• 대한산업공학회지
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• 제26권3호
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• pp.206-212
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• 2000

We consider the M/M/1/1 retrial queue where the maximum number of retrials is fixed by a constant. We present an efficient approximate procedure for mean performance measures and the loss probability. The approximate results are satisfactory when compared with simulation results.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1155-1171
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• 2023

This paper investigates a non Markovian M/G/1 queue with retrial policy, different kind of service rates as well as unsatisfied clients which is inspired by an example of a transmission medium access control in wireless communications. The server tends to work continuously until it finds at least one client in the system. The server will begin its maintenance tasks after serving all of the clients and if the system becomes empty. Provisioning periods in regular working periods and maintenance service periods should be evenly divided. Using supplementary variable technique, the amount of clients in the system as well as in the orbit were found. Further few performance measures of the system were demonstrated numerically.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.389-405
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• 2007

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability ${\gamma}$ and with probability $1-{\gamma}$ leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability ${\delta}\;(<\;1)$ and with probability $1-{\delta}$ leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

• 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.