• Title, Summary, Keyword: supplementary variable method

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THE M/G/1 FEEDBACK RETRIAL QUEUE WITH BERNOULLI SCHEDULE

  • Lee, Yong-Wan;Jang, Young-Ho
    • 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.

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ANALYSIS OF QUEUEING MODEL WITH PRIORITY SCHEDULING BY SUPPLEMENTARY VARIABLE METHOD

  • Choi, Doo Il
    • 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.

THE ${M_1},{M_/2}/G/l/K$ RETRIAL QUEUEING SYSTEMS WITH PRIORITY

  • Choi, Bong-Dae;Zhu, Dong-Bi
    • 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.

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ANALYSIS OF AN MMPP/G/1/K FINITE QUEUE WITH TWO-LEVEL THRESHOLD OVERLOAD CONTROL

  • Lee, Eye-Min;Jeon, Jong-Woo
    • 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.

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THE M/G/1 FEEDBACK RETRIAL QUEUE WITH TWO TYPES OF CUSTOMERS

  • Lee, Yong-Wan
    • 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 ${\delta}_k\;=\;0(k\;=\;1,\;2),\;{\lambda}_1\;=\;0\;or\;{\lambda}_2\;=\;0$.

On the Modified Supplementary Variable Technique for a Discrete-Time GI/G/1 Queue with Multiple Vacations (복수휴가형 이산시간 GI/G/1 대기체계에 대한 수정부가변수법)

  • Lee, Doo Ho
    • 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.

DISCRETE-TIME QUEUE WITH VARIABLE SERVICE CAPACITY

  • LEE YUTAE
    • Journal of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.517-527
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    • 2005
  • This paper considers a discrete-time queueing system with variable service capacity. Using the supplementary variable method and the generating function technique, we compute the joint probability distribution of queue length and remaining service time at an arbitrary slot boundary, and also compute the distribution of the queue length at a departure time.

An Analysis on the M/G/1 Bernoulli Feedback System with Threshold in Main Queue (Main Queue에 Threshold가 있는 M/G/1 Bernoulli Feedback 시스템 분석)

  • Lim, Si-Yeong;Hur, Sun
    • 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.

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MMPP,M/G/1 retrial queue with two classes of customers

  • Han, Dong-Hwan;Lee, Yong-Wan
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.481-493
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    • 1996
  • We consider a retrial queue with two classes of customers where arrivals of class 1(resp. class 2) customers are MMPP and Poisson process, respectively. In the case taht arriving customers are blocked due to the channel being busy, the class 1 customers are queued in priority group and are served as soon as the channel is free, whereas the class 2 customers enter the retrial group in order to try service again after a random amount of time. We consider the following retrial rate control policy, which reduces their retrial rate as more customers join the retrial group; their retrial times are inversely proportional to the number of customers in the retrial group. We find the joint generating function of the numbers of custormers in the two groups by the supplementary variable method.

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MAP/G/1/K QUEUE WITH MULTIPLE THRESHOLDS ON BUFFER

  • Choi, Doo-Il
    • Communications of the Korean Mathematical Society
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    • v.14 no.3
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    • pp.611-625
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    • 1999
  • We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

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