• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.107-116
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• 2009

We consider a single server multi-class queueing model with Poisson arrivals and relative priorities. For this queue, we derive a system of equations for the transform of the queue length distribution. Using this system of equations we find the moments of the queue length distribution as a solution of linear equations.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.46 no.2
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• pp.57-71
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• 2023

In this study, we analyze a finite-buffer M/G/1 queueing model with randomized pushout space priority and nonpreemptive time priority. Space and time priority queueing models have been extensively studied to analyze the performance of communication systems serving different types of traffic simultaneously: one type is sensitive to packet delay, and the other is sensitive to packet loss. However, these models have limitations. Some models assume that packet transmission times follow exponential distributions, which is not always realistic. Other models use general distributions for packet transmission times, but their space priority rules are too rigid, making it difficult to fine-tune service performance for different types of traffic. Our proposed model addresses these limitations and is more suitable for analyzing communication systems that handle different types of traffic with general packet length distributions. For the proposed queueing model, we first derive the distribution of the number of packets in the system when the transmission of each packet is completed, and we then obtain packet loss probabilities and the expected number of packets for each type of traffic. We also present a numerical example to explore the effect of a system parameter, the pushout probability, on system performance for different packet transmission time distributions.

• Journal of Korean Institute of Industrial Engineers
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• v.15 no.1
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• pp.1-15
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• 1989

In the past few years, increasing numbers of automatic storage/retrieval system (AS/RS) using computer controlled storage/retrieval machine have been installed. This paper introduces two modeling approaches to determine the best operating policy for AS/RS : an M/G/1 queueing model and a computer simulation model. The operating policy consists of three elements. : the operation command cycle, the storage location method, and the operation dispatching rule. The analysis based on M/G/1 model is suitable for a quick and approximate evaluation, due to its inherent strict assumptions. The computer simulation can be used to perform a more realistic analysis. It is shown through the study that a significant improvement in the throughput and/or the space requirement can be expected by determining the best operating policy to a particular system. Most important, the computer simulation demonstrates its powerful capability in evaluating dynamic stochatic systems with imperfect information.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.171-190
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• 2008

With growing applications of wireless video streaming, an efficient video traffic model featuring modern high-compression techniques is more desirable than ever, because the wireless channel bandwidths are ever limited and time-varying. We propose a modeling and analysis method for video traffic by a class of stochastic processes, which we call '$GEO^Y/G/{\infty}$ input processes'. We model video traffic by $GEO^Y/G/{\infty}$ input process with gamma-distributed batch sizes Y and Weibull-like autocorrelation function. Using four real-encoded, full-length video traces including action movies, a drama, and an animation, we evaluate our modeling performance against existing model, transformed-M/G/${\infty}$ input process, which is one of most recently proposed video modeling methods in the literature. Our proposed $GEO^Y/G/{\infty}$ model is observed to consistently provide conservative performance predictions, in terms of packet loss ratio, within acceptable error at various traffic loads of interest in practical multimedia streaming systems, while the existing transformed-M/G/${\infty}$ fails. For real-time implementation of our model, we analyze G/D/1/K queueing systems with $GEO^Y/G/{\infty}$ input process to upper estimate the packet loss probabilities.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.661-666
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• 2001

In this paper we consider an M/G/1 queue where the server of the system has a vacation time and the service policy is limited-1. In this system, upon termination of a vacation the server returns to the queue and serves at most one message in the queue before taking another vacation. We consider two models. In the first, if the sever finds the queue empty at the end of a cacation, then the sever immediately takes another vacation. In the second model, if no message have arrived during a vacation, the sever waits for the first arrival to serve. The analysis of this system is particularly useful for a priority class polling system. We derive Laplace-Stieltjes transforms of the waiting time for both models, and compare their mean waiting times.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.3
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• pp.63-70
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• 2010

