• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.287-299
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• 2007

We consider a multiclass queue where queued customers are served in their order of arrival at a rate which depends on the customer type. By using the asymptotic results obtained by Dabrowski et al. (2006) we calculate the sharp asymptotics of the stationary distribution of the number of customers of each class in the system and the distribution of the number of customers of each class when the total number of customers reaches a high level before emptying. We also obtain a fast simulation algorithm to estimate the overflow probability and compare it with the general simulation and asymptotic results.

• Management Science and Financial Engineering
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• v.2 no.1
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• pp.123-145
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• 1996

We consider a priority-based multiclass queue with probabilistic feed-back. There are J service stations. Each customer belongs to one of the several priority classes, and the customers of each class arrive at each station in a Poisson process. A single server serves queued customers on a priority basis with a nonpreemptive scheduling discipline. The customers who complete their services feed back to the system instantaneously and join one of the queues of the stations or depart from the system according to a given probability. In this paper, we propose a new method to simplify the analysis of these queueing systems. By the analysis of busy periods and regenerative processes, we clarify the underlying system structure, and systematically obtain the mean for the sojourn time, i.e., the time from the arrival to the departure from the system, of a customer at every station. The mean for the number of customers queued in each station at an arbitrary time is also obtained simultaneously.

• 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.

• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.747-757
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• 2010

This paper studies the Markov modeling of multiclass loss systems supporting several kinds of customers. The concept of unit for loss systems is introduced and the method of equal probability allocation among units is especially considered. Equilibrium equations and limiting distribution of the loss systems are studied and loss probabilities are computed. We analyze an example of a simple system to gain an insight about general systems.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.261-264
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• 2000

When there ate several classes of customers demanding service times with different distributions at some stations of a queueing network, the stability problem becomes suddenly complicated compared with the single class case. Recently many researchers had tried to find some kind of stability conditions for multiclass queueing networks, but did not get significant results except in very limited 2-station cases. In this study, we try to develop some dynamic control techniques which can guarantee the stability under the nominal traffic condition. Our approach includes the randomization method and the leaky bucket control scheme. Also, we mention other possibilities such as the discrete-review approach and the generalized round-robin technique. Both theoretical and experimental results will be presented.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.2
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• pp.267-288
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• 1995

We investigate a multiclass priority system with a mixed service discipline, and propose a new approach to the analysis of performance measures (mean waiting times) of the system. Customers are preferentially served in the order of priority. The service discipline at each station is either gated or exhaustive discipline. We formulate mean waiting times as functions on the state of the system. We first consider the system at an arbitrary system state to obtain explicit formulae for the mean waiting times, and then derive their steady state values by using the property of Poisson arrivals to see time averages and the generalized Little's formula.