延迟多重休假离散时间的Geomx/G/1可修排队系统---一些排队指标

Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (2): 546-558.

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The Discrete Time Geom^x/G/1 Repairable Queueing System with Delay Multiple Vacations---Some Queueing Indices

TANG Ying-Hui¹, YU Miao-Miao^1,2, LI Cai-Liang³, HUANG Shu-Juan⁴, YUN Xi⁴

1.School of Mathematics &|Software Science, Sichuan Normal University, Chengdu 610066|2.School of Science, Sichuan University of Science and Engineering, Sichuan |Zigong 643000|3.Department of Information and Computer Science, Chengdu Electro-mechanical College, Chengdu 610032|4.School of Mathematics, University of Electronic Science &|Technology of China, Chengdu 610054

Received:2008-09-25 Revised:2010-12-13 Online:2011-04-25 Published:2011-04-25
Supported by:
国家自然科学基金(70871084)、教育部高校博士点专项研究基金(200806360001)和四川省教育厅自然科学基金(08ZC028)资助

Abstract

Abstract:

This paper firstly considers the discrete time Geom^x/G/1 repairable queue system with delay multiple vacations. It's assumed that both the inter-arrival times and the life of the service station are independent random variables with geometric distribution, while the service time, the delayed vacation time, the vacation time and the repair time have general discrete distribution. By introducing the server busy period and using the total probability decomposition technique we discuss the transient properties of the queue length from the beginning of any initial state i~(i=0,1,…), and obtain the z-transformation of the transient distribution of the queue length. Furthermore, we obtain the recursion expressions of the steady distribution and the stochastic decomposition of the queue length at a random point in equilibrium. Especially we can obtain some corresponding results of the discrete queue system under some special cases.

Key words: Discrete time queue, Geom^x/G/1, Repairable, Transient distribution, Steady distribution, Stochastic
decomposition

CLC Number:

60K25

TANG Ying-Hui, YU Miao-Miao, LI Cai-Liang, HUANG Shu-Juan, YUN Xi. The Discrete Time Geom^x/G/1 Repairable Queueing System with Delay Multiple Vacations---Some Queueing Indices[J].Acta mathematica scientia,Series A, 2011, 31(2): 546-558.

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The Discrete Time Geom^x/G/1 Repairable Queueing System with Delay Multiple Vacations---Some Queueing Indices

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The Discrete Time Geomx/G/1 Repairable Queueing System with Delay Multiple Vacations---Some Queueing Indices

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The Discrete Time Geom^x/G/1 Repairable Queueing System with Delay Multiple Vacations---Some Queueing Indices