• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.517-527
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• 2005

This paper considers a discrete-time queueing system with variable service capacity. Using the supplementary variable method and the generating function technique, we compute the joint probability distribution of queue length and remaining service time at an arbitrary slot boundary, and also compute the distribution of the queue length at a departure time.

• Smart Structures and Systems
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• v.21 no.5
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• pp.591-600
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• 2018

The probabilistic characterization of wind field characteristics is a significant task for fatigue reliability assessment of long-span railway bridges in wind-prone regions. In consideration of the effect of wind direction, the stochastic properties of wind field should be represented by a bivariate statistical model of wind speed and direction. This paper presents the construction of the bivariate model of wind speed and direction at the site of a railway arch bridge by use of the long-term structural health monitoring (SHM) data. The wind characteristics are derived by analyzing the real-time wind monitoring data, such as the mean wind speed and direction, turbulence intensity, turbulence integral scale, and power spectral density. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method is proposed to formulate the joint distribution model of wind speed and direction. For the probability density function (PDF) of wind speed, a double-parameter Weibull distribution function is utilized, and a von Mises distribution function is applied to represent the PDF of wind direction. The SQP algorithm with multi-start points is used to estimate the parameters in the bivariate model, namely Weibull-von Mises mixture model. One-year wind monitoring data are selected to validate the effectiveness of the proposed modeling method. The optimal model is jointly evaluated by the Bayesian information criterion (BIC) and coefficient of determination, $R^2$. The obtained results indicate that the proposed SQP algorithm-based finite mixture modeling method can effectively establish the bivariate model of wind speed and direction. The established bivariate model of wind speed and direction will facilitate the wind-induced fatigue reliability assessment of long-span bridges.

• Wind and Structures
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• v.20 no.5
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• pp.701-718
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• 2015

The joint distribution of wind speed and wind direction at a bridge site is vital to the estimation of the basic wind speed, and hence to the wind-induced vibration analysis of long-span bridges. Instead of the conventional way relying on the weather stations, this study proposed an alternate approach to obtain the original records of wind speed and the corresponding directions based on field measurement supported by the Structural Health Monitoring System (SHMS). Specifically, SHMS of Sutong Cable-stayed Bridge (SCB) is utilized to study the basic wind speed with directional information. Four anemometers are installed in the SHMS of SCB: upstream and downstream of the main deck center, top of the north and south tower respectively. Using the recorded wind data from SHMS, the joint distribution of wind speed and direction is investigated based on statistical methods, and then the basic wind speeds in 10-year and 100-year recurrence intervals at these four key positions are calculated. Analytical results verify the reliability of the recorded wind data from SHMS, and indicate that the joint probability model for the extreme wind speed at SCB site fits well with the Weibull model. It is shown that the calculated basic wind speed is reduced by considering the influence of wind direction. Compared to the design basic wind speed in the Specification of China, basic wind speed considering the influence of direction or not is much smaller, indicating a high safety coefficient in the design of SCB. The results obtained in this study can provide not only references for further wind-resistance research of SCB, but also improve the understanding of the safety coefficient for wind-resistance design of other engineering structures in the similar area.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.1
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• pp.49-58
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• 1999

A new channel access function is proposed to enhance the performance of the Joint CDMA/PRMA. It is obtained in consideration of the number of terminals in reservation mode and the number of terminals in contention mode whose probability distribution is estimated by applying pseudo Bayesian approach. Simulation results show that the performance of the Joint CDMA/PRMA can be improved by applying new channel access function under voice-only traffic and mixed voice/random-data traffic.

