• Title, Summary, Keyword: multi-server retrial queue

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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.

STOCHASTIC ORDERS IN RETRIAL QUEUES AND THEIR APPLICATIONS

  • Shin Yang Woo
    • Proceedings of the Korean Statistical Society Conference
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    • pp.105-108
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    • 2000
  • We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes (C(t), N(t)) representing the number of customers C(t) in the service facility and N(t) one in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. Some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

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Stochastic Comparisons of Markovian Retrial Queues

  • Shin, Yang-Woo;Kim, Yeong-Cheol
    • Journal of the Korean Statistical Society
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    • v.29 no.4
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    • pp.473-488
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    • 2000
  • We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes(C(t), N(t)) representing the number of customers C(t) in the service facility and one N(t) in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

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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.

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.