• Title/Summary/Keyword: M/G/1 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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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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AN APPROXIMATION FOR THE DISTRIBUTION OF THE NUMBER OF RETRYING CUSTOMERS IN AN M/G/1 RETRIAL QUEUE

  • Kim, Jeongsim;Kim, Jerim
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.405-411
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    • 2014
  • Queueing systems with retrials are widely used to model many problems in call centers, telecommunication networks, and in daily life. We present a very accurate but simple approximate formula for the distribution of the number of retrying customers in the M/G/1 retrial queue.

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

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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BUSY PERIOD DISTRIBUTION OF A BATCH ARRIVAL RETRIAL QUEUE

  • Kim, Jeongsim
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.425-433
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    • 2017
  • This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.