• ETRI Journal
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• v.5 no.1
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• pp.10-16
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• 1983

When analyzing a complex system with repair environments, it is necessary to calculate such parameters as availability and various kinds of failure time measures. These measures are defined and methods of calculating them using Markov process are presented. Analyzing the various system states, numerical values of the reliability measures can be obtained by calculating the state probabilities. And these techniques are widely applied to reliability prediction and also to maintenance strategy.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.29-42
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• 2018

We combine the integer-valued GARCH(1, 1) model with a generalized regime-switching model to propose a dynamic count time series model. Our model adopts Markov-chains with time-varying dependent transition probabilities to model dynamic count time series called the generalized regime-switching integer-valued GARCH(1, 1) (GRS-INGARCH(1, 1)) models. We derive a recursive formula of the conditional probability of the regime in the Markov-chain given the past information, in terms of transition probabilities of the Markov-chain and the Poisson parameters of the INGARCH(1, 1) process. In addition, we also study the forecasting of the Poisson parameter as well as the cumulative impulse response function of the model, which is a measure for the persistence of volatility. A Monte-Carlo simulation is conducted to see the performances of volatility forecasting and behaviors of cumulative impulse response coefficients as well as conditional maximum likelihood estimation; consequently, a real data application is given.

• Communications for Statistical Applications and Methods
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• v.29 no.2
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• pp.151-160
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• 2022

The total system is composed of the main system (MS) and the failure detection equipment (FDE) which detects failures of MS. The analysis of system reliability is performed when the failure of FDE is possible. Several repair policies are considered to determine the order of repair of failed systems, which are sequential repair (SQ), priority repair (PR), independent repair (ID), and simultaneous repair (SM). The states of MS-FDE systems are represented by Markov models according to repair policies and the main purpose of this paper is to derive the system availabilities of the Markov models. Analytical solutions of the stationary equations are derived for the Markov models and the system availabilities are immediately determined using the stationary solutions. A simple illustrative example is discussed for the comparison of availability values of the repair policies considered in this paper.

• Journal of the Earthquake Engineering Society of Korea
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• v.26 no.5
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• pp.191-202
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• 2022

Markov envelope as a theoretical solution of the parabolic wave equation with Markov approximation for the von Kármán type random medium is studied and approximated with the convolution of two probability density functions (pdf) of normal and gamma distributions considering the previous studies on the applications of Radiative Transfer Theory (RTT) and the analysis results of earthquake records. Through the approximation with gamma pdf, the constant shape parameter of 2 was determined regardless of the source distance r_o. This finding means that the scattering process has the property of an inhomogeneous single-scattering Poisson process, unlike the previous studies, which resulted in a homogeneous multiple-scattering Poisson process. Approximated Markov envelope can be treated as the normalized mean square (MS) envelope for ground acceleration because of the flat source Fourier spectrum. Based on such characteristics, the path duration is estimated from the approximated MS envelope and compared to the empirical formula derived by Boore and Thompson. The results clearly show that the path duration increases proportionately to r_o^1/2-r_o², and the peak value of the RMS envelope is attenuated by exp (-0.0033r_o), excluding the geometrical attenuation. The attenuation slope for r_o≤100 km is quite similar to that of effective attenuation for shallow crustal earthquakes, and it may be difficult to distinguish the contribution of intrinsic attenuation from effective attenuation. Slowly varying dispersive delay, also called the medium effect, represented by regular pdf, governs the path duration for the source distance shorter than 100 km. Moreover, the diffraction term, also called the distance effect because of scattering, fully controls the path duration beyond the source distance of 300 km and has a steep gradient compared to the medium effect. Source distance 100-300 km is a transition range of the path duration governing effect from random medium to distance. This means that the scattering may not be the prime cause of peak attenuation and envelope broadening for the source distance of less than 200 km. Furthermore, it is also shown that normal distribution is appropriate for the probability distribution of phase difference, as asserted in the previous studies.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.10
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• pp.4825-4847
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• 2016

