• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.107-116
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• 2009

We consider a single server multi-class queueing model with Poisson arrivals and relative priorities. For this queue, we derive a system of equations for the transform of the queue length distribution. Using this system of equations we find the moments of the queue length distribution as a solution of linear equations.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.95-102
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• 2016

Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.

• Journal of Korean Tunnelling and Underground Space Association
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• v.18 no.1
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• pp.41-52
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• 2016

When the queue length of congestion vehicles in tunnel fire is extended beyond tunnel length, the capacity of smoke control system needs to be increased in line with ventilation resistance. However, the vehicle queue length is not defined, so a rational equation is necessary in current fire prevention guideline. This study is intended to propose an equation to calculate the queue length considering the number of vehicles in queue in tunnel fire and evaluate the applicability by tunnel length as well. When it comes to normal tunnel, it is necessary to compare the vehicle queue length with tunnel length up to the length of 1,200 m in a bid to avoid applying the vehicle queue length excessively in case of fire. As a result of evaluation of applicability to model a tunnel, saving the number of jet fan for smoke control appeared to be effective. Besides, quantitative approach to explain the vehicle queue length through the relationship between the percentage of large vehicles and tunnel length was presented. Consequently, when the queue length of the congestion vehicles exceeds the tunnel length in determining the capacity of smoke control system in case of fire, the number of vehicles beyond the tunnel length needs to be excluded from estimating the ventilation resistance by vehicles.

• Proceedings of the KAIS Fall Conference
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• 2003.11a
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• pp.236-242
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• 2003

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.

• 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.

• 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 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.

• Journal of Industrial Technology
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• v.19
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• pp.423-428
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• 1999

In this paper, We propose a new flow control scheme based on Queue Dynamics and it's Estimate Information in order to achieve higher throughput and network efficiency using control of the best-effort traffic. The feedback Information gives a result that compare queue length with queue threshold. Traffic changes at the time when queue length is cross over under the queue thresholds. The performance of the purposed scheme has been analyzed mathematically and we verify efficiency of the proposed method by means of simulation.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.523-533
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• 2006

We analyze two finite buffers queueing system with priority scheduling dependent upon queue length. Customers are classified into two types ( type-l and type-2 ) according to their characteristics. Here, the customers can be considered as traffics such as voice and data in telecommunication networks. In order to support customers with characteristics of burstiness and time-correlation between interarrival, the arrival of the type-2 customer is assumed to be an Markov- modulated Poisson process(MMPP). The service order of customers in each buffer is determined by the queue length of two buffers. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, performance measures such as loss and mean delay are derived.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.15 no.3
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• pp.45-51
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• 2016

Existing real-time signal control system was brought up typical problems which are supersaturated condition, point detection system and loop detection system. For that reason, the next generation signal control system of advanced form is required. Following thesis aimed at calculating queue length for the next generation signal control system to utilize basic parameter of signal control in crossing queue instead of the volume of real-time through traffic. Overflow saturated condition which was appeared as limit of existing system was focused to set-up range. Real-time location information of individual vehicle which is collected by GPS data. It converted into the coordinate to apply shock wave model with an linear equation that is extracted by regression model applied by a least square. Through the calculated queue length and link length by contrast, If queue length exceed the link, queue of downstream intersection is included as queue length that upstream queue vehicle is judeged as affecting downstream intersection. In result of operating correlation analysis among link travel time to judge confidence of extracted queue length, Both of links were shown over 0.9 values. It is appeared that both of links are highly correlated. Following research is significant using real-time data to calculate queue length and contributing to signal control system.