在第二类故障期间以概率p进入的M/G/1可修排队系统

Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (6): 1149-1157.

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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

Abstract

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

CLC Number:

60K25

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

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