• Title, Summary, Keyword: retrial time

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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.

DIMENSION REDUCTION FOR APPROXIMATION OF ADVANCED RETRIAL QUEUES : TUTORIAL AND REVIEW

  • SHIN, YANG WOO
    • Journal of applied mathematics & informatics
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    • v.35 no.5_6
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    • pp.623-649
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    • 2017
  • Retrial queues have been widely used to model the many practical situations arising from telephone systems, telecommunication networks and call centers. An approximation method for a simple Markovian retrial queue by reducing the two dimensional problem to one dimensional problem was presented by Fredericks and Reisner in 1979. The method seems to be a promising approach to approximate the retrial queues with complex structure, but the method has not been attracted a lot of attention for about thirty years. In this paper, we exposit the method in detail and show the usefulness of the method by presenting the recent results for approximating the retrial queues with complex structure such as multi-server retrial queues with phase type distribution of retrial time, impatient customers with general persistent function and/or multiclass customers, etc.

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.

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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Sensitivity of M/M/c Retrial Queue with Respect to Retrial Times : Experimental Investigation (M/M/c 재시도대기체계에서 재시도시간의 민감성에 대한 실험적 고찰)

  • Shin, Yang-Woo;Moon, Dug-Hee
    • Journal of Korean Institute of Industrial Engineers
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    • v.37 no.2
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    • pp.83-88
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    • 2011
  • The effects of the moments of the retrial time to 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 some performance measures related with the number of customers in orbit can be severely affected by the fourth or higher moments of retrial time.

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.

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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WAITING TIME DISTRIBUTION IN THE M/M/M RETRIAL QUEUE

  • Kim, Jeongsim;Kim, Jerim
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1659-1671
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    • 2013
  • In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS

  • SHIN, YANG WOO;MOON, DUG HEE
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.4
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    • pp.443-457
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    • 2015
  • We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.