• Industrial Engineering and Management Systems
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• v.9 no.2
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• pp.165-177
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• 2010

This paper discusses a method for pricing the storage of inbound containers in a container yard. The pricing structure is characterized by a free-time-limit and a storage price for the storage time that extends beyond the free-time-limit. A cost model is developed from the viewpoint of a public terminal operator as well as a private terminal operator. Unlike a previous study on this issue, this study assumes that the retrieval times follow a discrete probability distribution, which is more realistic than the previous study. A solution procedure is suggested and illustrated by using numerical examples.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.87-107
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• 2003

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail behavior of the queue length of the system is equivalent to that of the same queueing system with the D-BMAP being replaced by a batch renewal process. In the finite buffer case (of buffer size K), we derive upper and lower bounds of the asymptotic behavior of the loss probability as $K\;\longrightarrow\;\infty$.

• Computers and Concrete
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• v.34 no.2
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• pp.231-245
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• 2024

A 3D discrete element model integrating the rough surface contact concept with the flat-joint model is suggested to examine the mechanical characteristics of the interfacial transition zone (ITZ) in concrete. The essential components of our DEM procedure include the calculation of the actual contact area in an element contact-pair related to the bonded factor using a Gaussian probability distribution of asperity height, as well as the determination of the contact probability-relative displacement form using the least square method for further computing the force-displacement of ITZs. The present formulations are implemented in MUSEN, an open source development environment for discrete element analysis that is optimized for high performance computation. The model's meso-parameters are calibrated by using uniaxial compression and splitting tensile simulations, as well as laboratory tests of concrete from the literature. The present model's DEM predictions accord well with laboratory experimental tests of pull-out concrete specimens published in the literature.

• Journal of Korea Water Resources Association
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• v.34 no.5
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• pp.499-509
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• 2001

2-D transport model based on a discrete probability distribution for a particle displacement was developed too solve advection-diffusion problems in natural stream. In this proposed model, the probabilities expressed as an average and variance function were used to predict the mass transfer between cells in one time step. The proposed model produces solutions without numerical dispersion for constant velocity, diffusion coefficient, and cross-sectional area. When the stability and positivity restrictions were satisfied, the model produced excellent results compared to analytical solutions and other finite difference methods. The proposed model is tested against the dispersion data collected in the Grand River, Canada. The simulation results show that the proposed model can properly describe the two-dimensional mixing phenomena in the natural stream.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.287-301
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• 2024

From the mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. Herein, we consider the distributions of runs and patterns related to the run lengths of multi-state sequences, especially for four states (A, B, C, D). Let X₁, X₂, . . . be a sequence of four state independent and identically distributed trials taking values in the set 𝒢 = {A, B, C, D}. In this study, we obtain exact formulas for the probability distribution function for the discrete distribution of runs of B's of order k. We obtain longest run statistics, shortest run statistics, and determine the distributions of waiting times and run lengths.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.13-18
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• 1984

The probability distribution of hold-in time and that of the time to reject false lock are investigated for the tracking procedure in spread spectrum communication systems. These are helpful in deciding dwell time and threshold level of correlatoi circuits. The probability distributions are derived by series expansion of generating function for discrete probability function and summation of the coefficients for corresponding terms. And the formulas described by general system parameters are obtained.

• The Journal of the Acoustical Society of Korea
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• v.16 no.2
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• pp.71-79
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• 1997

In this paper, a codeword-dependent distance normalization(CDDN) and an instar-formed fuzzy smoothing of output distribution are proposed for robust estimation of output probabilities in the FVQ(fuzzy vector quantization)-DHMM(discrete hidden Markov model). The FVQ-DHMM is a variant of DHMM in which the state output probability is estimated by the sum oft he product of the output probability and its weighting factor for each codeword on an input vector. As the performance of the FVQ-DHMM is influenced by weighting factor and output distribution from a state, it is required to get a method to get robust estimation of weighting factors and output distribution for each state. From experimental results, the proposed CDDN method has reduced 24% of error rate over the conventional FVQ-DHMM, and also reduced 79% of error rate when the smoothing of output distribution is also applied to the computation of an output probability. These results indicate that the use of CDDN and the fuzzy smoothing of output distribution to the FVQ-DHMM lead to improved recognition, and therefore it may be used as an alternative to the robust estimation of output probabilities for HMMs.

• Journal of Communications and Networks
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• v.16 no.2
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• pp.193-201
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• 2014

In cognitive radio networks, the packet transmissions of the secondary users (SUs) can be interrupted randomly by the primary users (PUs). That is to say, the PU packets have preemptive priority over the SU packets. In order to enhance the quality of service (QoS) for the SUs, we propose a spectrum access strategy with an ${\alpha}$-Retry policy. A buffer is deployed for the SU packets. An interrupted SU packet will return to the buffer with probability ${\alpha}$ for later retrial, or leave the system with probability (1-${\alpha}$). For mathematical analysis, we build a preemptive priority queue and model the spectrum access strategy with an ${\alpha}$-Retry policy as a two-dimensional discrete-time Markov chain (DTMC).We give the transition probability matrix of the Markov chain and obtain the steady-state distribution. Accordingly, we derive the formulas for the blocked rate, the forced dropping rate, the throughput and the average delay of the SU packets. With numerical results, we show the influence of the retrial probability for the strategy proposed in this paper on different performance measures. Finally, based on the trade-off between different performance measures, we construct a cost function and optimize the retrial probabilities with respect to different system parameters by employing an iterative algorithm.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.191-201
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• 2008

In this paper, we consider an insurance risk model governed by a compound Binomial arrival claim process and by a compound Binomial arrival premium process. Some formulas for the probabilities of ruin and the distribution of ruin time are given, we also prove the integral equation of the ultimate ruin probability and obtain the Lundberg inequality by the discrete martingale approach.

• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.1
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• pp.1-4
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• 2015

This paper presents a heuristic approach to derive the Laplace-Stieltjes transform (LST) and the probability generating function (PGF) of the waiting time distributions of a continuous- and a discrete-time GI/G/1 queue, respectively. This is a new idea to derive the well-known results, the waiting time distribution of GI/G/1 queue, in a different way.