Based on the known results of the expected busy periods for the triadic Min (N, T, D) and Max (N, T, D) operating policies applied to a controllable M/G/1 queueing model, a relation between them is constructed. Such relation is represented in terms of the expected busy periods for the simple N, T and D, and the dyadic Min (N, T), Min (T, D) and Min (N, D) operating policies. Hence, if any system characteristics for one of the two triadic operating policies are known, unknown corresponding system characteristics for the other triadic operating policy could be obtained easily from the constructed relation.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.1 no.1
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• pp.51-64
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• 2002

This paper analyzes performance measures of a Bluetooth_based mobile home network system. The home network system consists of terminals with Bluetooth interfaces, access points (AP), a home PC, and a gateway A mobile host in wireless terminals uses Mobile IP for supporting the mobility This paper considers four types of data traffic, which are new connection traffic, handoff traffic, Internet data traffic, and control data traffic and suggests a queueing system model of the home network system, where the AP and the home PC are modeled as M/G/1 with four priority queues and the gateway is modeled as M/G/1 with a single queue The generation rate and service time of individual traffic influence their performance measures. Based ell the suggested model, we propose the elapsed time of data traffic in terms of the number of cells, the number of Home PCs, arrival rates of four types of traffic and the service rates of AP/Home PCs/Gateway To analyze influences on the elapsed time with respect to arrival rate of four types of traffic, some examples are given.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.40 no.3
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• pp.66-75
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• 2017

Priority disciplines are an important scheme for service systems to differentiate their services for different classes of customers. (N, n)-preemptive priority disciplines enable system engineers to fine-tune the performances of different classes of customers arriving to the system. Due to this virtue of controllability, (N, n)-preemptive priority queueing models can be applied to various types of systems in which the service performances of different classes of customers need to be adjusted for a complex objective. In this paper, we extend the existing (N, n)-preemptive resume and (N, n)-preemptive repeat-identical priority queueing models to the (N, n)-preemptive repeat-different priority queueing model. We derive the queue-length distributions in the M/G/1 queueing model with two classes of customers, under the (N, n)-preemptive repeat-different priority discipline. In order to derive the queue-length distributions, we employ an analysis of the effective service time of a low-priority customer, a delay cycle analysis, and a joint transformation method. We then derive the first and second moments of the queue lengths of high- and low-priority customers. We also present a numerical example for the first and second moments of the queue length of high- and low-priority customers. Through doing this, we show that, under the (N, n)-preemptive repeat-different priority discipline, the first and second moments of customers with high priority are bounded by some upper bounds, regardless of the service characteristics of customers with low priority. This property may help system engineers design such service systems that guarantee the mean and variance of delay for primary users under a certain bounds, when preempted services have to be restarted with another service time resampled from the same service time distribution.

• Korean Management Science Review
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• v.19 no.1
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• pp.29-38
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• 2002

Due to the rapid increase In the Internet traffic volume, ISPs are faced with the definite need of the expansion of server capacity. In order to Provide prompt services for customers and still prevent excessive facility cost, it is critical to determine the optimum level of internet server capacity. The purpose of this Paper is to provide a simple but effective strategy on the expansion of servers capacity according to the increase in internet traffic. We model an internet server as an M/G/m/m queueing system and derive an efficient method to compute the loss probability which, In turn, Is used as a basis to determine proper server capacity. The Process of estimating the traffic parameter values at each server based on log data analysis is also given. All the procedures are numerically demonstrated through the process of analyzing actual log data collected from a game company.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.1
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• pp.58-63
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• 2013

Using the known result of the expected busy period for the triadic Med (N, T, D) operating policies applied to a controllable M/G/1 queueing model, its upper and lower bounds are derived to approximate its corresponding actual values. Both bounds are represented in terms of the expected busy periods for the dyadic Min (N, T), Min (N, D) and Min (T, D) or Max (N, T), Max (N, D) and Max (T, D) with the simple N, T and D operating policies without using any other types of triadic operating policies such as Min (N, T, D) and Max (N, T, D) policies. All three input variables N, T and D are equally contributed to construct such bounds for estimation of the expected busy period.