• IE interfaces
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• v.25 no.3
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• pp.283-289
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• 2012

M/G/1 queue with server vacations period depending on the previous vacation and customer's arrival is considered. Most existing studies on M/G/1 queue with server vacations assume that server vacations are independent of customers' arrival. However, some vacations are terminated by some class of customers' arrival in certain queueing systems. In this paper, therefore, we investigate M/G/1 queue with server vacations where each vacation period has different distribution and vacation length is influenced by customers' arrival. Laplace-Stieltjes transform of the waiting time distribution and the distribution of number of customers waiting for each class of customers are respectively derived. As performance measures, mean waiting time and average number of customers waiting for each class of customers are also derived.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.729-738
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• 1995

We consider a priority-based packet-switching system with three phases of the packet transmission time. Each packet belongs to one of several priority classes, and the packets of each class arrive at a switch in a Poison process. The switch transmits queued packets on a priority basis with three phases of preemption mechanism. Namely, the transmission time of each packet consists of a preemptive-repeat part for the header, a preemptive-resume part for the information field, and a nonpreemptive part for the trailer. By an exact analysis of the associated queueing model, we obtain the Laplace-Stieltjes transform of the distribution function for the delay, i.e., the time from arrival to transmission completion, of a packet for each class. We derive a set of equations that calculates the mean response time for each class recursively. Based on this result, we plot the numerical values of the mean response times for several parameter settings. The probability generating function and the mean for the number of packets of each class present in the system at an arbitrary time are also given.

• Wind and Structures
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• v.29 no.6
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• pp.389-403
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• 2019

In this study, two original spectral representations of stationary stochastic fields, say the continuous proper orthogonal decomposition (CPOD) and the frequency-wavenumber spectral representation (FWSR), are derived from the Fourier-Stieltjes integral at first. Meanwhile, the relations between the above two representations are discussed detailedly. However, the most widely used conventional Monte Carlo schemes associated with the two representations still leave two difficulties unsolved, say the high dimension of random variables and the incompleteness of probability with respect to the generated sample functions of the stochastic fields. In view of this, a dimension-reduction model involving merely one elementary random variable with the representative points set owing assigned probabilities is proposed, realizing the refined description of probability characteristics for the stochastic fields by generating just several hundred representative samples with assigned probabilities. In addition, for the purpose of overcoming the defects of simulation efficiency and accuracy in the FWSR, an improved scheme of non-uniform wavenumber intervals is suggested. Finally, the Fast Fourier Transform (FFT) algorithm is adopted to further enhance the simulation efficiency of the horizontal stochastic wind velocity fields. Numerical examplesfully reveal the validity and superiorityof the proposed methods.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.153-162
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• 1997

M/G/1 queueing system is one of the most widely used one to model the real system. When operating a real systems, since it often takes cost, some control policies that change the operation scheme are adopted. In particular, the N-policy is the most popular among many control policies. Almost all researches on queueing system are based on the assumption that the arrival rates of customers into the queueing system is constant, In this paper, we consider the M/G/1 queueing system whose arrival rate varies according to the servers status : idle, set-up and busy states. For this study, we construct the steady state equations of queue lengths by means of the supplementary variable method, and derive the PGF(probability generating function) of them. The L-S-T(Laplace Stieltjes transform) of waiting time and average waiting time are also presented. We also develop an algorithm to find the optimal N-value from which the server starts his set-up. An analysis on the performance measures to minimize total operation cost of queueing system is included. We finally investigate the behavior of system operation cost as the optimal N and arrival rate change by a numerical study.