• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.805-814
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• 1999

We consider an MMPP/G/1/K finite queue with two-level threshold overload control. This model has frequently arisen in the design of the integrated communication systems which support a wide range applications having various Quality of Service(QoS) requirements. Through the supplementary variable method, se derive the queue length distribution.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.285-295
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• 2001

We consider a queueing system under overload control to support bursty traffic. The queueing system under overload control is modelled by MMBP/D1/K queue with two thresholds on buffer. Arrival of customer is assumed to be a Markov-modulated Bernoulli process (MMBP) by considering burstiness of traffic. Analysis is done in discrete-time case. Using the generating function method, we obtain the stationary queue length distribution. Finally, the loss probability and the waiting time distribution of a customer are given.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.721-732
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• 2008

A single server infinite capacity queueing system with Poisson arrival and a general service time distribution along with repeated attempt and server vacation is considered. We made a comprehensive analysis of the system including ergodicity and limiting behaviour. Some operating characteristics are derived and numerical results are presented to test the feasibility of the queueing model.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.405-414
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• 2004

This paper considers overload control in telecommunication networks. Markov-modulated Bernoulli process ( MMBP ) has been extensively used to model bursty traffics with time-correlation. Thus, we investigate the transient behavior of the queueing system MMBP/D/l/K queue with two thresholds. The model is analyzed recursively by using the generating function method. We obtain the transient queue length distribution and waiting time distribution at an arbitrary time. The transient behavior of the queueing system helps observing the temporary system behavior.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.11
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• pp.2170-2178
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• 1994

Our previously proposed method is further applied to find the queue length distribution of MMPP/D1 in an ATM multiplexer. We derive some useful relationship between the queue distribution seen by arriving cells and for a server befor each service. The relations were used to improve out approximation. For MMPP/D1 the calculated results show a good agreement with those obtained by a simulation of the system. Furthermore, our approximation provides fast numerical algorithms for general traffic models. These advantages demomstrate that our approximation method is useful for a fast and accurate traffic analysis in ATM networks.

• Journal of Korea Society of Industrial Information Systems
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• v.22 no.1
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• pp.23-32
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• 2017

In this paper, We suggest a unified approach for the analysis of discrete-time MAP/G/1 queueing system. Many researches on the D-MAP/G/1 queue have been used different approach to analyze system queue length and waiting time for the same system. Therefore, a unified framework for analyzing a system is necessary from a viewpoint of system design and management. We first derived steady-state workload distribution, and then waiting time and sojourn time are derived by the result of workload analysis. Finally, system queue length distribution is derived with generating function from the sojourn time distribution.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.5
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• pp.1554-1566
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• 2014

Cloud Computing allows application providers seamlessly scaling their services and enables users scaling their usage according to their needs. In this paper, using queuing game model, we present service scheduling schemes which are used in software as a service (SaaS). The object is maximizing the Cloud Computing platform's (CCP's) payoff via controlling the service requests whether to join or balk, and controlling the value of CCP's admission fee. Firstly, we treat the CCP as one virtual machine (VM) and analyze the optimal queue length with a fixed admission fee distribution. If the position number of a new service request is bigger than the optimal queue length, it balks. Otherwise, it joins in. Under this scheme, the CCP's payoff can be maximized. Secondly, we extend this achievement to the multiple VMs situation. A big difference between single VM and multiple VMs is that the latter one needs to decide which VM the service requests turn to for service. We use a corresponding algorithm solve it. Simulation results demonstrate the good performance of our schemes.

• 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 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 Society of Transportation
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• v.23 no.8 s.86
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• pp.181-191
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• 2005

This study developed an algorithm for real-time signal control based on the detection system that can collect sectional travel time. The signal control variable is maximum queue length per cycle and this variable has a sectional meaning. When a individual vehicle pass through the detector, we can gather the vehicle ID and the detected time. Therefor we can compute the travel time of an individual vehicle between consecutive detectors. This travel time informations were bisected including the delay and not. We can compute queue withdrawing time using this bisection and the max queue length is computed using the deterministic delay model. The objective function of the real-time signal control aims equalization of queue length for all direction. The distribution of the cycle is made by queue length ratios.