In this paper, we focus on the per-flow throughput analysis of IEEE 802.11 multi-hop ad hoc networks. The importance of an accurate saturation throughput model lies in establishing the theoretical foundation for effective protocol performance improvements. We argue that the challenge in modeling the per-flow throughput in IEEE 802.11 multi-hop ad hoc networks lies in the analysis of the freezing process and probability of collisions. We first classify collisions occurring in the whole transmission process into instantaneous collisions and persistent collisions. Then we present a four-dimensional Markov chain model based on the notion of the fixed length channel slot to model the Binary Exponential Backoff (BEB) algorithm performed by a tagged node. We further adopt a continuous time Markov model to analyze the freezing process. Through an iterative way, we derive the per-flow throughput of the network. Finally, we validate the accuracy of our model by comparing the analytical results with that obtained by simulations.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.1
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• pp.40-46
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• 2000

In this paper, a transient identification based on a Hidden Markov Model (HMM) has been suggested and evaluated experimentally for the classification of transients in the dynamic process. The transient can be identified by its unique time dependent patterns related to the principal variables. The HMM, a double stochastic process, can be applied to transient identification which is a spatial and temporal classification problem under a statistical pattern recognition framework. The HMM is created for each transient from a set of training data by the maximum-likelihood estimation method. The transient identification is determined by calculating which model has the highest probability for the given test data. Several experimental tests have been performed with normalization methods, clustering algorithms, and a number of states in HMM. Several experimental tests have been performed including superimposing random noise, adding systematic error, and untrained transients. The proposed real-time transient identification system has many advantages, however, there are still a lot of problems that should be solved to apply to a real dynamic process. Further efforts are being made to improve the system performance and robustness to demonstrate reliability and accuracy to the required level.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.51
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• pp.231-240
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• 1999

A major concern in Concurrent Engineering is the control and management of workload in a period of process. As a general rule, leveling the peak of workload in certain period is difficult because concurrent processing is comprised of various processes, including overlapping, paralleling looping and so on. Therefore, the workload management with resource constraints is so beneficial that effective methods to analyze design process are momentous. This study presents the Timed Petri Nets approach of precedence logic networks, and provides an alternative for users to analyze constraint processes to resolve conflicts of resources. Another approach to Continuous Time Markov Chain using Stochastic Petri Nets is also proposed. These approaches are expected to facilitate resolving resource constrained scheduling problems more systematically in Concurrent Engineering environment.

• IE interfaces
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• v.12 no.2
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• pp.312-318
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• 1999

This paper considers the cell loss probability(CLP) in a multiplexer with the superposition of heterogeneous ON/OFF sources. The input traffic is composed of k classes. Traffic of class i is the superposition of M_(i) ON/OFF sources. Recently, the method based on the Markov modulated deterministic process(MMDP) is presented. Basically, it is the discretized model of stochastic fluid flow process(SFFP) and gives the CLP very fast, but under-estimates the CLP especially when the value of estimated CLP is very low. This paper develops the discretized model of Markov modulated Poisson process(MMPP). It is a special type of switched batch Bernoulli process(SBBP). Combining the transition probability matrix of MMDP and SBBP according to the state which is characterized by the arrival rate, this paper presents hybrid algorithm. The hybrid algorithm gives better estimate of CLP than that of MMDP and faster than SBBP.

• Journal of KIISE
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• v.42 no.6
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• pp.748-754
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• 2015

This paper proposes a sequential state estimation model consisting of continuous and discrete variables, as a way of generalizing all discrete-state factorial HMM, and gives a design of gait motion model based on the idea. The discrete state variable implements a Markov chain that models the gait dynamics, and for each state of the Markov chain, we created a Gaussian process over the space of the continuous variable. The Markov chain controls the switching among Gaussian processes, each of which models the rotation or various views of a gait state. Then a particle filter-based algorithm is presented to give an approximate filtering solution. Given an input vector sequence presented over time, this finds a trajectory that follows a Gaussian process and occasionally switches to another dynamically. Experimental results show that the proposed model can provide a very intuitive interpretation of video-based gait into a sequence of poses and a sequence of posture states.

• 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.