• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.227-274
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• 2001

In this paper we intended to discuss the following topics: (1) Notation, generalities, Markov processes. The close relationship between (generators of) Markov processes and the martingale problem is exhibited. A link between the Korovkin property and generators of Feller semigroups is established. (2) Feynman-Kac semigroups: 0-order regular perturbations, pinned Markov measures. A basic representation via distributions of Markov processes is depicted. (3) Dirichlet semigroups: 0-order singular perturbations, harmonic functions, multiplicative functionals. Here a representation theorem of solutions to the heat equation is depicted in terms of the distributions of the underlying Markov process and a suitable stopping time. (4) Sets of finite capacity, wave operators, and related results. In this section a number of results are presented concerning the completeness of scattering systems (and its spectral consequences). (5) Some (abstract) problems related to Neumann semigroups: 1st order perturbations. In this section some rather abstract problems are presented, which lie on the borderline between first order perturbations together with their boundary limits (Neumann type boundary conditions and) and reflected Markov processes.

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.3
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• pp.208-219
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• 2012

As the number of end-of-life vehicles (ELVs) has kept increasing, the management of ELV has also become one of the academic research focuses and European Union recently adopted the directive on ELVs. For the stakeholders has become a principle agent of dealing with all about ELVs, it is relevant investment decision to set up and to decide high-cost ELVs entity locations and to forecast future ELVs' amount in advance. In this paper, transition probability matrixes between months are made by using Markov Chain and the number of ELVs is predicted with them. This study will perform a great role as a fundamental material in Korea where just started having interests about recycling resources and studies related to the topic. Moreover, the forecasting method developed for this research can be adopted for other enhancements in different but comparable situations.

• ETRI Journal
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• v.40 no.2
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• pp.237-245
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• 2018

The Distributed Modulated Wideband Converter (DMWC) is a networking system developed from the Modulated Wideband Converter, which converts all sampling channels into sensing nodes with number variables to implement signal undersampling. When the number of sparse subbands changes, the number of nodes can be adjusted flexibly to improve the reconstruction rate. Owing to the different attenuations of distributed nodes in different locations, it is worthwhile to find out how to select the optimal sensing node as the sampling channel. This paper proposes the spectrum sensing of DMWC based on a Markov random field (MRF) to select the ideal node, which is compared to the image edge segmentation. The attenuation of the candidate nodes is estimated based on the attenuation of the neighboring nodes that have participated in the DMWC system. Theoretical analysis and numerical simulations show that neighboring attenuation plays an important role in determining the node selection, and selecting the node using MRF can avoid serious transmission attenuation. Furthermore, DMWC can greatly improve recovery performance by using a Markov random field compared with random selection.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.657-676
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• 2011

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.537-556
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• 2021

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.5
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• pp.805-814
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• 1994

In this paper, we introduce a new method which is available for analyzing the throughput of the packet radio network by using the auxiliary Markov transient matrix with a failure state and a success state. And we consider the effect of symbol error for the network state(X, R) consisted of the number of transmitting PRU X and receiving PRU R. We examine the packet radio network of a continuous time Markov chain model, and the direct sequence binary phase shift keying CDMA radio channel with hard decision Viterbi decoding and bit-by-bit changing spreading code. For the unslotted distributed multi-hop packet radio network, we assume that the packet error due to a symbol error of radio channel has Poisson process, and the time period of an error occurrence is exponentially distributed. Through the throughputs which are found as a function of radio channel parameters, such as the received signal to noise ratio and chips of spreading code per symbol, and of network parameters, such as the number of PRU and offered traffic rate, it is shown that this composite analysis enables us to combine the Markovian packet radio network model with a coded DS/BPSK CDMA radio channel.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.505-511
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• 2007

In this paper, we examine the Markov chain $\{X_k,\;N_k;\;k=0,\;1,...$. We show that the marginal steady state distribution of Xk is discrete phase type. The implication of this result is that the queue length distribution of phase type for large number of examples where this Markov chain is applicable and shows a queueing application by matrix geometric methods.

• Journal of the Korean Society of Systems Engineering
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• v.14 no.1
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• pp.36-43
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• 2018

The availability of the weapon system can be analyzed through state modeling and simulation using the Markov process. In this paper, show how to analyze the availability of the weapon system and can use the Markov process to analyze the system's steady state as well as the RAM at a transient state in time. As a result of the availability analysis of tracked vehicles, the inherent availability was 2.6% and the operational availability was 1.2% The validity criterion was defined as the case where the difference was within 3%, and thus it was judged to be valid. We have identified the faulty items through graphs of the number of visits per state among the results obtained through the MPS and can use them to provide design alternatives.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1915-1926
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• 1995

The Fatigue characteristics of 8-harness satin woven CFRP composites with a circular hole are experimentally investigated under constant amplitude tension-tension loading. It is found in this study that the fatigue damage accumulation behavior is very random and history-independent, and the fatigue cumulative damage is linearly related with the mean number of cycles to a specified damage state. From these results, it is known that the fatigue characteristics of CFRP composites satisfy the basic assumptions of Markov chain theory and the parameter of Markov chain model can be determined only by mean and variance of fatigue lives. The predicted distribution of the fatigue cumulative damage using Markov chain model shows a good agreement with the test results. For the fatigue life distribution, Markov chain model makes similar accuracy to 2-parameter Weibull distribution function.

• ETRI Journal
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• v.5 no.2
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• pp.3-8
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• 1983

This paper derives the Markov model to calculate the reliability of the Digital Switching System being developed by KETRI. Using the failure states extracted from the system in the course of the modelling, we calculated the reliability of both the service grade and the function of the system. Especially, by including the repair rate into the model, we took optimum advantage of theMarkov process and solved the difficulties in the calculation by reducing the number of states of the system.