• Korean Journal of Mathematics
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• 제29권2호
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• pp.371-386
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• 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto S policy where as the second model is based on order placement by a fixed quantity Q, where Q = S - s, whenever the inventory level falls to s. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

• 한국시뮬레이션학회논문지
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• 제13권3호
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• pp.1-10
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• 2004

The cell loss probability required in the ATM network is in the range of 10$^{-9}$ ∼10$^{-12}$ . If Monte Carlo simulation is used to analyze the performance of the ATM node, an enormous amount of computer time is required. To obtain large speed-up factors, importance sampling may be used. Since the Markov-modulated processes have been used to model various high-speed network traffic sources, we consider discrete time single server queueing systems with Markov-modulated arrival processes which can be used to model an ATM node. We apply importance sampling based on the Large Deviation Theory for the performance evaluation of, MMBP/D/1/K, ∑MMBP/D/1/K, and two stage tandem queueing networks with Markov-modulated arrival processes and deterministic service times. The simulation results show that the buffer overflow probabilities obtained by the importance sampling are very close to those obtained by the Monte Carlo simulation and the computer time can be reduced drastically.

• 한국통신학회논문지
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• 제28권9B호
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• pp.783-792
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• 2003

We consider a finite-buffer discrete-time queueing system with fixed-size bulk-service discipline: Geo/ $G^{B}$1/K＋B. The main purpose of this paper is to present a performance analysis of this system that has a wide range of applications in Asynchronous Transfer Mode (ATM) and other related telecommunication systems. For this purpose, we first derive the departure-epoch probabilities based on the embedded Markov chain method. Next, based on simple rate in and rate out argument, we present stable relationships for the steady-state probabilities of the queue length at different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of number of packets in the system at three different epochs and the loss probability. The numerical results are presented for a deterministic service-time distribution - a case that has gained importance in recent years.s.

• 한국산업정보학회논문지
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• 제23권2호
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• pp.29-39
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• 2018

본 논문에서는 일량제어정책과 복수휴가정책이 혼합된 서버제어정책 하에서 운영되는 이산시간 대기행렬시스템을 다룬다. 고객들은 베르누이 도착과정으로 시스템에 도착하고, 서버는 한대가 운영되며 시스템 내 서비스할 고객이 없으면 유휴기간을 갖는 서버가 이산 확률변수 V만큼의 휴가를 떠났다가 돌아와서 대기 중인 고객들의 총 일량이 임계값 D를 넘길 때까지 휴가를 반복한다. 본 논문에서는 이산시간 시스템을 대상으로 하여 보다 현실적이며 유연한 혼합제어 정책 하에서 운영되는 대기행렬시스템의 안정상태 일량분포를 유도하고 평균일량을 계산하였다. 이는 시스템 내 고객수, 대기시간, 체재시간과 같은 시스템의 여러 성능척도를 분석하는데 기본이 된다.

• ETRI Journal
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• 제25권4호
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• pp.238-246
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• 2003

This paper introduces the modeling and analysis of a discrete-time, two-phase queueing system for both exhaustive batch service and gated batch service. Packets arrive at the system according to a Bernoulli process and receive batch service in the first phase and individual services in the second phase. We derive the probability generating function (PGF) of the system size and show that it is decomposed into two PGFs, one of which is the PGF of the system size in the standard discrete-time Geo/G/1 queue without vacations. We also present the PGF of the sojourn time. Based on these PGFs, we present useful performance measures, such as the mean number of packets in the system and the mean sojourn time of a packet.

• 대한수학회지
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• 제40권1호
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• pp.87-107
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• 2003

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail behavior of the queue length of the system is equivalent to that of the same queueing system with the D-BMAP being replaced by a batch renewal process. In the finite buffer case (of buffer size K), we derive upper and lower bounds of the asymptotic behavior of the loss probability as $K\;\longrightarrow\;\infty$.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2002년도 춘계공동학술대회
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• pp.859-862
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• 2002

In this paper, we consider a discrete-time two-phase queueing system. We derive the PCF of the system size and show that it is decomposed into two probabilty generating functions (PCFs), one of which is the PGF of the system size in the standard Ceo/G/1 queue. Based on this PGF, we present the performance measure of interest such as the mean number of customers In the system.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.1101-1103
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• 2006

For a broad class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process) arrivals, we present a distributional Little's law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue for example, we illustrate how to utilize this relation to get the desired distribution of the number of customers.

• 한국산업정보학회논문지
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• 제23권1호
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• pp.53-63
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• 2018

본 논문에서는 D-정책을 갖는 이산시간 BMAP/G/1 대기행렬시스템의 대기시간을 분석한다. 고객(또는 패킷)들은 마코비안 도착과정을 따라 집단으로 시스템에 도착하며, 유휴한 서버는 시스템에 도착한 고객집단의 서비스시간의 총합이 이미 정해놓은 임계값 D를 초과하면 시스템에 더 이상 서비스할 고객이 없을 때까지 서비스를 제공한다. 시스템의 안정상태 대기시간 분포를 변환 형태로 구하고 성능척도로서 평균값을 유도하였다. 시뮬레이션을 통하여 이론값들의 타당성을 검증하고 간단한 수치예제를 보였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1758-1763
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• 2004

This paper focuses on congestion control for ATM network with uncertain time-variant delays. The time-variant delays can be distinguished into two distinct components. The first one is represented by time-variant queueing delays in the intermediate switches that are occurred in the return paths of RM cells. The next one is a forward path delay. It is solved by the VBR model which quantifies the data propagation from the sources to the switch. Robust $H_8$ control is studied for solving congestion problem with norm-bounded time-varying uncertain parameters. The suitable robust $H_8$ controller is obtained from the solution of a convex optimization problem through LMI technique.