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

被引：1
|
作者：
Kim, Bara [1 ]
Kim, Jeongsim [2 ]
机构：
[1] Korea Univ, Dept Math, 145 Anam Ro, Seoul 02841, South Korea
[2] Chungbuk Natl Univ, Dept Math Educ, 1 Chungdae Ro, Cheongju 28644, Chungbuk, South Korea
来源：
STATISTICS & PROBABILITY LETTERS | 2018年 / 134卷
基金：
新加坡国家研究基金会;
关键词：
Impatient customers; Loss probability; Girsanov-type change of measure;
D O I：
10.1016/j.spl.2017.10.007
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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 rho is less than 1. We give a formula for the loss probability applicable for any values of rho > 0, by proving that the loss probability is analytic in rho on (0, infinity) through a Girsanov-type change of measure. (C) 2017 Elsevier B.V. All rights reserved.
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页码：54 / 62
页数：9
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