• Title, Summary, Keyword: retrial queue

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Approximation of M/G/c Retrial Queue with M/PH/c Retrial Queue

  • Shin, Yang-Woo;Moon, Dug-Hee
    • Communications for Statistical Applications and Methods
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    • v.19 no.1
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    • pp.169-175
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    • 2012
  • The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The service time distribution is fitted with phase type(PH) distribution by matching the first three moments of service time and the M/G/c retrial queue is approximated by the M/PH/c retrial queue. Approximations are compared with the simulation results.

TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN MX/G/1 RETRIAL QUEUE

  • KIM, JEONGSIM
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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    • pp.343-350
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    • 2015
  • We consider an MX/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the MX/G/1 retrial queue.

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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AN APPROXIMATION FOR THE QUEUE LENGTH DISTRIBUTION IN A MULTI-SERVER RETRIAL QUEUE

  • Kim, Jeongsim
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.1
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    • pp.95-102
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    • 2016
  • Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.

ALGORITHMIC SOLUTION FOR M/M/c RETRIAL QUEUE WITH $PH_2$-RETRIAL TIMES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.803-811
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    • 2011
  • We present an algorithmic solution for the stationary distribution of the M/M/c retrial queue in which the retrial times of each customer in orbit are of phase type distribution of order 2. The system is modeled by the level dependent quasi-birth-and-death (LDQBD) process.

ON APPROXIMATIONS FOR GI/G/c RETRIAL QUEUES

  • Shin, Yang Woo;Moon, Dug Hee
    • Journal of applied mathematics & informatics
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    • v.31 no.1_2
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    • pp.311-325
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    • 2013
  • The effects of the moments of the interarrival time and service time on the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility and orbit are numerically investigated. The results reveal the performance measures are more sensitive with respect to the interarrival time than the service time. Approximation for $GI/G/c$ retrial queues using $PH/PH/c$ retrial queue is presented.

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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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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INTERPOLATION APPROXIMATION OF $M/G/c/K$ RETRIAL QUEUE WITH ORDINARY QUEUES

  • Shin, Yang-Woo
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.531-540
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    • 2012
  • An approximation for the number of customers at service facility in $M/G/c/K$ retrial queue is provided with the help of the approximations of ordinary $M/G/c/K$ loss system and ordinary $M/G/c$ queue. The interpolation between two ordinary systems is used for the approximation.