在第二类故障期间以概率p进入的M/G/1可修排队系统

数学物理学报 ›› 2012, Vol. 32 ›› Issue (6): 1149-1157.

在第二类故障期间以概率p进入的M/G/1可修排队系统

李才良¹, 唐应辉², 牟永聪², 余玅妙³

1.成都工业学院信息与计算科学系成都 610031;
2.四川师范大学数学与软件科学学院成都 610066;
3.四川理工学院理学院四川自贡 643000

收稿日期:2010-12-21 修回日期:2012-03-27 出版日期:2012-12-25 发布日期:2012-12-25
基金资助:
国家自然科学基金(71171138, 70871084)和教育部高校博士点专项基金(200806360001)资助

M/G/1Repairable Queueing System with p-Entering Discipline During Second Type Failure Times

LI Cai-Liang¹, TANG Ying-Hui², MU Yong-Cong², YU Miao-Miao³

1.Department of Information &|Computer Science, Chengdu Technological University, Chengdu 610031;
2.School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066;
3.School of Science, Sichuan University of Science &|Engineering, Sichuan Zigong 643000

Received:2010-12-21 Revised:2012-03-27 Online:2012-12-25 Published:2012-12-25
Supported by:
国家自然科学基金(71171138, 70871084)和教育部高校博士点专项基金(200806360001)资助

摘要/Abstract

摘要：

在研究的M/G/1可修系统中, 假设服务台在忙期和闲期内都可能发生故障, 且具有不同的故障率, 并且在闲期的故障状态期间到达顾客以概率
p(0≤p≤1)进入系统. 使用全概率分解技术和利用拉普拉斯变换、母函数等工具, 研究了系统的瞬态队长分布和稳态队长分布, 获得一系列结果,
并且讨论了p=0和p=1等特殊情况.

关键词: 可修排队系统, 故障, p -进入规则, 队长分布, 全概率分解

Abstract:

This paper considers the M/G/1 repairable queueing system in which the service station may fail and have different failure rates during its busy and idle periods. While the customers who arrive during second type failure times enter the system with probability p(0≤p≤1). By using the total probability decomposition, Laplace transform and generating function, both the transient distribution and steady distribution of the queue size are directly studies, and some important results are obtained. At last, some special cases, such as p=0, p=1, and so on, are also discussed.

Key words: Repairable queueing system, Breakdown, p-entering discipline, Queue-length distribution, Total probability decomposition

中图分类号:

60K25

李才良, 唐应辉, 牟永聪, 余玅妙. 在第二类故障期间以概率p进入的M/G/1可修排队系统[J]. 数学物理学报, 2012, 32(6): 1149-1157.

LI Cai-Liang, TANG Ying-Hui, MU Yong-Cong, YU Miao-Miao. M/G/1Repairable Queueing System with p-Entering Discipline During Second Type Failure Times[J]. Acta mathematica scientia,Series A, 2012, 32(6): 1149-1157.

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