• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.169-175
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• 2012

The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The service time distribution is fitted with phase type(PH) distribution by matching the first three moments of service time and the M/G/c retrial queue is approximated by the M/PH/c retrial queue. Approximations are compared with the simulation results.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.1
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• pp.36-43
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• 2002

We analyze bulk service $M/G^{b}/1$ queues using the arrival time approach of Chae et al. (2001). As a result, the decomposition property of the M/G/1 queue with generalized vacations is extended to the $M/G^{b}/1$ queue in which the batch size is exactly a constant b. We also demonstrate that the arrival time approach is useful for relating the time-average queue length PGF to that of the departure time, both for the $M/G^{b}/1$queue in which the batch size is as big as possible but up to the maximum of constant b. The case that the batch size is a random variable is also briefly mentioned.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.343-350
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• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.273-277
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• 2002

In this paper, with martingale argument we derive the explicit formula for the Laplace transform of the busy period of M/M/1 queue with bounded workload which is also called finite dam. Much simpler derivation than appeared in former literature provided.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.19-29
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• 1995

In this paper, we investigate the asymptotic distributions of maximum queue length for M/G/1 and GI/M/1 systems which are positive recurrent. It is well knwon that for any positive recurrent queueing systems, the distributions of their maxima linearly normalized do not have non-degenerate limits. We show, however, that by concerning an array of queueing processes limiting behaviors of these maximum queue lengths can be established under certain conditions.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.3
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• pp.1-5
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• 2014

We study the paper Zhernovyi and Zhernovyi [Zhernovyi, K.Y. and Y.V. Zhernovyi, "An $M^{\Theta}/G/1/m$ system with two-threshold hysteresis strategy of service intensity switching," Journal of Communications and Electronics, Vol.12, No.2(2012), pp.127-140]. In the paper, authors used the Korolyuk potential method to obtain the stationary queue length distribution. Instead, our note makes an attempt to apply the most frequently used methods : the embedded Markov chain and the supplementary variable method. We derive the queue length distribution at a customer's departure epoch and then at an arbitrary epoch.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.523-533
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• 1999

We consider the M/G/1 queueing model with D-policy. The server is turned off at the end of each busy period and is activated again only when the sum of the service times of all waiting customers exceeds a fixed value D. We obtain the distribution of unfinished work and show that the unfinished work decomposes into two random variables, one of which is the unfinished work of ordinary M/G/1 queue. We also derive the distribution of queue waiting time.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.301-306
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• 2004

We consider the $P_\lambda\;^M$ service policy for an M/G/1 queue in which the service rate is increased from 1 to M at the exponential setup time after the level of workload exceeds $\lambda$. The stationary distribution of the workload is explicitly obtained through the level crossing argument.

• 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.

• International Journal of Reliability and Applications
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• v.3 no.4
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• pp.165-171
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• 2002

An optimization of the M/M/1 queue with impatient customers is studied. The impatient customer does not enter the system if his or her virtual waiting time exceeds the threshold K ＞ 0. After assigning three costs to the system, a cost proportional to the virtual waiting time, a penalty to each impatient customer, and also a penalty to each unit of the idle period of the server, we show that there exists a threshold K which minimizes the long-run average cost per unit time.