• 충청수학회지
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• 제29권1호
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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.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.173-196
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• 2021

This paper treats a retrial queue with phase type retrial times and a threshold type-policy, where each server is subject to breakdowns and repairs. Upon a server failure, the customer whose service gets interrupted will be handed over to another available server, if any; otherwise, the customer may opt to join the retrial orbit or depart from the system according to a Bernoulli trial. We analyze such a multi-server retrial queue using the recently introduced threshold-based retrial times for orbiting customers. Applying the matrix-analytic method, we carry out the steady-state analysis and report a few illustrative numerical examples.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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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.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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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.

• Journal of the Korean Statistical Society
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• 제29권4호
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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.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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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.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.601-616
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• 2021

Retrial queueing models have been studied extensively in the literature. These have many practical applications, especially in service sectors. However, retrial queueing models have their own limitations. Typically, analyzing such models involve level-dependent quasi-birth-and-death processes, and hence some form of a truncation or an approximate method or simulation approach is needed to study in steady-state. Secondly, in general, the customers are not served on a first-come-first-served basis. The latter is the case when a new arrival may find a free server while prior arrivals are waiting in the retrial orbit due to the servers being busy during their arrivals. In this paper, we take a different approach to the study of multi-server retrial queues in which the signals are generated in such a way to provide a reasonably fair treatment to all the customers seeking service. Further, this approach makes the study to be level-independent quasi-birth-and-death process. This approach is different from any considered in the literature. Using matrix-analytic methods we analyze MAP/M/c-type retrial queueing models along with Poisson signals in steady-state. Illustrative numerical examples including a comparison with previously published retrial queues are presented and they show marked improvements in providing a quality of service to the customers.

• 대한산업공학회지
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• 제37권2호
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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.