• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.10a
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• pp.161-164
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• 2000

A cyclic shop is a production system that repeatedly produces identical sets of jobs, called minimal part sets, in the same loading and processing sequence. We consider a version of cyclic shop where the operations are processed and unloaded within time limits, so called a time window. We model the shop using an event graph model, a class of Petri nets. To represent the time window constraint, we introduce places with negative time delays. From the shop modeling graph, we develop a linear system model based on the max- plus algebra and characterize the conditions on the existence of a stable schedule.

• Korean Management Science Review
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• v.24 no.1
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• pp.25-34
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• 2007

In this study, we consider stationary waiting times in finite-buffer 3-node single-server queues in series with a Poisson arrival process and with either constant or non-overlapping service times. We assume that each node has a finite buffer except for the first node. The explicit expressions of waiting times in all areas of the stochastic system were driven as functions of finite buffer capacities. These explicit forms show that a system sojourn time does not depend on the finite buffer sizes, and also allow one to compute and compare characteristics of stationary waiting times at all areas under two blocking rules communication and manufacturing blocking. The goal of this study is to apply these results to an optimization problem which determines the smallest buffer capacities satisfying predetermined probabilistic constraints on stationary waiting times at all nodes. Numerical examples are also provided.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.519-522
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• 2001

In this paper, I propose double parallel manipulator for machining work. And I derive an kinematics by combining the kinematics of the central axis and the kinematics of the link train of linear actuator. The Jacobian of the central axis and the Jacobian of the link train of the linear actuators are induced by a motor algebra and they are combined to an entire Jacobian matrix to transform the velocity of the end effector to those of linear actuators. And then this paper presents the development of control system and user interface program for machining work.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.67.5-67
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• 2001

A closed loop system with a linear plant and nonlinearity in the feedback connection is analyzed for its quasi-static orbital stability by a state-space approach. First a periodic orbit is assumed to exist in the loop which is determined by describing function method for the given nonlinearity. This is possible by selecting a proper nonlinearity and a rigorous justification of the describing function method.[1-3, 18, 20]. Then by introducing residual operator, a linear perturbed model can be formulated. Using various transformations like a modified eigenstructure decomposition, periodic-averaging, charge of variables and coordinate transformation, the stability of the periodic orbit, as a solution of harmonic balance, can be shown by investigating a simple scalar function and result of linear algebra. This is ...

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.3
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• pp.47-56
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• 1999

제한된 출력 즉 오차 측정된 출력 값만을 사용하여 원하는 목표치에 도달하도록 하는 제어 문제를 푸는데 많은 연구가 진행되어 왔다. 종종 그러한 제어기를 설계할 때 해를 구하기 어려운 Non Linear Two Point Boundary Value Problem에 직면하게 된다. 특히 Reduced order 추정자 알고리즘은 백색 잡음에 의하여 영향을 받은 선형 시스템의 측정된 상태 뿐 만 아니라 보조 상태를 추정하기 위하여 개발되었다. 추정자를 설계할 때 상태는 무편향성이고 추정자의 편차는 추정자 및 추정상태와 공통되는 상태에 대한 모든 출력의 subspace에 수직이 된다. 특히 reduced order에서의 필터 성능은 full order에서의 필터 성능에 대해 suboptimal 이지만 상응한 Riccati equation을 푸는데 계산시간이 줄고 memory사용이 적은 이점이 있다. 본 논문에서는 Kronecker algebra와 선택행렬을 이용하여 Non Linear Two Point Boundary Value Problem을 Linear Two Point Boundary Value Problem으로 변환시켜 부수적으로 수반되는 대수적인 Riccati equation을 유도함으로써 문제를 쉽게 해결하는데 있다.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• Journal of the Korea Society for Simulation
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• v.17 no.4
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• pp.241-247
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• 2008

In this study we consider an M/D/1 queue with a finite buffer. Due to the finiteness of the buffer capacity arriving customers can not join the system and turn away without service when the buffer is full. Even though a computational method for blocking probabilities in an M/D/1/K queue is already known, it is very complex to use. The aim of this study is to propose a new way to compute blocking probability by using (max,+)-algebra. Our approach provide a totally different and easier way to compute blocking probabilities and it is, moreover, immediately applicable to more generous queueing systems.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.459-474
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• 2018

Cao et al. in (Numer. Linear. Algebra Appl. 18 (2011) 875-895) proposed a splitting method for saddle point problems which unconditionally converges to the solution of the system. It was shown that a Krylov subspace method like GMRES in conjunction with the induced preconditioner is very effective for the saddle point problems. In this paper we first modify the iterative method, discuss its convergence properties and apply the induced preconditioner to the problem. Numerical experiments of the corresponding preconditioner are compared to the primitive one to show the superiority of our method.

• ETRI Journal
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• v.36 no.4
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• pp.609-616
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• 2014

Even though many computational methods (recursive formulae) for blocking probabilities in finite-capacity M/D/1 queues have already been produced, these are forms of transforms or are limited to single-node queues. Using a distinctly different approach from the usual queueing theory, this study introduces explicit (transform-free) formulae for a blocking probability, a stationary probability, and mean sojourn time under either production or communication blocking policy. Additionally, the smallest buffer capacity subject to a given blocking probability can be determined numerically from these formulae. With proper selection of the overall offered load ${\rho}$, the approach described herein can be applicable to more general queues from a computational point of view if the explicit expressions of random vector $D_n$ are available.

• Journal of the Korea Society for Simulation
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• v.21 no.4
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• pp.11-24
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• 2012

We compared a DBR(drum-buffer-rope) system with a CONWIP(constant work-in-process) system in a production line with constant processing times. Based on the observation that a WIP-controlled line production system such as DBR and CONWIP is equivalent to a m-node tandem queue with finite buffer, we applied a max-plus algebra based solution method for the tandem queue to evaluate the performance of two systems. Numerical examples with 6 workstations were also used to demonstrate the proposed analysis. The mathematical analyses support that CONWIP outperforms DBR in terms of expected waiting time and WIP. Unlike the CONWIP case, sequencing workstations in a DBR affects the performance of the system. Delaying a bottleneck station in a DBR reduces expected waiting time.