• 대한산업공학회지
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• 제42권1호
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• pp.30-37
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• 2016

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers' service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

• 산업공학
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• 제24권4호
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• pp.323-329
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• 2011

We develop a stochastic model to predict the score of a soccer match. We describe the scoring process of the soccer match as a markovian arrival process (MAP). To do this, we define a two-state underlying Markov chain, in which the two states represent the offense and defense states of the two teams to play. Then, we derive the probability vector generating function of the final scores. Numerically inverting this generating function, we obtain the desired probability distribution of the scores. Sample numerical examples are given at the end to demonstrate how to utilize this result to predict the final score of the match.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.553-568
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• 1999

This paper is of concern to queueing analysis of the dynamic rate leaky bucket(LB) scheme in which the token generation interval changes according to the buffer state at a token generation epoch. Cell arrivals are assumed to follow a Markovian arrival process (MAP) which is weakly dense in the class of the stationary point processes. By using the embedded Markov chain method we obtain the probability distribution of the system state at a token generation epoch and an arbitrary time. Some simple numerical examples also are provided to show the effects of the proposed LB scheme.

• 제어로봇시스템학회논문지
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• 제17권2호
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• pp.139-144
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• 2011

We consider the stabilization problem for a class of networked control systems with random delays in the discrete-time domain. The controller-to-actuator and sensor-to-controller time-delays are modeled as two Markov chains, and the resulting closed-loop systems are Markovian jump nonlinear systems with two modes. The T-S (Takagi-Sugeno) fuzzy model is employed to represent a nonlinear system with Markovian jump parameters. The aim is to design a fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. The necessary and sufficient conditions on the existence of stabilizing fuzzy controllers are established in terms of LMIs (Linear Matrix Inequalities). It is shown that fuzzy controller gains are mode-dependent. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.1045-1053
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• 2003

Markovian EWMA control chart for simultaneously monitoring mean vector of the several correlated quality characteristics is investigated. Properties of multivariate Shewhart chart and EWMA chart are evaluated for matched FSI (fixed sampling interval) and VSI(variable sampling interval) scheme. We obtained VSI EWMA chart is more efficient than Shewhart chart for small or moderate shifts. And, we obtained stablized numerical results with Markov chain method when the number of transient state is greater than 100.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2009년도 정보 및 제어 심포지움 논문집
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• pp.390-392
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• 2009

This paper is concerned with the stabilization problem of nonlinear networked control systems with time-delay via Takagi-Sugeno(T-S) fuzzy control approach. The T-S fuzzy models are employed to represent nonlinear systems with Markovian jump parameters and time-delay. The purpose of this paper is to design a fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. Based on a stocastic Lyapunov function, stabilization sufficient conditions using a mode-independent fuzzy controller are derived for the Markovian jump fuzzy system in terms of Linear Matrix Inequalities(LMIs). Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2009년도 정보 및 제어 심포지움 논문집
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• pp.329-331
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• 2009

This paper is concerned with the stabilization problem of nonlinear networked control systems with time-delay via Takagi-Sugeno(T-S) fuzzy control approach. The T-S fuzzy models are employed to represent nonlinear systems with Markovian jump parameters and time-delay. The purpose of this paper is to design a fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. Based on a stocastic Lyapunov function, stabilization sufficient conditions using a mode-independent fuzzy controller are derived for the Markovian jump fuzzy system in terms of Linear Matrix Inequalities(LMIs). Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

• 품질경영학회지
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• 제11권2호
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• pp.2-9
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• 1983

As will be seen, this paper is tries that the research on the mathematical structure of Markov process and Markovian sequential decision process (the policy improvement iteration method,) moreover, that it analyze the logic and the characteristic of behavior of mathematical model of Markov process. Therefore firstly, it classify, on research of mathematical structure of Markov process, the forward equation and backward equation of Chapman-kolmogorov equation and of kolmogorov differential equation, and then have survey on logic of equation systems or on the question of uniqueness and existence of solution of the equation. Secondly, it classify, at the Markovian sequential decision process, the case of discrete time parameter and the continuous time parameter, and then it explore the logic system of characteristic of the behavior, the value determination operation and the policy improvement routine.

• 산업경영시스템학회지
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• 제30권1호
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• pp.33-40
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• 2007

A multi-server queueing system with finite buffer is considered. The input flow is the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Customers from the BMAP enter the system according to the discipline of partial admission. Besides ordinary (positive) customers, the Markovian flow (MAP) of negative customers arrives to the system. A negative customer can delete an ordinary customer in service if the state of its PH-service process belongs to some given set. In opposite case the ordinary customer is considered to be protected of the effect of negative customers. The stationary distribution and the main performance measures of the considered queueing system are calculated.

• 전기학회논문지
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• 제60권2호
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• pp.376-382
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• 2011

This paper proposes delay-dependent stability conditions of the fuzzy Markovian jumping Hopfield neural networks of neutral type with time-varying delays. By constructing a suitable Lyapunov-Krasovskii's (L-K) functional and utilizing Finsler's lemma, new delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. A numerical example is given to illustrate the effectiveness of the proposed methods.