### 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 |
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Pages (from-to) | 54-62 |

Number of pages | 9 |

Journal | Statistics and Probability Letters |

Volume | 134 |

DOIs | |

Publication status | Published - 2018 Mar 1 |

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### 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.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 134, pp. 54-62. https://doi.org/10.1016/j.spl.2017.10.007

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TY - JOUR

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

AU - Kim, Bara

AU - Kim, Jeongsim

PY - 2018/3/1

Y1 - 2018/3/1

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

UR - http://www.scopus.com/inward/citedby.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

VL - 134

SP - 54

EP - 62

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -