• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.505-511
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• 2007

In this paper, we examine the Markov chain $\{X_k,\;N_k;\;k=0,\;1,...$. We show that the marginal steady state distribution of Xk is discrete phase type. The implication of this result is that the queue length distribution of phase type for large number of examples where this Markov chain is applicable and shows a queueing application by matrix geometric methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.6
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• pp.940-945
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• 2016

In this paper, zero sequence equivalent circuit of Yg-Yg three phase core-type transformer is analyzed. Many problems by iron core structure of the three phase transformer due to asymmetric three phase lines, which includes line disconnection, ground fault, COS OFF, and unbalanced load are reported in the distribution system. To verify a feasibility of zero sequence impedance of Yg-Yg type three phase transformer, fault current generation in the three phase core and shell-type Yg-Yg transformer is compared by PSCAD/EMTDC when single line ground fault is occurred. As a result, shell-type transformer does not affect the flow of fault current, but core-type transformer generate an adverse effect by the zero sequence impedance. The adverse effect is explained by the zero sequence equivalent circuit of core-type transformer and Yg-Yg type three phase core-type transformer supplies a zero sequence fault current to the distribution system.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.443-457
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• 2015

We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.09a
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• pp.99-107
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• 1995

The Phase-type(PH) distribution, defined as a distribution of the time until the absorption in a finite continuous-time Markov chain state with one absorbing state, has been widely used for various stochastic modelling. But great computational burdens often make us hesitate to apply PH methods. In this paper, we propose a seemingly efficient approximation method for phase type distributions. We first describe methods to bound the first passage time distribution in continuous-time Markov chains. Next, we adapt these bounding methods to approximate phase-tupe distributions. Numerical computation results are given to verify their efficiency.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.8
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• pp.1203-1210
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• 2004

It was reported recently that the pump head degradation near the best efficiency point from single-phase flow to the break-down due to air entrainment became less in a screw-type centrifugal pump than in a general centrifugal pump. In this paper, I carried out internal pressure measurements and visualizations, and investigated the various physical phenomena occurring inside a screw-type centrifugal pump operated in air-water two-phase flow. The results could give some characteristics about the degradation of pump performance on air-water two-phase flow.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.10
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• pp.1536-1541
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• 2012

The study analyzed problems by iron core structure of the three phased transformer on asymmetric three phase lines, which included line disconnections, ground faults, COS OFF, and unbalanced loads on the power distribution system. In particular, by analyzing PT combustion cases within the MOF, the study was able to analyze the combustion cause of the core-type transformer and its effect on the system, conduct simulations and practice demonstrations on the characteristics for each iron core structure of the three phase transformer using PSCAD/EMTDC, and suggest measures to prevent the combustion of the core-type transformer.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.169-175
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• 2012

The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The service time distribution is fitted with phase type(PH) distribution by matching the first three moments of service time and the M/G/c retrial queue is approximated by the M/PH/c retrial queue. Approximations are compared with the simulation results.

• The KSFM Journal of Fluid Machinery
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• v.4 no.3 s.12
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• pp.39-45
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• 2001

It is reported recently that the pump head deterioration near the best efficiency point, from single-phase flow to the choke due to air entrainment became less in a screw-type centrifugal pump than in a general centrifugal pump. Moreover, at a narrow tip clearance, the pump head became partially higher in two-phase flow than that in single-phase flow. However, the internal pressure fluctuations on this pump due to air entrainment have not been studied yet. For that reason, we have examined the influences of void fraction, flow coefficient and impeller tip clearance on pressure fluctuations in the casing. The void fraction became larger, the influence of tip clearance on pressure distribution became less.

• Atmosphere
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• v.29 no.2
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• pp.227-239
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• 2019

This paper reviews various bulk-type cloud microphysics parameterizations (BCMPs). BCMP, predicting the moments of size distribution of hydrometeors, parameterizes the grid-resolved cloud and precipitation processes in atmospheric models. The generalized gamma distribution is mainly applied to represent the hydrometeors size distribution in BCMPs. BCMP can be divided in three different methods such as single-moment, double-moment, and triple-moment approaches depending on the number of prognostic variables. Single-moment approach only predicts the hydrometeors mixing ratio. Double-moment approach predicts not only the hydrometeors mixing ratio but also the hydrometeors number concentration. Triple-moment approach predicts the dispersion parameter of hydrometeors size distribution through the prognostic reflectivity, together with the number concentrations and mixing ratios of hydrometeors. Triple-moment approach is the most time expensive method because it has the most number of prognostic variables. However, this approach can allow more flexibility in representing hydrometeors size distribution relative to single-moment and double-moment approaches. At the early stage of the development of BMCPs, warm rain processes were only included. Ice-phase categories such as cloud ice, snow, graupel, and hail were included in BCMPs with prescribed properties for densities and sedimentation velocities of ice-phase hydrometeors since 1980s. Recently, to avoid fixed properties for ice-phase hydrometeors and ad-hoc category conversion, the new approach was proposed in which rimed ice and deposition ice mixing ratios are predicted with total ice number concentration and volume.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.351-373
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• 2020

There is an extensive literature on retrial queueing models. While a majority of the literature on retrial queueing models focuses on the retrial times to be exponentially distributed (so as to keep the state space to be of a reasonable size), a few papers deal with nonexponential retrial times but with some additional restrictions such as constant retrial rate, only the customer at the head of the retrial queue will attempt to capture a free server, 2-state phase type distribution, and finite retrial orbit. Generally, the retrial queueing models are analyzed as level-dependent queues and hence one has to use some type of a truncation method in performing the analysis of the model. In this paper we study a retrial queueing model with threshold-type policy for orbiting customers in the context of nonexponential retrial times. Using matrix-analytic methods we analyze the model and compare with the classical retrial queueing model through a few illustrative numerical examples. We also compare numerically our threshold retrial queueing model with a previously published retrial queueing model that uses a truncation method.