• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.275-282
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• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.813-820
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• 2006

We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, ${\beta}-mixing$ property and existence of moments of the model are given via Markovian representation technique.

• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.473-488
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• 2000

We consider a Markovian retrial queue with waiting space in which the service rates and retrial rates depend on the number of customers in the service facility and in the orbit, respectively. Each arriving customer from outside or orbit decide either to enter the facility or to join the orbit in Bernoulli manner whose entering probability depend on the number of customers in the service facility. In this paper, a stochastic order relation between two bivariate processes(C(t), N(t)) representing the number of customers C(t) in the service facility and one N(t) in the orbit is deduced in terms of corresponding parameters by constructing the equivalent processes on a common probability space. some applications of the results to the stochastic bounds of the multi-server retrial model are presented.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.4 no.4
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• pp.560-574
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• 2010

In this paper, the relationship between the energy efficiency and spectrum efficiency in a two-cell cellular network is obtained, and the impact of multi-antenna on the energy efficiency of cellular network is analyzed and modeled based on two-state Markovian wireless channels. Then, the energy efficiency of multi-cell cellular networks with co-channel interference is investigated. Simulation results verify the proposed model and the energy-spectrum efficiency tradeoffs in cellular networks with multi-antenna and co-channel interference.

• Proceedings of the Korean Reliability Society Conference
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• 2002.06a
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• pp.263-272
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• 2002

Reliability of multi-phased mission system is represented where redundant components are repairable. Failures and repairs of components follow Markovian property Under some constraints, 4 models are available. Two models are represented here. The solutions are obtained as recursive equations using Markov model and eigenvalue system.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.639-645
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• 2009

Fractional Brwonian motion(fBm) has properties of behaving tails and exhibiting long memory while remaining Gaussian. In particular, it is well known that interest rates show some long memories and non-Markovian. We present no aribitrage condition for HJM model under the multi-factor fBm reflecting the long range dependence in the interest rate model.

• Journal of the Korea Society for Simulation
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• v.2 no.1
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• pp.46-54
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• 1993

Analytic and simulation models for prioritized token ring are presented in this paper. Its protocol is based on prioritized token ring with reservation (R-PTR). Since the protocol of the R-PTR is simple and the performance of the R-PTR is not inferior to that of the IEEE-PTR under almost all traffic load environments, we use the R-PTR as our token ring model. By using the properties of Markovian process, the expressions for average throughput and average packet transmission delay are derived. The results obtained from the analytic model are compared with that of the discrete event simulation model.

• Journal of the Korean Regional Science Association
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• v.11 no.1
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• pp.31-60
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• 1995

The distribution of economic activity over a mutually exclusive and exhaustive categorical industry-region matrix is modeled as a composition of two random components: the probability-like share distribution of jobs and the dynamic evolution of absolute aggregates. The former describes the individual activity location choice by comparing the predicted profitability of the current industry-region pair against that of all other alternatives based on the available information on industry-specific, region specific, or activity specific attributes. The latter describes the time evolution of macro-level aggregates using a dynamic reduced from model. With the seperation of micro choice behavior and macro dynamic aggregate constraint, the usual independence and identicality assumptions become consistent with the activity share distribution, hence multi-regional industrial migration can be represented by a set of probability evolution equations in a conservative Markovian from. We call this a Micro-Macro Composition Approach since the product of the aggregate prediction and the predicted activity share distribution gives the predicted activity distribution gives the predicted activity distribution which explicitly considers the underlying individual choice behavior. The model can be applied to interesting practical problems such as the plant location choice of multinational enterprise, the government industrial ploicy to attract international firms, and the optimal tax-transfer mix to influence activity location choice. We consider the latter as an example.

• IE interfaces
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• v.10 no.3
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• pp.217-222
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• 1997

An economic sortie model involving N identical aircrafts attacking a single active target is developed. Using the concepts of Markovian properties, mathematical expressions for the probability of the various events associated with the sortie are obtained. The obtained results are used to derive cost related measures of effectiveness. Then, the most economic sortie time attacking the given target is computed based on maximization of the expected gain of the sortie. A numerical example is provided.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.40 no.10
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• pp.16-23
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• 2003

In this paper, we propose a new optical hybrid switching system that takes advantage of both Optical Burst Switching (OBS) and Optical Circuit Switching (OCS) technologies. This system classifies incoming IP traffic flows into short-lived and long-lived flows for hybrid switching. For performance analysis, we model the system as a single server queue in a Markovian environment. The burst generation process is assumed to follow a two-state Markov Modulated Poisson Process (MMPP), and the service rate fluctuates based on the number of concurrent OCS sessions. Results of the mean delay and queue size for OBS bursts are derived.