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

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

Access to Document

10.1016/j.spl.2017.10.007

Cite this

@article{8da74d15f5dc43dfb75f52f4d705e1a1,

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 = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = mar,

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

language = "English",

volume = "134",

pages = "54--62",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Extension of the loss probability formula to an overloaded queue with impatient customers

AU - Kim, Bara

AU - Kim, Jeongsim

PY - 2018/3

Y1 - 2018/3

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

UR - http://www.scopus.com/inward/record.url?scp=85034592459&partnerID=8YFLogxK

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

Access to Document

Other files and links

Fingerprint

Cite this