• Journal of Power System Engineering
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• v.13 no.2
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• pp.63-70
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• 2009

This paper discusses the influence on long-tenn predictions of the ship response in ocean by using the Global Wave Statistics data, GWS, and wave information from the remote sensing satellites. GWS's standard scatter diagrams of significant wave height and zero-crossing wave period are suggested to be corrected to a round number of 0.01/1000 fitted with a statistical analytic model of the conditional lognormal distribution for zero-crossing wave period. The GEOSAT satellite data are utilized which presented by I. R. Young and G. J. Holland (1996, named as GEOSAT data). At first, qualities of this data are investigated, and statistical characteristic trends are studied by means of applying known probability distribution functions. The wave height data of GEOSAT are compared to the data observed onboard merchant ships, the data observed by measure instrument installed on the ocean-going container ship and so on. To execute a long-tenn prediction of ship response, joint probability functions between wave height and wave period are introduced, therefore long-term statistical predictions are executed by using the functions.

• Journal of Communications and Networks
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• v.11 no.4
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• pp.406-415
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• 2009

In this work, we consider performance modeling of a wireless sensor network with a time division multiple access (TDMA) media access protocol with slot reuse. It is assumed that all the nodes are peers of each other and they have two modes of operation, active and sleep modes. We model the sensor network as a Jackson network with unreliable nodes with on and off states. Active and sleep modes of sensor nodes are modeled with on and off states of unreliable nodes. We determine the joint distribution of the sensor node queue lengths in the network. From this result, we derive the probability distribution of the number of active nodes and blocking probability of node activation. Then, we present the mean packet delay, average sleep period of a node and the network throughput. We present numerical results as well as simulation results to verify the analysis. Finally, we discuss how the derived results may be used in the design of sensor networks.

• Nuclear Engineering and Technology
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• v.53 no.2
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• pp.357-367
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• 2021

In general, common cause failures (CCFs) have been modeled with the assumption that components within the same group are symmetric. This assumption reduces the number of parameters required for the CCF probability estimation and allows us to use a parametric model, such as the alpha factor model. Although there are various asymmetric conditions in nuclear power plants (NPPs) to be addressed, the traditional CCF models are limited to symmetric conditions. Therefore, this paper proposes the copulabased CCF model to deal with asymmetric as well as symmetric CCFs. Once a joint distribution between the components is constructed using copulas, the proposed model is able to provide the probability of common cause basic events (CCBEs) by formulating a system of equations without symmetry assumptions. In addition, Bayesian inferences for the parameters of the marginal and copula distributions are introduced and Markov Chain Monte Carlo (MCMC) algorithms are employed to sample from the posterior distribution. Three example cases using simulated data, including asymmetry conditions in total failure probabilities and/or dependencies, are illustrated. Consequently, the copula-based CCF model provides appropriate estimates of CCFs for asymmetric conditions. This paper also discusses the limitations and notes on the proposed method.

• School Mathematics
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• v.17 no.2
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• pp.241-255
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• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.376-381
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• 2003

The reliability analysis of overtopping probability is proposed. In order to estimate the expected overtopping probability of the rubble mound breakwater, the experimental results of individual wave runup height is applied for the analysis of irregular wave system. The joint distribution of wave heights and periods is used for the input data of runup calculation because the runup height depends on the wave height and period. The runup heights during the one event that the design wave attacks the rubble mound breakwater extend to the one life cycle of 60 years. Utilizing the Monte-Carlo method, the one life cycle is tried more about 60 times for obtaining the expected value of overtopping probability. It is found that the inclusion of the variability of wave tidal and wave steepness has great influence on the computation of the expected overtopping probability of rubble mound breakwater. The previous design disregarding the tidal fluctuation largely overestimates or underestimates the expected overtopping probability depending on tidal range and wave steepness.

• Journal of electromagnetic engineering and science
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• v.11 no.4
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• pp.262-268
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• 2011

In this paper, we evaluate the outage performance of cooperative transmission in two-dimensional random networks. Firstly, we derive the joint distributions of the source-relay and the relay-destination links. Secondly, the outage probability for the decode-and-forward relaying system is derived when selection combining (SC) is employed at the destination. Finally, we calculate the average outage probability of the system and then attempt to express it by a simple approximate expression. The simulation results are presented to verify the accuracy of the derivations. Similar to deterministic networks, the cooperative transmission in random networks outperforms direct transmission at a high signal-to-noise ratio (SNR).