• 호남수학학술지
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• 제17권1호
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• pp.141-147
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• 1995

We find a method finding the steady-state probabilities of M/M/3/3 retrial queueing system.

• 한국시뮬레이션학회논문지
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• 제23권3호
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• pp.1-9
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• 2014

전통적인 워크플로우 시간분석은 단위작업을 독립적인 M/M/1 대기행렬모형에 적용하여 수행해왔다. M/M/1 시스템 성능척도의 일반해들을 활용하면 여러 가지 분석이 가능해진다. 특히 워크플로우 시스템의 AND 구조를 분석함에 있어 M/M/1 시스템 성능척도를 활용하면 그 체재시간에 대한 분석이 가능하다. 그러나 실질적인 AND 구조를 정확히 묘사하기 위해서는 각각의 M/M/1 시스템이 독립이라는 가정이 없어야 한다. 본 연구는 이러한 한계를 극복하기 위해 한 업무에 대한 모든 단위작업이 동시에 시작하는 상황으로 가정한다. 이 가정 하에서는 M/G/1 시스템의 성능척도를 이용하여 이론적 분석이 가능해진다. 또한 시뮬레이션을 이용하여 실질적인 AND 구조를 정확히 묘사할 수 있는 방법론을 소개한다. 마지막으로 가상의 시스템을 구성하여 이론적인 해와 시뮬레이션 결과들을 수록함으로써 제안된 방법론들을 검증한다. 본 연구에서 사용된 주요 시스템 성능척도는 평균대기시간과 평균체재시간이다.

• 대한산업공학회지
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• 제21권3호
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• pp.345-356
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• 1995

The aim of this paper is to analyze the batch service queueing model M/M(a, b ; ${\mu}_k/1$) under general bulk service rule with mean service rate ${\mu}_k$ for a batch of k units, where $a{\leq}k{\leq}b$. This queueing model consists of the two-dimensional state space so that it is characterized by two-dimensional state Markov process. The steady-state solution and performane measure of this process are derived by using Matrix Geometric method. Meanwhile, a new approach is suggested to calculate the two-dimensional traffic density R which is used to obtain the steady-state solution. In addition, to determine the optimal service initiation threshold a, a decision model of this queueing system is developed evaluating cost of service per batch and cost of waiting per customer. In a job order production system, the decision-making procedure presented in this paper can be applicable to determining when production should be started.

• 대한산업공학회지
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• 제35권2호
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• pp.171-177
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• 2009

This study presents the switching strategy between admission control and pricing control policies and clarifies the properties of the switching strategy in an M/M/1/K queueing system. In addition, this study demonstrates that employing the switching strategy can significantly improve the maximum total expected profit.

• 산업경영시스템학회지
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• 제20권43호
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• pp.153-162
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• 1997

M/G/1 queueing system is one of the most widely used one to model the real system. When operating a real systems, since it often takes cost, some control policies that change the operation scheme are adopted. In particular, the N-policy is the most popular among many control policies. Almost all researches on queueing system are based on the assumption that the arrival rates of customers into the queueing system is constant, In this paper, we consider the M/G/1 queueing system whose arrival rate varies according to the servers status : idle, set-up and busy states. For this study, we construct the steady state equations of queue lengths by means of the supplementary variable method, and derive the PGF(probability generating function) of them. The L-S-T(Laplace Stieltjes transform) of waiting time and average waiting time are also presented. We also develop an algorithm to find the optimal N-value from which the server starts his set-up. An analysis on the performance measures to minimize total operation cost of queueing system is included. We finally investigate the behavior of system operation cost as the optimal N and arrival rate change by a numerical study.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.483-498
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• 1994

Suppose that a stationary process ${X_t}$ has a marginal distribution whose support consists of sufficiently large integers. We are concerned with some analogous law of large numbers for such distribution function F. In particular, we determine a weak law of large numbers for maximum queueing length in $M/M\infty$ system. We also present a limiting behavior for the maxima based on AR(1) process with binomial thining and poisson marginals (INAR(1)) introduced by E. Mckenzie. It turns out that the result of AR(1) process is the same as that of $M/M/\infty$ queueing process in limit when we observe the queues at regularly spaced intervals of time.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.871-880
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• 1999

The main purpose of queueing theory is to find the optimal solution for maintaining systems such as service facilities. Analyzing the overfolw process provides an important information for the solution in queueing systems with finite capacity. In this thesis we approximate the expected time until the first overflow in M/G/1/K/N queueing systems. Results will be applied to approximate the expected time until the first reduction of source population system. Simulation results show that our approximation is applicable to real situations.

• 한국경영과학회지
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• 제31권1호
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• pp.83-90
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• 2006

By defining the partial busy period of the M/M/c/K queueing system as the time interval during which at least one server is in service, we derive the first two moments of both the partial busy period and the number of customers served during it. All expressions are given in explicit forms.

• Journal of Communications and Networks
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• 제17권3호
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• pp.265-266
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• 2015

In a recent paper [1], the authors investigated the maximum stable throughput region of a network composed of a rechargeable primary user and a secondary user plugged to a reliable power supply. The authors studied the cases of an infinite and a finite energy queue at the primary transmitter. However, the results of the finite case are incorrect. We show that under the proposed energy queue model (a decoupled M/D/1 queueing system with Bernoulli arrivals and the consumption of one energy packet per time slot), the energy queue capacity does not affect the stability region of the network.

• 전자공학회논문지CI
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• 제38권4호
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• pp.1-9
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• 2001

본 논문에서는 한 개의 서버와 시스템용량 K를 갖는 M/M/1/K 큐잉네트워크모델에 펴지집합이론을 적용한 퍼지 M/M/1/K 큐잉네트워크모델을 제안하였다. 작업의 도착율과 서버의 서비스율의 형태가 언어적 속성으로 표현될 때， 이 모델을 사용하여 시스템의 해석이 가능해진다. 시스템의 평가를 위해서 시스템내 평균작업수， 작업 평균진입률， 그리고 작업 평균소요시간 등 시스템의 주요 평가측도를 유도하였다. 퍼지 작업 환경에서 이러한 결과식들의 유효함을 검증하기 위하여， 제안된 모델에 다양한 퍼지도착율 ${\lambda}$와 퍼지서비스율 ${\mu}$에 대하여 시스템용량 K 값의 변화에 따른 성능평가를 컴퓨터 시뮬레이션하였다. 그 결과가 제안한 퍼지 모델에서 예측한 평가와 일치함을 확인하였다.