• 한국경영과학회지
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• 제30권4호
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• pp.99-115
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• 2005

For an analysis of the performance of a computer system, the minimum cycle time method has been widely used. The minimum cycle time method is a mathematical technique with which we can find the minimum duration time needed to fire all the transitions at least once and coming back to the Initial marking in a timed net. A timed net is a modified version of a Petri net where a transition is associated with a delay time. In the real world, an event is associated with a probability of occurrence. However, a timed net is not equipped with any facility of specifying probability of event occurrence. Therefore, the minimum cycle time method applied on a timed net can easily overlook probabilities of occurrences of events and yield a wrong result. We are proposing 'Timed Net with Probabilities of Choices' where a transition can be associated with both delay time and a probability of occurrence. We also introduce an algorithm for minimum cycle time analysis on a 'Timed Net with Probabilities of Choices'. As an example of application, we are performing an analysis of the location based service system using 'Timed Net with Probabilities of Choices'.

• 대한수학회지
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• 제60권3호
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• pp.537-564
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• 2023

In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ℤ^d, whose one-step transition probability is comparable to |x - y|^-dϕ_j (|x - y|)^-1 with ϕ_j being a positive regularly varying function on [1, ∞) with index α ∈ [2, ∞). For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

• International Journal of Control, Automation, and Systems
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• 제5권3호
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• pp.307-316
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• 2007

In real system application, the interacting multiple model (IMM) based algorithm operates with the following problems: it requires less computing resources as well as a good performance with respect to the various target maneuvering, it requires a robust performance with respect to the time-varying measurement noise, and further, it requires an easy design procedure in terms of its structures and parameters. To solve these problems, an adaptive fuzzy interacting multiple model (AFIMM) algorithm, which is based on the basis sub-models defined by considering the maneuvering property and the time-varying mode transition probabilities designed by using the mode probabilities as the inputs of the fuzzy decision maker whose widths are adjusted, is proposed. To verify the performance of the proposed algorithm, a radar target tracking is performed. Simulation results show that the proposed AFIMM algorithm solves all problems in the real system application of the IMM based algorithm.

• Bulletin of the Korean Chemical Society
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• 제8권2호
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• pp.111-114
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• 1987

Temperature-dependent, solution EPR spectra of two mixed-valence copper(II)-copper(I) complexes have been simulated by using modified Bloch equations. The transition probability for the intramolecular electron transfer is determined from the simulation. The transition probabilities have been fitted to the Arrhenius equation to derive the activation energies. The transition probability also varies according to the solvent used.

• 한국수자원학회논문집
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• 제42권9호
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• pp.747-758
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• 2009

본 논문에서는 연속자료로서 세계 최장의 기록을 보유하고 있는 서울지점의 강우량 자료를 이용하여 강우 발생특성의 장기 변동성을 분석하였다. 우선 마코프 연쇄에 근거한 전이확률 및 발생특성을 분석하여 측우기 자료의 정확성을 강우의 발생확률적 측면에서 평가하였다. 그리고 2차원 LOWESS 회귀방법을 이용하여 전이확률의 월간 장기변화특성을 분석하였다. 전이확률 및 발생특성 분석결과 원자료 계열의 CWK와 MRG는 발생특성이 다르게 나타났다. 강우사상의 특성은 과거에 비해 강우사상의 발생빈도가 높아지고 있으며 각 강우사상의 지속기간은 짧아지고 있는 것으로 나타났다. 그리고 전이확률의 월간 장기 변화특성을 분석한 결과, M20을 기준으로 CWK와 MRG의 무강우지속기간은 크게 차이를 보이지 않고 있으며, 강우지속기간은 1830년대 이후 지속적으로 감소하는 경향을 보이고 있는 것으로 나타났다. 특히 최근 9월 강우지속기간의 감소 경향이 두드러지게 나타났다. 이러한 결과를 최근 강우량의 증가양상과 더불어 고려하면 강우사상의 빈도와 심도(강우강도)가 증가하는 추세라고 해석할 수 있다.

