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Stationary Analysis and Optimal Control Under multiple working Vacation Policy in a GI/Ma,b/1 Queue

Journal of Systems Science & Complexity 2018年第4期31卷 1003-1023页

作者： PANDA Gopinath BANIK Abhijit Datta GUHA Dibyajyoti School of Mathematical Sciences National Institute of Science Education and Research Bhubaneswar-752050 India School of Basic Sciences Indian Institute of Technology Bhubaneswar-752050 India International Management Institute Kolkata-700027 India

This paper considers an infinite buffer renewal input queue with multiple working vacation policy wherein customers are served by a single server according to general bulk service （a,b）-rule （1 ≤ a ≤ b）. If the number of waiting customers in the system at a service completion epoch （during a normal busy period） is lower than ＇a＇, then the server starts a vacation. During a vacation if the number of waiting customers reaches the minimum threshold size ＇a＇, then the server starts serving this batch with a lower rate than that of the normal busy period. After completion of a batch service during working vacation, if the server finds less than takes another vacation, otherwise the server rate. The maximum allowed size of a batch a＇ customers accumulated in the system, then the server continues to serve the available batch with that lower in service is ＇b＇. The authors derive both queue-length and system-length distributions at pre-arrival epoch using both embedded Markov chain approach and the roots method. The arbitrary epoch probabilities are obtained using the classical argument based on renewal theory. Several performance measures like average queue and system-length, mean waiting-time, cost and profit optimization are studied and numerically computed.

关键词： Bulk service cost optimization mean idle period multiple working vacations roots method system-length

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维普期刊数据库

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THE BULK INPUT M~[X]/M/1 QUEUE WITH working vacations

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Journal of Systems Science and Systems Engineering 2009年第3期18卷 358-368页

作者： Xiu-li XU Ming-xin LIU Xiao-hua ZHAO College of Science Yanshan University Qinhuangdao 066004 Hebei China College of Information Science and Engineering Yanshan University Qinhuangdao 066004 Hebei China

In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.

关键词： M^[X]/M/1 queue bulk input multiple working vacations stochastic decomposition the Laplace transform order

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维普期刊数据库

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The M/M/1 Queue with Bernoulli Feedback under multiple working Vacation Policy

The M/M/1 Queue with Bernoulli Feedback under Multiple Worki...

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第五届中国不确定系统年会

作者： Shunli Yang Naishuo Tian Yanshan University College of Science Hebei Qinhuangdao,066004,China

＜正＞Consider an M/M/1 queue with Bernoulli feedback under multiple working vacation *** server works at a lower rate rather than com- pletely stopping during a vacation *** quasi- birth-and-death process and matrix-geometric so- lution method,we gain concise expressions of the steady-state distributions for queue length and con- ditional response time which have intuitive proba- bilistic ***,we get the stochastic de- composition structure of queue length in the station- ary state and the distribution for additional queue ***,we indicate the equation that LST of regular busy period satisfies,the expectation of regular busy period,bnsy cycle and global working vacation.

关键词： Bernoulli feedback multiple working vacations Stochastic decomposition property Quasi birth-death process and matrix-geometric solution Regular busy period

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