• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.309-320
• /
• 1999

Models of single-server queues with vacations have been widely used to study the performance of many computer communi-cation and production systems. In this paper we analyze an M/G/1 queue with generalized vacations and exhaustive service. This sys-tem has been shown to possess a stochastic decomposition property. That is the customer waiting time in this system is distributed as the sum of the waiting time in a regular M/G/1 queue with no va-cations and the additional delay due to vacations. Herein a general formula for the additional delay is derived for a wide class of vacation policies. The formula is also extended to cases with multiple types of vacations. Using these new formulas existing results for certain vacation models are easily re-derived and unified.

• Journal of the Korea Society for Simulation
• /
• v.17 no.4
• /
• pp.241-247
• /
• 2008

In this study we consider an M/D/1 queue with a finite buffer. Due to the finiteness of the buffer capacity arriving customers can not join the system and turn away without service when the buffer is full. Even though a computational method for blocking probabilities in an M/D/1/K queue is already known, it is very complex to use. The aim of this study is to propose a new way to compute blocking probability by using (max,+)-algebra. Our approach provide a totally different and easier way to compute blocking probabilities and it is, moreover, immediately applicable to more generous queueing systems.

• Journal of the Korean Statistical Society
• /
• v.33 no.3
• /
• pp.283-298
• /
• 2004

We present a trial solution approach to GI/M/l queues with generalized vacations. Specific types of generalized vacations we consider are N -policy and a combination of N-policy and exponential multiple vacations. Discussions about how to find trial solutions are given.

• Journal of Korean Society of Transportation
• /
• v.14 no.2
• /
• pp.59-88
• /
• 1996

This study has determined optimal type, and location of loop detector to measure accurately traffic condition influenced by traffic variation with real time. Optimal type of loop detector for through vehicle at stop bar was determined by confidences of occupancy period, and nonoccupancy period, and so appropriate detector type for application to real time traffic control system has been decided on special loop detector.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.875-887
• /
• 2005

In M/G/1 retrial queueing system with two types of customers and feedback, we derived the joint generating function of the number of customers in two groups by using the supplementary variable method. It is shown that our results are consistent with those already known in the literature when ${\delta}_k\;=\;0(k\;=\;1,\;2),\;{\lambda}_1\;=\;0\;or\;{\lambda}_2\;=\;0$.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1993.04a
• /
• pp.57-57
• /
• 1993

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.41 no.4
• /
• pp.17-24
• /
• 2004

Call blocking probabilities of streaming data service in CDMA system with access point(AP) of WLAN are analyzed for different cell geometry of base station and AP and queuing is modeled. The considered system leads to successful handoffs between the APs of WLAN. Blocking probabilities are enumerated as a function for ratio of base station and AP sizes, their locations and the number of buffer in the queue. Results show that blocking probability is not influenced by base station and AP locations but mainly by ratio of their sizes. For CDMA system of radius 100m, 5 buffers in the queue and 7㏈ noise rise(NR), in order to obtain 1% call blocking probability, a cell with hot spot of radius 20m has more 0.6Erlang than that of radius 60m.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.26 no.4
• /
• pp.39-45
• /
• 2001

Maximum and minimum of rendom variables are frequently encountered in the stochastic modelling for various OR problems. We summarize and extend characteristics of maximum and minimum, emphasizing the case in which random variables are independent and all of them except one are distributed exponential. As an application, we derive a transform-free expression for the M/G/1 queue length distribution.

• Management Science and Financial Engineering
• /
• v.1 no.1
• /
• pp.1-19
• /
• 1995

In this paper, we analyze an M / M / 1 queueing system where there are incentive conflicts among customers. Self-interested customers' decisions whether to join the system or not may not necessarily induce a socially optimal congestion level. As a way to alleviate the over-congestion, toll imposition was used in Naor's paper [3]. Instead of using a toll mechanism, we study the usefulness of imperfect information on system state (queue size, for example) as a way to reduce the over-congestion by self-interested customers. The main conclusion of this paper is that by purposefully giving fuzzy or imperfect information on the current queue size we can improve the congestion in the system. This result might look contradictory to rough intuition since perfect information should give better performance than imperfect information. We show how this idea is verified. In deriving this result, we use the concept of Nash equilibrium (pure and mixed strategy) as introduced in game theory. In some real situations, using imperfect information is easier to apply than imposing a toll, and thus the result of this paper has practical implications.

• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.32A no.4
• /
• pp.15-23
• /
• 1995

In this paper, we evaluate the performance of a transient queueing approximation when it is applied to modeling computer communication networks. An operational computer network that uses the ISO IS-IS(Intermediate System-Intermediate System) routing protocol is modeled as a Jackson network. The primary goal of the approximation pursued in the study was to provide transient queue statistics comparable in accuracy to the results from conventional Monte Carlo simulations. A closure approximation of the M/M/1 queueing system was extended to the general Jackson network in order to obtain transient queue statistics. The performance of the approximation was compared to a discrete event simulation under nonstationary conditions. The transient results from the two simulations are compared on the basis of queue size and computer execution time. Under nonstationary conditions, the approximations for the mean and variance of the number of packets in the queue erer fairly close to the simulation values. The approximation offered substantial speed improvements over the discrete event simulation. The closure approximation provided a good alternative Monte Carlo simulation of the computer networks.