• 한국경영과학회지
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• 제16권2호
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• pp.159-163
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• 1991

For a continuous-time absorvation Markov chain, we apply and simplify the general method of finding the transition rates given the transition probabilities obtained from discrete observation of the continuous system. An example is given.

• 한국수자원학회논문집
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• 제41권3호
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• pp.265-276
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• 2008

수공구조물의 설계를 위해서는 충분한 기간의 관측자료가 필요하지만, 우리나라의 수문자료는 대부분 충분한 수의 관측자료를 보유하고 있지 못하는 실정이다. 따라서 본 연구에서는 핵밀도함수를 이용한 비동질성 Markov 모형을 통해 시간강수량 자료를 모의하였다. 첫 번째로 시간강수량 자료에 변동핵밀도함수를 이용하여 천이확률을 산정하였으며, 두 번째로 난수와 천이확률을 통해 강수가 발생하는 시간을 결정하였다. 세 번째로 강수가 발생한 시간의 강수량의 크기를 핵밀도함수를 통해 추정하였다. 분석결과에서 모의된 시간강수량은 관측시간강수량과 비슷한 통계적 특성을 보이고 있는 것으로 나타났다. 또한, 시간강수량의 모의발생을 위하여 산정한 천이확률을 이용해 강수의 무차원시간분포곡선을 유도하였다.

• 자원ㆍ환경경제연구
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• 제13권3호
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• pp.417-440
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• 2004

미국의 PJM(Pennsylvania-New Jersey-Maryland) 전기도매시장의 전기 가격을 가변 전환확률 국면전환모형(regime switching model with time-varying transition probability model)을 이용해서 추정해보았다. 전기수요뿐만 아니라 기온을 전환확률 방정식의 설명변수로 포함시킴으로써 전기가격이 낮은 국면에서 높은 국면으로 전환할 확률의 문턱점(threshold) 효과가 뚜렷이 향상되었다. 따라서 도매전기가격의 스파이크(spike) 발생을 예측할 수 있게 되는 것이다. 이는 또한 미국의 도매시장 전기가격의 스파이크는 기온에 의해서도 잘 설명되며, 이를 이용하여 날씨관련 파생상품이나 계약을 통해서 도매전기 구입비용의 위험을 해지할 수 있다는 것을 의미한다.

• 대한산업공학회지
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• 제21권4호
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• pp.609-628
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• 1995

This paper presents a reliability model and a data-analytic procedure for a repairable unit subject to failures due to multiple non-identifiable causes. We regard a failure cause as a state and assume the life distribution for each cause to be exponential. Then we represent the dependency among the causes by a Markov switching model(MSM) and estimate the transition probabilities and failure rates by maximum likelihood(ML) method. The failure data are incomplete due to masked causes of failures. We propose a specific version of EM(expectation and maximization) algorithm for finding maximum likelihood estimator(MLE) under this situation. We also develop statistical procedures for determining the number of significant states and for testing independency between state transitions. Our model requires only the successive failure times of a unit to perform the statistical analysis. It works well even when the causes of failures are fully masked, which overcomes the major deficiency of competing risk models. It does not require the assumption of stationarity or independency which is essential in mixture models. The stationary probabilities of states can be easily calculated from the transition probabilities estimated in our model, so it covers mixture models in general. The results of simulations show the consistency of estimation and accuracy gradually increasing according to the difference of failure rates and the frequency of transitions among the states.

• 대한산업공학회지
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• 제11권2호
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• pp.1-9
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• 1985

In this study, two stage transfer line with limited repair capability is modeled to formulate optimal dynamic repair priority policy. The method of Markov Chains is used to analyze the analytical model of this line. An efficient algorithm is developed, utilizing the block tridiagonal structure of the transition probability matrix, to obtain the steady state probabilities and system performance measures, such as the steady state production rate of the line and the average in-process inventory in the interstage buffer.