• 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.

• ETRI Journal
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• 제30권3호
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• pp.492-494
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• 2008

While the retrial phenomenon plays an important role in communication networks and should not be ignored, retrial systems do not present an exact analytic solution, so approximate techniques are required. To the best of our knowledge, all the existing techniques are based on computing the steady states probabilities. We propose another approach based on the relative state values which appear in the Howard equations. The results of the numerical evaluation carried out show that this solution outperforms previous approaches in terms of both accuracy and computation time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권4호
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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.