• Journal of Korea Society of Industrial Information Systems
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• v.29 no.1
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• pp.63-76
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• 2024

In this study, we analyzed queue length and sojourn time of discrete-time BMAP/G/1 queues under the workload control. Group customers (packets) with correlations arrive at the system following a discrete-time Markovian arrival process. The server starts busy period when the total service time of the arrived customers exceeds a predetermined workload threshold D and serves customers until the system is empty. From the analysis of workload and waiting time, distributions of queue length at the departure epoch and arbitrary time epoch and system sojourn time are derived. We also derived the mean value as a performance measure. Through numerical examples, we confirmed that we can obtain results represented by complex forms of equations, and we verified the validity of the theoretical values by comparing them with simulation results. From the results, we can obtain key performance measures of complex systems that operate similarly in various industrial fields and to analyze various optimization problems.

• Journal of Korean Society of Environmental Engineers
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• v.22 no.6
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• pp.1149-1158
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• 2000

A radioisotope tracer experiment was carried out in the submerged fixed bioreactor of a dye wastewater treatment facility to evaluate the flow behaviors in the 6 compartments of the reactor and to find any possible factors which may affect to the efficiency of the process. Approximately 20mCi of $^{131}I$ was injected into the system as a tracer and 8 radiation detectors were placed in the 6 compartments and at the inlet and the outlet of the system to measure the change of the tracer concentration with time. Using the Perfect Mixers in Series Model the measured data were analyzed to calculate the mean residence time and the characteristic parameters of the flow in the system. The mean residence time of the system was calculated as 17 hours which is 76% of the designed MRT(22.3hr). Among the 6 compartments, the first compartment doesn't show the characteristic of perfect mixer, whereas, the other 5 compartments are working as perfect mixers. The output response of the first compartment is fit well with the simulated output of a model which consists of a perfect mixer with an exchange volume. It indicates that a quarter of the tank volume is working as a dead volume or an exchange volume. From the measured residence time distributions in each compartment, the appropriate sampling times after the change of operational condition of the electron beam accelerator were evaluated.

• Journal of Korea Society of Industrial Information Systems
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• v.22 no.1
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• pp.23-32
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• 2017

In this paper, We suggest a unified approach for the analysis of discrete-time MAP/G/1 queueing system. Many researches on the D-MAP/G/1 queue have been used different approach to analyze system queue length and waiting time for the same system. Therefore, a unified framework for analyzing a system is necessary from a viewpoint of system design and management. We first derived steady-state workload distribution, and then waiting time and sojourn time are derived by the result of workload analysis. Finally, system queue length distribution is derived with generating function from the sojourn time distribution.

• Journal of the Korea Society for Simulation
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• v.33 no.1
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• pp.19-26
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• 2024

The phase-type, PH, distribution is defined as the time to absorption into a terminal state in a continuous-time Markov chain. As the PH distribution includes family of exponential distributions, it has been widely used in stochastic models. Since the PH distribution is represented and generated by an initial probability vector and a generator matrix which is called the Markovian representation, we need to find a vector and a matrix that are consistent with given set of moments if we want simulate a PH distribution. In this paper, we propose an approach to simulate a PH distribution based on distribution function which can be obtained directly from moments. For the simulation of PH distribution of order 2, closed-form formula and streamlined procedures are given based on the Jordan decomposition and the minimal Laplace transform which is computationally more efficient than the moment matching methods for the Markovian representation. Our approach can be used more effectively than the Markovian representation in generating higher order PH distribution in queueing network simulation.

• Proceedings of the Korea Society for Simulation Conference
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• 1999.10a
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• pp.192-196
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• 1999

본 연구에서는 변환을 취하지 않고 M/G/c 시스템의 고객수분포를 구하는 방법으로 2단계 분석을 제시한다. I 단계에서는 마코비안 서비스를 따르는 전통적인 고객수분포로부터 출발하여 여기에 새롭게 정의된 모수를 도입해서 근사하여 고객수가 c명일 때까지의 분포를 구한다. II단계에서는 선수 작업으로 하나의 대기행렬을 각각의 고객의 대기공간으로 구별하여 나눈 후에 현재 시스템내의 고객수에 따라 고객의 도착시점에서 바라 본 대기공간의 부하 유형별로 나누고, 해당 대기공간에 부하를 주는 정도에 따라 정리된 식으로부터 축차적으로 고객수분포를 유도한다. 유도된 고객수분포로부터 평균 시스템 체재시간과 평균 대기시간 등을 구하고 이를 시뮬레이션과 비교하여, 본 근사법의 유용성을 논의한다.

