• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.443-460
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• 1995

We consider a G/M/1 vacation model where the vacation time has k-stages generalized Erlang distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the limiting probabilities of the queue length at arrival time points and arbitrary time points simultaneously. Operational calculus technique is used for solving non-homogeneous difference equations.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.377-385
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• 2013

We consider a compound Poisson risk model in which the premium rate changes when the surplus exceeds a threshold. The explicit form of the ruin probability for the risk model is obtained by deriving and using the overflow probability of the workload process in the corresponding M/G/1 queueing model.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.1
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• pp.125-129
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• 1999

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.4
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• pp.419-423
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• 2007

In this paper, we consider the M/G/1 queueing system with randomized control of T-policy. Whenever the busy period ends, the server is turned off and takes multiple vacations whose interval is fixed time T with probability p or stays on and waits for arriving customers with probability 1-p. We introduce the cost function and determine the optimal combination of (p, T) to minimize the average cost per unit time.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.941-948
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• 2013

We introduce the $P^M_{{\lambda},{\tau}}$ service policy, as a generalized two-stage service policy of the $P^M_{\lambda}$ policy of Bae et al. (2002) for an M/G/1 queueing system. By using the level crossing theory and solving the corresponding integral equations, we obtain the explicit expression for the stationary distribution of the workload in the system.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.179-186
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• 1993

We derive the arbitrary time point system size distribution of M/ $G^{B}$1 queue in which late arrivals are not allowed to join the on-going service. The distribution is given by P(z) = $P_{4}$(z) $S^{*}$ (.lambda.-.lambda.z) where $P_{4}$ (z) is the probability generating function of the queue size and $S^{*}$(.theta.) is the Laplace-Stieltjes transform of the service time distribution function. We also derive the distribution of the service siez at arbitrary point of time. time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.2
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• pp.1-10
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• 2016

In this paper, we present a new way to derive the mean cycle time of the G/G/m failure prone queue when the loading of the system approaches to zero. The loading is the relative ratio of the arrival rate to the service rate multiplied by the number of servers. The system with low loading means the busy fraction of the system is low. The queueing system with low loading can be found in the semiconductor manufacturing process. Cluster tools in semiconductor manufacturing need a setup whenever the types of two successive lots are different. To setup a cluster tool, all wafers of preceding lot should be removed. Then, the waiting time of the next lot is zero excluding the setup time. This kind of situation can be regarded as the system with low loading. By employing absorbing Markov chain model and renewal theory, we propose a new way to derive the exact mean cycle time. In addition, using the proposed method, we present the cycle times of other types of queueing systems. For a queueing model with phase type service time distribution, we can obtain a two dimensional Markov chain model, which leads us to calculate the exact cycle time. The results also can be applied to a queueing model with batch arrivals. Our results can be employed to test the accuracy of existing or newly developed approximation methods. Furthermore, we provide intuitive interpretations to the results regarding the expected waiting time. The intuitive interpretations can be used to understand logically the characteristics of systems with low loading.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1035-1045
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• 2001

We present two decomposition approximations for the mean sojourn times in open single class queing networks. If there is a single bottleneck station, the approximations are asymptotically exact in both light and heavy traffic. When applied to a Jackson network or an M/G/1 queue, these approximations are exact for all values of the traffic intensity.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2450-2469
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• 2018

In this paper, we develop a spatiotemporal model to analysis of cellular user in underlay D2D communication by using stochastic geometry and queuing theory. Firstly, by exploring stochastic geometry to model the user locations, we derive the probability that the SINR of cellular user in a predefined interval, which constrains the corresponding transmission rate of cellular user. Secondly, in contrast to the previous studies with full traffic models, we employ queueing theory to evaluate the performance parameters of dynamic traffic model and formulate the cellular user transmission mechanism as a M/G/1 queuing model. In the derivation, Embedded Markov chain is introduced to depict the stationary distribution of cellular user queue status. Thirdly, the expressions of performance metrics in terms of mean queue length, mean throughput, mean delay and mean dropping probability are obtained, respectively. Simulation results show the validity and rationality of the theoretical analysis under different channel conditions.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.841-844
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• 2002

Recently there has been an increasing interest in queueing models with disasters. Upon arrival of a disaster, all the customers present are noshed out. Queueing models with disasters have been applied to the problems of failure recovery in many computer networks systems, database systems and telecommunication networks in this paper, we suffest the steady state and sojourn time distributions of the M/G/l model with disaster and mass alway when the system is empty.