• Journal of Korean Institute of Industrial Engineers
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• v.26 no.3
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• pp.283-288
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• 2000

We present several alternative expressions for the decomposition property of the M/G/1 queue with generalized vacations so that a user can choose the most convenient expression for his/her own purpose.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.295-300
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• 2004

We consider a G/M/1 queue with two-stage service policy. The server starts to serve with rate of ${\mu}1$ customers per unit time until the number of customers in the system reaches A. At this moment, the service rate is changed to that of ${\mu}2$ customers per unit time and this rate continues until the system is empty. We obtain the stationary distribution of the number of customers in the system.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.309-320
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• 1999

Models of single-server queues with vacations have been widely used to study the performance of many computer communi-cation and production systems. In this paper we analyze an M/G/1 queue with generalized vacations and exhaustive service. This sys-tem has been shown to possess a stochastic decomposition property. That is the customer waiting time in this system is distributed as the sum of the waiting time in a regular M/G/1 queue with no va-cations and the additional delay due to vacations. Herein a general formula for the additional delay is derived for a wide class of vacation policies. The formula is also extended to cases with multiple types of vacations. Using these new formulas existing results for certain vacation models are easily re-derived and unified.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.875-887
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• 2005

In M/G/1 retrial queueing system with two types of customers and feedback, we derived the joint generating function of the number of customers in two groups by using the supplementary variable method. It is shown that our results are consistent with those already known in the literature when ${\delta}_k\;=\;0(k\;=\;1,\;2),\;{\lambda}_1\;=\;0\;or\;{\lambda}_2\;=\;0$.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.39-45
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• 2001

Maximum and minimum of rendom variables are frequently encountered in the stochastic modelling for various OR problems. We summarize and extend characteristics of maximum and minimum, emphasizing the case in which random variables are independent and all of them except one are distributed exponential. As an application, we derive a transform-free expression for the M/G/1 queue length distribution.

• Journal of the Korean Operations Research and Management Science Society
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• v.41 no.3
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• pp.37-43
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• 2016

This note discusses the inter-loss time ofan M/G/1/1 queuing system. The inter-loss time is defined as the time duration between two consecutive losses of arriving customers. In this study, we present the explicit Laplace transform of the inter-loss time distribution of an M/G/1/1 queuing system.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.943-952
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• 1999

Models of single-server queues with vacation have been widely used to study the performance of many computer communica-tion and production system. In this paper we use the formula for a wide class of vacation policies and multiple types of vacations based on the M/G/1 queue with generalized vacations and exhaustive service. furthermore we derive the waiting times for many complex vacation policies which would otherwise be to analyze. These new results are also applicable to other related queueing models. if they conform with the basic model considered in this paper.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.57-57
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• 1993

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1251-1258
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• 2010

For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al. [1] conjectured that the conditional mean sojourn time is concave. However, Kim and Kim [5] showed that this conjecture is not true in general. In this paper, we show that this conjecture is true if the service times have a hyperexponential distribution.

• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.3
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• pp.1-7
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• 2004

We demonstrate in this paper that the level crossing technique can be applied to such a system that not only the state vector is two-dimensional but Its two components are heterogeneous. As an example system, we use the GI-G/c/K queue whose state vector consists of the number of customers in the system and the total unfinished work.