the idea that inspired us to write this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A4A01003813 ). Publisher Copyright: © 2017 Elsevier B.V.

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N2 - 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.

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

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DO - 10.1016/j.spl.2017.10.007

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EP - 62

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -

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

Abstract

Keywords

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