• 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 $K\;\longrightarrow\;\infty$.

• Journal of Korea Multimedia Society
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• v.18 no.12
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• pp.1475-1482
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• 2015

In network routers, buffers are used to resolve congestion and reduce packet loss rate whenever congestion occurs at bottleneck link. Most of the existing methods to manage such buffers focus only on queue-length-based control as one loop which have some issues of low link utilization and system stability. In this paper, we propose a novel framework which exploits two-loop control method, e.g. queue-length and congestion window size, combined with optimal margin method to facilitate parameter choices. Simulation results in ns-2 demonstrate that bottleneck link performance can be improved with higher link utilization (85%) and shorter queue length (22%) than the current deployed scheme in commercial routers (RED and DropTail).

• Journal of the Korea Society for Simulation
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• v.27 no.3
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• pp.45-52
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• 2018

We consider the busy period of an M/G/1/K queueing system with queue-length-dependent overload control policy. A variant of an oscillating control strategy that was recently analyzed by Choi and Kim (2016) is considered: two threshold values, $L_1({\leq_-}L_2)$ and $L_2({\leq_-}K)$, are assumed, and service rate and arrival rate are adjusted depending on the queue length to alleviate congestion. We investigate the busy period of an M/G/1/K queue with two overload control policies, and present the formulae to obtain the expected length of a busy period for each control policy. Based on the numerical examples, we conclude that the variability and expected value of the service time distribution have the most influence on the length of a busy period.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.36-48
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• 1991

In this study, an efficient algorithm is developed to compute steady state probabilities for the following M$_{x}$G/1 server vacation system under control-operating poligy: At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length at this time is equal to or greater than a prespecified threshold value r, he begins to serve the queue until it is empty.y.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.319-330
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• 2002

We consider BMAP/G/1 queueing system with N-policy and multiple vacations. We derive the vector generating functions of the queue length in a factorized form and interpret the factorization. We also derive the mean queue length.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.11
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• pp.1946-1958
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• 2011

Wireless Sensor Network (WSN) is made up of a number of sensor nodes and base stations. Traffic flow in WSN appears self-similar due to its data delivery process, and this impacts queue length greatly and makes queuing delay worse. Active queue management can be designed to improve QoS performance for WSN. In this paper, we propose self-similar traffic rate estimating algorithm named Power-Law Moving Averaging (PLMA) to regulate packet marking probability. This algorithm improves the availability of the rate estimation algorithm under the self-similar traffic condition. Then, we propose an adaptive Proportional Integral algorithm (SSPI) based on the estimation of the Self-Similar traffic rate by PLMA. Simulation results show that SSPI can achieve lower queue length jitter and smaller setting time than PI.

• Management Science and Financial Engineering
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• v.9 no.2
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• pp.1-12
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• 2003

For a stationary queue with BMAP arrivals, Takine and Takahashi [8] present a relationship between the queue length distributions at a random epoch and at a departure epoch by using the rate conservation law of Miyazawa [6]. In this note, we derive the same relationship by using the elementary balance equation, ‘rate-in = rate-out’. Along the same lines, we additionally derive relationships between the queue length distributions at a random epoch and at an arrival epoch. All these relationships hold for a broad class of finite-as well as infinite-capacity queues with BMAP arrivals.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.4
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• pp.390-396
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• 2002

We present a meaningful interpretation of the equations for the steady-state queue length distribution of the GI/GI/c/K queue so that the equations are better understood and become more applicable. As a byproduct, we present an exact expression of the mean queue waiting time for the M/GI/c queue.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.1
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• pp.110-122
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• 1993

When voice is transmitted through packet switching network, there needs a overload control, that is, a control for the congestion which lasts short periods and occurrs in local extents. In this thesis, we analyzed the performance of the statistical packet voice multiplexer using the overload control strategy by bit dropping. We assume that the voice is coded accordng to (4,2) embedded ADPCM and that the voice packet is generated and transmitted according to the procedures in the CCITT recomendation G. 764. For the performance analysis, we must model the superposed packet arrival process to the multiplexer as exactly as possible. It is well known that interarrival times of the packets are highly correlated and for this reason MMPP is more suited for the modelling in the viewpoint of accuracy. Hence the packet arrival process in modeled as MMPP and the matrix geometric method is used for the performance analysis. Performance analysis is similar to the MMPP IG II queueing system. But the overload control makes the service time distribution G dependent on system status or queue length in the multiplexer. Through the performance analysis we derived the probability generating function for the queue length and using this we derived the mean and standard deviation of the queue length and waiting time. The numerical results are verified through the simulation and the results show that the values embedded in the departure times and that in the arbitrary times are almost the same. Results also show bit dropping reduces the mean and the variation of the queue length and those of the waiting time.

• Journal of Internet Computing and Services
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• v.1 no.2
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• pp.29-37
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• 2000

Asynchronous transfer mode is flexible to support multimedia communication services using asynchronous time-sharing and statistical multimedia techniques to the existing data communication area, ATM ABR service controls network traffic using feedback information on the network congestion situation in order to guarantee the demanded service qualities and the available cell rates, In this paper we apply the control method using queue length prediction to the formation of feedback information for more efficient ABR traffic control. If backward node receive the longer delayed feedback information on the impending congestion, the switch can be already congested from the uncontrolled arriving traffic and the fluctuation of queue length can be inefficiently high in the continuing time intervals, The feedback control method proposed in this paper predicts the queue length in the switch using the slope of queue length prediction function and queue length changes in time-series, The predicted congestion information is backward to the node, NLMS and neural network are used as the predictive control functions, and they are compared from performance on the queue length prediction. Simulation results show the efficiency of the proposed method compared to the feedback control method without the prediction, Therefore, we conclude that the efficient congestion and stability of the queue length controls are possible using the prediction scheme that can resolve the problems caused from the longer delays of the feedback information.