• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.11
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• pp.440-446
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• 1984

This thesis investigates the quantitative aspect of epidemic phenomena utilizing the analytical method of discrete time systems based on the theory of Markov processes. In particular, the pattern on the epidemic character of Influenza was analyzed by the mathematical model of Influenza system, which is derived according to the ecologic relationship between five epidemiolgic states of individuals. The quantitative aspects of the model was characterized by digital computer simulations. The main results were obtained as follows: 1) A Markovian model of influenza system represents accurate spead curve. 2) The latent period of influenza has the standard deviation of 1.98 and also the incubation period is 2.68. 3) If the value of susceptibilities in the pre-epidemic period is less than 20% of the population, the epidemic will occur sporadically. 4) The initial value of susceptibilties obtained by this markov theory is less about 10% of total population than the obtained value according to the deterministic model.

• Journal of Korean Society for Quality Management
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• v.11 no.2
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.1
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• pp.28-35
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• 2012

This paper presents the method for $H_{\infty}$ fuzzy controller design of discrete-time fuzzy Markovian jump systems with state and input time delays. The Takagi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the fuzzy Markovian jump systems with state and input time delays. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller is given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficiency of the proposed design method.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.779-786
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• 2009

This paper deals with $H_{\infty}$ fuzzy control problem of discrete-time nonlinear Markovian jump systems with time delay. The Takgi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the Markovian jump fuzzy system with time delay. Stochastic Lyapunov function is dependent on the operation modes of the system. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller are given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficient of the proposed design methods.

• Proceedings of the Korean Society for Quality Management Conference
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• 2004.04a
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• pp.499-502
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• 2004

Multi-server Markovian retrial model with heterogeneous servers is analyzed. Arriving customers constitute the MMAP(Marked Markovian Arrival Process). Distribution of the primary customers among the servers is performed randomly depending on the type of a customer and the number of the server. Customers from the orbit have the exponential service time distribution with a parameter depending on the server only. The choice of the server for a retrial is made randomly as well. Multidimensional continuous time Markov chain describing operation of the model is investigated by means of reducing to asymptotically quasi-toeplitz Markov chaius.

• Journal of Communications and Networks
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• v.12 no.1
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• pp.43-51
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• 2010

IEEE 802.11 defines distributed coordination function (DCF), which is characterized by CSMA/CA and binary exponential backoff (BEB) algorithm. Most modifications on DCF so far have focused on updating of the contention window (CW) size depending on the outcome of own frame transmission without considering freezing periods experienced in the backoff interval. We propose two simple but novel schemes which effectively utilize the number of freezing periods sensed during the current backoff interval. The proposed schemes can be applied to DCF and its family, such as double increment double decrement (DIDD). Saturation throughput of the proposed schemes is analyzed by means of Bianchi's Markovian model. Computer simulation validates the accuracy of the analysis. Numerical results based on IEEE 802.11b show that up to about 20% improvement of saturation throughput can be achieved by combining the proposed scheme with conventional schemes when applied to the basic access procedure.

• Proceedings of the KIEE Conference
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• 1984.07a
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• pp.89-91
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• 1984

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.321-324
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• 2003

This paper discusses a robust stochastic stabilization of uncertain Takagi-Sugeno (T-S) fuzzy system with Markovian input delay. The finite Markovian process is adopted to model the input delay of the overall control system. It is assumed that the zero and hold devices are used for control input. The continuous-time T-S fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretixzd T-S fuzzy system is represented by a uncertain discrete-time T-S fuzy system with jumping parameters. The robust stochastic stabilizibility of the uncertain jump T-S fuzzy system is derived and formulated in terms of linear matrix inequalities (LMIs).

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.477-491
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• 2021

The Markov modulated Brownian motion is a substantial generalization of the classical Brownian Motion. On the other hand, the Markovian arrival process (MAP) is a point process whose family is dense for any stochastic point process and is used to approximate complex stochastic counting processes. In this paper, we consider a superposition of the Markov modulated Brownian motion (MMBM) and the Markovian arrival process of jumps which are distributed as the bilateral ph-type distribution, the class of which is also dense in the space of distribution functions defined on the whole real line. In the model, we assume that the inter-arrival times of the MAP depend on the underlying Markov process of the MMBM. One of the subjects of this paper is introducing how to obtain the first passage probabilities of the superposed process using a stochastic doubling algorithm designed for getting the minimal solution of a nonsymmetric algebraic Riccatti equation. The other is to provide eigenvalue and eigenvector results on the superposed process to make it possible to apply the GTH-like algorithm, which improves the accuracy of the doubling algorithm.

• Journal of KIISE:Information Networking
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• v.34 no.2
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• pp.134-142
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• 2007

Several mobility supporting protocols have been proposed across OSI reference layers. Each protocol has similar or different characteristics based on its operating layer which affect a handover latency. In this paper, we analyze handover performance of most representative protocols in each layer. For analysis, we use SUBNET model based Markovian model and movement model. In result, difference of protocol handover latency is not occurred by DAD but also by security, movement detection, message processing time.