• Journal of the Korean Operations Research and Management Science Society
• /
• v.33 no.1
• /
• pp.107-115
• /
• 2008

We consider the discrete-time GI/G/1/K queue under the early arrival system. Using a modified supplementary variable technique(SVT), we obtain the distribution of the steady-state queue length. Unlike the conventional SVT, the modified SVT yields transform-free results in such a form that a simple two-moment approximation scheme can be easily established.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.40 no.1
• /
• pp.1-4
• /
• 2015

This paper presents a heuristic approach to derive the Laplace-Stieltjes transform (LST) and the probability generating function (PGF) of the waiting time distributions of a continuous- and a discrete-time GI/G/1 queue, respectively. This is a new idea to derive the well-known results, the waiting time distribution of GI/G/1 queue, in a different way.

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

• Industrial Engineering and Management Systems
• /
• v.7 no.2
• /
• pp.143-149
• /
• 2008

There have been some approximation analysis methods for a GI/G/1 queueing system. As one of them, an approximation technique for the steady-state probability in the GI/G/1 queueing system based on the iteration numerical calculation has been proposed. As another one, an approximation formula of the average queue length in the GI/G/1 queueing system by using the diffusion approximation or the heuristics extended diffusion approximation has been developed. In this article, an approximation technique in order to analyze the GI/G/1 queueing system is considered and then the formulae of both the steady-state probability and the average queue length in the GI/G/1 queueing system are proposed. Through some numerical examples by the proposed technique, the existing approximation methods, and the Monte Carlo simulation, the effectiveness of the proposed approximation technique is verified.

• Journal of Korean Institute of Industrial Engineers
• /
• v.42 no.5
• /
• pp.304-313
• /
• 2016

This work suggests a new analysis approach for a discrete-time GI/G/1 queue with multiple vacations. The method used is called a modified supplementary variable technique and our result is an exact transform-free expression for the steady state queue length distribution. Utilizing this result, we propose a simple two-moment approximation for the queue length distribution. From this, approximations for the mean queue length and the probabilities of the number of customers in the system are also obtained. To evaluate the approximations, we conduct numerical experiments which show that our approximations are remarkably simple yet provide fairly good performance, especially for a Bernoulli arrival process.

• Journal of applied mathematics & informatics
• /
• v.31 no.1_2
• /
• pp.311-325
• /
• 2013

The effects of the moments of the interarrival time and service time on the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility and orbit are numerically investigated. The results reveal the performance measures are more sensitive with respect to the interarrival time than the service time. Approximation for $GI/G/c$ retrial queues using $PH/PH/c$ retrial queue is presented.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2005.05a
• /
• pp.1129-1132
• /
• 2005

Based on a discrete-time version of the distributional Little's law, we present a simple computational procedure to obtain the queue-length distribution of the discrete-time GI/G/1 queue from its waiting-time distribution that is available by various existing methods. We also discuss our numerical experience and address a couple of remarks on possible extensions of the procedure.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.29 no.3
• /
• pp.1-7
• /
• 2004

We demonstrate in this paper that the level crossing technique can be applied to such a system that not only the state vector is two-dimensional but Its two components are heterogeneous. As an example system, we use the GI-G/c/K queue whose state vector consists of the number of customers in the system and the total unfinished work.