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최두일 ( Choi Doo Il ),임대은 ( Lim Dae-eun ) 한국경영공학회 2016 한국경영공학회지 Vol.21 No.4
In this study, we analyze a manufacturing system with a variable production rate. The system produces an item upon a request. If an arriving request finds the system occupied, the request waits in the queue. The production (or service) time distribution of requests (or customers) upon production initiation is changed if the number of requests in the system reaches a predefined threshold L₂. Then, the changed production time distribution continues until the number of requests in the system is reduced to another threshold L₁(≤ L₂), and this process is repeated. We model this system as an MMPP/G/1/K queue with a modified state-dependent service rate and analyze the system using an embedded Markov chain and a supplementary variable method. The performance measures of the queue-length distributions at a customer`s departure epochs and at an arbitrary time are derived. Numerical examples are also presented.
A Note on the M/G/1/K Queue with Two-Threshold Hysteresis Strategy of Service Intensity Switching
Doo Il Choi(최두일),Bo Keun Kim(김보근),Doo Ho Lee(이두호) 한국경영과학회 2014 韓國經營科學會誌 Vol.39 No.3
We study the paper Zhernovyi and Zhernovyi [Zhernovyi, K.Y. and Y.V. Zhernovyi, “An M <SUP>θ</SUP>/G/1/m system with two-threshold hysteresis strategy of service intensity switching,” Journal of Communications and Electronics, Vol.12, No.2(2012), pp.127-140]. In the paper, authors used the Korolyuk potential method to obtain the stationary queue length distribution. Instead, our note makes an attempt to apply the most frequently used methods : the embedded Markov chain and the supplementary variable method. We derive the queue length distribution at a customer"s departure epoch and then at an arbitrary epoch.
Choi Doo Il(최두일) 한국통신학회 2009 한국통신학회 학술대회논문집 Vol.2009 No.6
Traffics are classified into two types, real-time traffic such as voice and video and nonreal-time traffic such as data. By properties of burstiness and correlation between interarrival, it is assumed the arrival of real-time traffic to be a Markovian Arrival Process ( MAP ). The nonreal-time traffic follows a Poisson Process. We compare performance of diverse scheduling schemes to support real-time and nonreal-time traffic. Concretely, Head of Line priority scheme, Shortest Job First scheme, Longest Job First scheme, Bernoulli scheme, QLT scheme and QLT scheme with Bernoulli, are investigated, and their performance measures, loss and delay, are compared. Finally, this investigation helps the system designer to select optimal scheduling scheme, while satisfying the Quality of Service(QoS) of each traffics.
시스템 내 고객 수에 따라 서비스율과 도착율을 조절하는 M/G/1/K 대기행렬의 분석
최두일,임대은,Choi, Doo-Il,Lim, Dae-Eun 한국시뮬레이션학회 2015 한국시뮬레이션학회 논문지 Vol.24 No.3
대기행렬 시스템에는 고객들의 대기시간이 지나치게 길어지는 것을 막기 위해 다양한 정책들이 적용되는데, 본 연구에서는 고객숫자에 따른 제어 정책을 갖는 유한용량 M/G/1/K 대기행렬을 분석한다. 고객의 숫자에 따라 서버의 서비스율과 고객의 도착율을 조절하는 정책이다. 두 개의 한계점(thresholds) $L_1$과 $L_2$($${\geq_-}$$L1)를 설정하고 시스템 내 고객의 숫자가 $L_1$보다 작을 때는 시스템은 보통(또는 상대적으로 느린)의 서비스율(service rate)과 보통의 도착율(arrival rate)을 갖는다. 고객의 숫자가 증가하여 $L_1$이상이고 $L_2$보다 작으면 도착율은 그대로 이지만 서비스율을 증가시켜 빠르게 서비스한다. 이후 고객의 숫자가 더욱 증가하여 $L_2$ 이상이면 고객의 도착율도 작은 값으로 바꾸어 고객을 덜 입장시킨다. 위 정책을 갖는 M/G/1/K 대기행렬을 내재점 마코프 체인과 준-마코프 과정을 이용하여 분석하고 수치예제를 제시한다. We analyze an M/G/1/K queueing system with queue-length dependent service and arrival rates. There are a single server and a buffer with finite capacity K including a customer in service. The customers are served by a first-come-first-service basis. We put two thresholds $L_1$ and $L_2$($${\geq_-}L_1$$ ) on the buffer. If the queue length at the service initiation epoch is less than the threshold $L_1$, the service time of customers follows $S_1$ with a mean of ${\mu}_1$ and the arrival of customers follows a Poisson process with a rate of ${\lambda}_1$. When the queue length at the service initiation epoch is equal to or greater than $L_1$ and less than $L_2$, the service time is changed to $S_2$ with a mean of $${\mu}_2{\geq_-}{\mu}_1$$. The arrival rate is still ${\lambda}_1$. Finally, if the queue length at the service initiation epoch is greater than $L_2$, the arrival rate of customers are also changed to a value of $${\lambda}_2({\leq_-}{\lambda}_1)$$ and the mean of the service times is ${\mu}_2$. By using the embedded Markov chain method, we derive queue length distribution at departure epochs. We also obtain the queue length distribution at an arbitrary time by the supplementary variable method. Finally, performance measures such as loss probability and mean waiting time are presented.