• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.147-154
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• 2013

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.691-712
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• 1998

We consider an M$_1$, M$_2$/G/1/ K retrial queueing system with a finite priority queue for type I calls and infinite retrial group for type II calls where blocked type I calls may join the retrial group. These models, for example, can be applied to cellular mobile communication system where handoff calls have higher priority than originating calls. In this paper we apply the supplementary variable method where supplementary variable is the elapsed service time of the call in service. We find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form and give some performance measures of the system.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.259-266
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• 2009

We consider an M/G/1 feedback retrial queue with Bernoulli schedule in which after being served each customer either joins the retrial group again or departs the system permanently. Using the supplementary variable method, we obtain the joint generating function of the numbers of customers in two groups.

• 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 applied mathematics & informatics
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• v.5 no.3
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• pp.827-837
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• 1998

We consider the M/G/1 queue with instantaneous feed-back. The probabilities of feedback are determined by the state of the underlaying Markov chain. by using the supplementary variable method we derive the generating function of the number of customers in the system. In the analysis it is required to calculate the matrix equations. To solve the matrix equations we use the notion of Ex-tended Laplace Transform.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.805-814
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• 1999

We consider an MMPP/G/1/K finite queue with two-level threshold overload control. This model has frequently arisen in the design of the integrated communication systems which support a wide range applications having various Quality of Service(QoS) requirements. Through the supplementary variable method, se derive the queue length distribution.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.5
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• pp.304-313
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• 2016

This work suggests a new analysis approach for a discrete-time GI/G/1 queue with multiple vacations. The method used is called a modified supplementary variable technique and our result is an exact transform-free expression for the steady state queue length distribution. Utilizing this result, we propose a simple two-moment approximation for the queue length distribution. From this, approximations for the mean queue length and the probabilities of the number of customers in the system are also obtained. To evaluate the approximations, we conduct numerical experiments which show that our approximations are remarkably simple yet provide fairly good performance, especially for a Bernoulli arrival process.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.1-12
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• 1998

We consider G/M/1 queues with multiple vacation disci-pline where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vaca-tion time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.325-332
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• 2002

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.11-17
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• 2001

We consider the M/G/1 with Bernoulli feedback, where the served customers wait in the feedback queue for rework with probability p. It is important to decide the moment of dispatching in feedback systems because of the dispatching cost for rework. Up to date, researches have analyzed for the instantaneous-dispatching model or the case that dispatching epoch is determined by the state of feedback queue. In this paper we deal with a dispatching model whose dispatching epoch depends on main queue. We adopt supplementary variable method for our model and a numerical example is given for clarity.