• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.819-833
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• 2021

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol [27] proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.8
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• pp.1674-1683
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• 2003

The performance of a packet data multiplexer with stop­and­wait ARQ protocols under Markovian interruption is considered in this work It is assumed that the input process, into the system is Poisson process, and that the output channel is divided into a series of time slots and a data packet can be transmitted in a slot time. In this system the round­trip propagation delay is defined to be the frame time. It is modeled that the output channel can be blocked by some Markevian interruption, whose state change between the blocking and non­-blocking states is given by Markov process. The overall system has been analyzed by constructing a relationship, taking the Markovian interruption into account, about the buffer behavior between the successive frames of slots. The validity of this analytical results has been verified by computer simulation.

• The Journal of the Acoustical Society of Korea
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• v.16 no.3E
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• pp.32-36
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• 1997

This study models mobile communication channels as a discrete finite Markovian process, and Markovian jump linear system having parallel Kalman filter type is applied. What is newly proposed in this paper is an equation for obtaining the transition matrix according to sampling time by using a weighted Gaussian sum approximation and its simple calculation process. Experiments show that the proposed method has superior performance and reuires computation compared to the existing MJLS using the ransition matrix given by a statistical method or from priori information.

• Journal of Korea Society of Industrial Information Systems
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• v.10 no.2
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• pp.42-47
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• 2005

A single-server queueing model with the Batch Markovian Arrival Process and disaster ow correlated with the arrival process is analyzed. The numerically stable algorithm for calculating the steady state distribution of the system is presented.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.153-156
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• 2001

This paper discusses a stochastic stabilization of Takagi-Sugeno (75) 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 75 fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretized 75 fuzzy system is represented by a discrete-time 75 fuzzy system with jumping parameters. The stochastic stabilizibility of the jump 75 fuzzy system is derived and formulated in terms of linear matrix inequalities (LMls).

• IE interfaces
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• v.24 no.4
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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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• v.6 no.2
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.1
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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.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.299-302
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• 2004

A Markovian approach is introduced to find the Laplace transform of the forward recurrence time in the renewal process at finite time t > 0. Until now, most works on the forward recurrence time have been done through renewal arguments.