带有优先权、不耐烦顾客及负顾客的$M_1,M_2/G_1,G_2/1$可修重试排队系统

梁玉哲; 王金亭; 齐英

doi:10.12341/jssms08416

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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 750-760. DOI: 10.12341/jssms08416

论文

带有优先权、不耐烦顾客及负顾客的 $M_{1}, M_{2} / G_{1}, G_{2} / 1$ 可修重试排队系统

梁玉哲(1), 王金亭(1), 齐英(3)

作者信息 +

Repairable $M_{1}, M_{2} / G_{1}, G_{2} / 1$ Retrial Queues with Priority Customers, Impatient Subscribers and Negative Arrivals

LIANG Yuzhe(1), WANG Jinting(2), QI Ying(3)

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文章历史 +

摘要

研究了带有优先权、不耐烦顾客及负顾客的

M_{1}, M_{2} / G_{1}, G_{2} / 1

可修重试排队系统.假设两类顾客的优先级不同且各自的到达过程分别服从独立的泊松过程.有优先权的顾客到达系统时如服务器忙,则以概率

H_{1}

排队等候服务,以概率

1 - H_{1}

离开系统;而没有优先权的顾客只能一定的概率进入Orbit中进行重试,直到重试成功.此外,假设有服从Poisson过程的负顾客到达:当负顾客到达系统时,若发现服务台忙,将带走正在接受服务的顾客并使机器处于修理状态;若服务台空闲或已经处于失效状态,则负顾客立即消失,对系统没有任何影响.应用补充变量及母函数法给出了该模型的系统指标稳态解的拉氏变换表达式,并得到了此模型主要的排队指标及可靠性指标.

Abstract

M_{1}, M_{2} / G_{1}, G_{2} / 1

retrial queuing system is presented with two types of customers: priority and non-priority customers, which arrive according to independent Poisson flows. The influence of impatient subscribers on system is
also considered. In the case of blocking the first type customers can be queued with probability

H_{1}

whereas the second type customers must leave the service area but return after some random period of time with probability

H_{1}

to try again. Moreover, the influence on the arrival of negative customers may lead to server breakdown. By using Supplementary Variable Method, a steady state solution for queuing measures is obtained.

导出引用

梁玉哲 , 王金亭 , 齐英. 带有优先权、不耐烦顾客及负顾客的

M_{1}, M_{2} / G_{1}, G_{2} / 1

可修重试排队系统. 系统科学与数学, 2009, 29(6): 750-760. https://doi.org/10.12341/jssms08416

LIANG Yuzhe , WANG Jinting , QI Ying. Repairable

M_{1}, M_{2} / G_{1}, G_{2} / 1

Retrial Queues with Priority Customers, Impatient Subscribers and Negative Arrivals. Journal of Systems Science and Mathematical Sciences, 2009, 29(6): 750-760 https://doi.org/10.12341/jssms08416

中图分类号： 60K25 90B22

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收稿日期	修回日期	出版日期
2007-09-27	2008-09-21	2009-06-25
发布日期
2009-06-25

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