• 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.

• 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.

• 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 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 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 Operations and Management Science Society Conference
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• 2006.05a
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• pp.1104-1110
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• 2006

In this paper we present a simple approach to the joint queue length distribution in the nonpreemptive priority M/G/1 queue. Without using the supplementary variable technique, we derive the joint probability generating function of the stationary queue length at arbitrary time.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.747-752
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• 2012

When the service time distribution has a finite exponential moment, we present a large deviations result for the busy period distribution in the M/G/1 queue without the assumption of Abate and Whitt (1997) and Kyprianou (1971).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.687-693
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• 2011

This paper gives the stochastic comparison results for the first passage time distributions in the M/G/1 retial queue.

• IE interfaces
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• v.25 no.3
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• pp.283-289
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• 2012

M/G/1 queue with server vacations period depending on the previous vacation and customer's arrival is considered. Most existing studies on M/G/1 queue with server vacations assume that server vacations are independent of customers' arrival. However, some vacations are terminated by some class of customers' arrival in certain queueing systems. In this paper, therefore, we investigate M/G/1 queue with server vacations where each vacation period has different distribution and vacation length is influenced by customers' arrival. Laplace-Stieltjes transform of the waiting time distribution and the distribution of number of customers waiting for each class of customers are respectively derived. As performance measures, mean waiting time and average number of customers waiting for each class of customers are also derived.

• 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.