• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.547-557
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• 2005

In this paper, we investigate the packet delay distribution of a dynamic bandwidth allocation(DBA) scheme in an Ethernet passive optical network(EPON). We focus on the gated-exhaustive vacation system. We assume that input packets arrive at an optical network unit(ONU) according to general interarrival distribution. We use a discrete time queueing model in order to find the packet delay distribution of the gated-exhaustive system with the primary transmission queue and the secondary input queue. We give some numerical examples to investigate the mean packet delays of the proposed queueing model to analyze the DBA scheme in an EPON.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.483-498
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• 1994

Suppose that a stationary process ${X_t}$ has a marginal distribution whose support consists of sufficiently large integers. We are concerned with some analogous law of large numbers for such distribution function F. In particular, we determine a weak law of large numbers for maximum queueing length in $M/M\infty$ system. We also present a limiting behavior for the maxima based on AR(1) process with binomial thining and poisson marginals (INAR(1)) introduced by E. Mckenzie. It turns out that the result of AR(1) process is the same as that of $M/M/\infty$ queueing process in limit when we observe the queues at regularly spaced intervals of time.

• Korean Management Science Review
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• v.4
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• pp.60-75
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• 1987

This paper introduces the outlines of the state-of-the-art in studying FMSs using analytical queueing network models. These include Jackson networks, reversible networks and approximate models of non-product-form networks. the focus is on identifying the major features of models as they relate to the operational characteristics of FMSs. Prescriptive models concerning the optimal design and/or operational control of FMS networks are also discussed. We notice that the presentation of materials in this paper basically follows Yao and Buzacott, On Queueing Network Models of Flexible Manufacturing Systems(FMSs), invited and published on Queueing Systems, Theory and Application 1(1986). For other analytical models of FMSs, refer to Buzacott and Yao, Flexible Manufacturing Systems : A Review of Analytical Models, Management Science 32, No.7(1986).

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.4
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• pp.297-302
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• 2005

Kopzon and Weiss adopted the notion of push-pull into the queueing system recently. We extend this queueing system to the ($N_1,N_2$)-policy version such that the original system corresponds to the special case $N_1=N_2=1$. For the extended system, we perform the cycle analysis and obtain the PGF of the stationary number of customers in the system.

• Industrial Engineering and Management Systems
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• v.15 no.2
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• pp.131-142
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• 2016

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.

• Korean Management Science Review
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• v.28 no.1
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• pp.117-127
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• 2011

In the Multi-Echelon maintenance environment, METRIC(Multi-Echelon Technique for Repairable Item Control) has been used in several different inventory level selection models, such as MOD-METRIC, Vari-METRIC, and Dyna- ETRIC. While this model's logic is easy to be implemented, a critical assumption of infinite maintenance capacity would deteriorate actual values, especially Expected Back Order(EBO)s for each item. To improve the accuracy of EBO, we develop two models using simulation and queueing theory that calculates EBO considering finite capacity. The result of our numerical example shows that the expected backorder from our model is much closer to the true value than the one from Vari-METRIC. The queueing model is preferable to the simulation model regarding the computational time.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.553-568
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• 1999

This paper is of concern to queueing analysis of the dynamic rate leaky bucket(LB) scheme in which the token generation interval changes according to the buffer state at a token generation epoch. Cell arrivals are assumed to follow a Markovian arrival process (MAP) which is weakly dense in the class of the stationary point processes. By using the embedded Markov chain method we obtain the probability distribution of the system state at a token generation epoch and an arbitrary time. Some simple numerical examples also are provided to show the effects of the proposed LB scheme.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.879-890
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• 2002

In this paper we consider open queueing system with a Poisson arrival process which have a finite upper bound on the arrival rate for which the system is stable. Interpolation approximations for quantities of interest, such as moments of the sojourn time distribution, have previously been developed for such systems, utilizing exact light and heavy traffic limits. These limits cannot always be easily computed for complex systems. Thus we consider an interpolation approximation where all of the relevant information is estimated via simulation. We show that all the relevant information can in fact be simultaneously estimated in a single regenerative simulation at any arrival rate. In addition to light and heavy traffic limits, both the quantity of interest and its derivative (with respect to the arrival rate) are estimated at the arrival rate of the simulation. All of the estimates are then combined, using a least squares procedure, to provide an interpolation approximation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.261-264
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• 2000

When there ate several classes of customers demanding service times with different distributions at some stations of a queueing network, the stability problem becomes suddenly complicated compared with the single class case. Recently many researchers had tried to find some kind of stability conditions for multiclass queueing networks, but did not get significant results except in very limited 2-station cases. In this study, we try to develop some dynamic control techniques which can guarantee the stability under the nominal traffic condition. Our approach includes the randomization method and the leaky bucket control scheme. Also, we mention other possibilities such as the discrete-review approach and the generalized round-robin technique. Both theoretical and experimental results will be presented.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.89-94
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• 2001

There are many queueing systems where customers wait for service up to a certain amount of time and leave the system if they are not served during that time. This paper considers a finite capacity multi-server queueing system with Poisson input and Erlang service time, where a customer becomes a lost customer when his service has not begun within an exponential patient time after his arrival. Performance measures such as average queue length, the average number of customers in service, and the proportion of lost customers can be obtained exactly through the proposed numerical solution procedure.