• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.453-460
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• 2006

A discrete-time priority queueing system with place reservation discipline is studied, in which two different types of packets arrive according to batch geometric streams. It is assumed that there is a reserved place in the queue. Whenever a high-priority packet enters the queue, it will seize the reserved place and make a new reservation at the end of the queue. Low-priority arrivals take place at the end of the queue in the usual way. Using the probability generating function method, the joint distribution of system state and the delay distribution for each type are obtained.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.419-438
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• 1995

We investigate a tansient diffusion approximation of queue size distribution in $M^{X}/G^{Y}/c$ system using the diffusion process with elementary return boundary. We choose an appropriate diffusion process which approxiamtes the queue size in the system and derive the transient solution of Kolmogorov forward equation of the diffusion process. We derive an approximation formula for the transient queue size distribution and mean queue size, and then obtain the stationary solution from the transient solution. Accuracy evalution is presented by comparing approximation results for the mean queue size with the exact results or simulation results numerically.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.5
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• pp.304-313
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• 2016

This work suggests a new analysis approach for a discrete-time GI/G/1 queue with multiple vacations. The method used is called a modified supplementary variable technique and our result is an exact transform-free expression for the steady state queue length distribution. Utilizing this result, we propose a simple two-moment approximation for the queue length distribution. From this, approximations for the mean queue length and the probabilities of the number of customers in the system are also obtained. To evaluate the approximations, we conduct numerical experiments which show that our approximations are remarkably simple yet provide fairly good performance, especially for a Bernoulli arrival process.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.1
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• pp.36-43
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• 2002

We analyze bulk service $M/G^{b}/1$ queues using the arrival time approach of Chae et al. (2001). As a result, the decomposition property of the M/G/1 queue with generalized vacations is extended to the $M/G^{b}/1$ queue in which the batch size is exactly a constant b. We also demonstrate that the arrival time approach is useful for relating the time-average queue length PGF to that of the departure time, both for the $M/G^{b}/1$queue in which the batch size is as big as possible but up to the maximum of constant b. The case that the batch size is a random variable is also briefly mentioned.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.523-533
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• 1999

We consider the M/G/1 queueing model with D-policy. The server is turned off at the end of each busy period and is activated again only when the sum of the service times of all waiting customers exceeds a fixed value D. We obtain the distribution of unfinished work and show that the unfinished work decomposes into two random variables, one of which is the unfinished work of ordinary M/G/1 queue. We also derive the distribution of queue waiting time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1104-1110
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• 2006

In this paper we present a simple approach to the joint queue length distribution in the nonpreemptive priority M/G/1 queue. Without using the supplementary variable technique, we derive the joint probability generating function of the stationary queue length at arbitrary time.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.1
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• pp.107-115
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• 2008

We consider the discrete-time GI/G/1/K queue under the early arrival system. Using a modified supplementary variable technique(SVT), we obtain the distribution of the steady-state queue length. Unlike the conventional SVT, the modified SVT yields transform-free results in such a form that a simple two-moment approximation scheme can be easily established.

• IE interfaces
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• v.13 no.4
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• pp.738-744
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• 2000

This Paper presents a method for unfinished work transition probability distribution of modulated $n^*D/D/l$ queue with overload period. The Modulated $n^*D/D/l$ queue is well known as a performance analysis model of ATM multiplexer with superposition of homogeneous periodic on-off traffic sources. Theory of probability by conditioning and results of $N^*D/D/l$ queue are used for analytic methodology. The results from this paper are expected to be applied to general modulated $n^*D/D/l$ queue.

• 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.

• The Transactions of the Korea Information Processing Society
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• v.6 no.11
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• pp.3097-3107
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• 1999

Recently many studies have been done on the Random Early Detection(RED) algorithm as an active queue management and congestion avoidance scheme in the Internet. In this paper we first overview the characteristics of RED and the modified RED algorithms in order to understand the current status of these studies. Then we analyze the RED dynamics by investigating how RED parameters affect router queue behavior. We show the cases when RED fails since it cannot react to queue state changes aggressively due to the deterministic use of its parameters. Based on the RED parameter analysis, we propose a self-adaptive algorithm to cope with this RED weakness. In this algorithm we make two parameters be adjusted themselves depending on the queue states. One parameter is the maximum probability to drop or mark the packet at the congestion state. This parameter can be adjusted to react the long burst of traffic, consequently reducing the congestion disaster. The other parameter is the queue weight which is also adjusted aggressively in order for the average queue size to catch up with the current queue size when the queue moves from the congestion state to the stable state.