• Journal of Korean Society of Environmental Engineers
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• v.27 no.2
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• pp.177-183
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• 2005

The effluent quality is directly affected by the separation of biological solids in a final clarifier because the majority of discharged $BOD_5$ and SS are virtually dependent on the results of biological solids in the sedimentation tank effluent. If a final clarifier is effectively designed and operated, the desired goal of clarification for wastewater can be achieved together with the cost reduction in the treatment of wastewater. To this end flow characteristics and the removal efficiency of SS are numerically investigated especially by the change of the inlet position and the installation of baffle to improve the performance of a rectangular final clarifier. The 2-D computer program developed in a rectangular coordinates has been successfully validated against experimental residence time distribution(RTD) curves obtained by tracing radio-isotope. The lowering of the inlet position weakens the density current and induces the settling of SS in the front zone of a clarifier. Thus the decreased traveling distance of the sludge increases the removal efficiency of SS in the effluent. The inlet baffle installed in the front region of clarifier prevents the short circuiting flow and induces to flow into the dense underflow, which eventually improves the effluent quality. In the case of lower inlet position, however, installation of baffle results in degradation of effluent quality. Consequently it is strongly recommended that in-depth numerical study be performed in advance for optimizing a clarifier design and retrofitting to improve effluent quality in a final clarifier.

• Journal of Radiation Industry
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• v.4 no.1
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• pp.85-89
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• 2010

The radioactive experiments are carried out for diagnosis of a variety of industrial processes in terms of the operation condition and the efficiency by measuring the residence time distribution. However, it is not easy to interpret the residence time distribution using the conventional methods when the flow rate is not constant and a number of processes are coupled in a complicated manner. In these cases, they can be analyzed by describing the system with mathematical models that can be defined with the state-space equations. In this paper, the residence time distribution of sludge was measured with a radiotracer, $^{46}Sc-EDTA$, in the digester of which the flow rate varies with time. The digester was assumed as a linear time variant system since the flow rate changed during the experiment and the operation efficiency of the digester was calculated by applying the state-spae equations.

• Journal of Radiation Protection and Research
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• v.32 no.3
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• pp.117-122
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• 2007

The hydrodynamic behaviors of the clarifier with an interior baffle in a wastewater treatment plant was investigated by using a radiotracer $^{99m}Tc$(30 40 mCi) to verify the results of CFD(computational fluid dynamics) modelling in the previous study. The clarifier model was manufactured with consideration to the hydraulic similarity(1/21) of a real plant($L{\times}W{\times}H:2.6{\times}0.4{\times}0.2m$). By installation of an interior baffle to the clarifier, the strong density current at the bottom of the clarifier decreased substantially and increased the area of sludge settling zone, which were visualized successfully from the radiotracer experiment. Also the portion of short circuit stream changed from 48 % to 32 % and the mean residence time of sludge decreased from 940 sec to 810 sec, which corresponds to the results of CFD modelling. As a result, it is anticipated that radiotracer technology can be used as an important tool for designing new wastewater treatment plants and verifying their performances after structural modifications.

• Journal of the Korea Safety Management & Science
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• v.9 no.5
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• pp.57-66
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• 2007

본 논문에서는 통신망의 트래픽 제어를 위한 무한버퍼, 단일 서버와 배치도착과정을 갖는 대기행렬 모형을 고려하였다. 또한 고객 도착 형태와 서비스의 분포는 지수분포를 배치 흐름은 포아송 정상과정 및 배치크기는 기하분포를 따른다고 가정하였다. 서비스를 받기 위해 시스템으로 들어오는 배치의 크기는 시스템의 상태에 따라서 트래픽 제어가 가능하다. 이와 같은 조건에서 시스템에 있는 고객의 수와 배치크기에 대한 결합 확률분포를 분석하였고, 행렬기법을 적용하여 시스템 체재시간에 대한 분석이 수행되었다. 마지막으로 시스템의 주요 성능평가 척도에 대한 효율적인 제어기법에 대한 언급과 수치예제를 통해서 증명하였다.

• Journal of Korea Society of Industrial Information Systems
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• v.23 no.2
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• pp.29-39
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• 2018

In this paper, we discuss a discrete-time queueing system with dyadic server control policy that combines workload control and multiple vacations. Customers arrive at the system with Bernoulli arrival process. If there is no customer to serve in the system, an idle single server spends a vacation of discrete random variable V and returns. The server repeats the vacation until the total service time of waiting customers exceeds the predetermined workload threshold D. In this paper, we derived the steady-state workload distribution of a discrete-time queueing system which is operating under a more realistic and flexible server control policy. Mean workload is also derived as a performance measure. The results are basis for the analysis of system performance measures such as queue lengths, waiting time, and sojourn time.