• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.385-393
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• 2008

This paper gives transient distributions for the number of customers in the system in the Geo/Geo/1 queue for both the early arrival and the late arrival models.

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.83-91
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• 1996

We first obtain the departure process of a D-BMAP/Geo/1/K queue. The departure process is then exactly characterized by a k-state MMBP in order to capture the burstiness and correlation of the departure process.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.91-105
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• 2019

Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

• The Journal of Natural Sciences
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• v.7
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• pp.75-82
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• 1995

We obtain the departure process of a D-BMAP/Geo/1/K queue. We also study the burstiness and correlation of the departure process. We have observed that the autocorrelation coefficients of the interdeparture time(correlogram) of the departure process may oscillated.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.2
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• pp.51-61
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• 2002

By using the arrival time approach of Chae et at. [6], we derive various performance measures including the queue length distributions (in PGFs) and the waiting time distributions (in LST and PGF) for both M$^{x}$ /G/1 and Geo$^{x}$ /G/1 queueing systems, both under the assumption that the server, when it becomes idle, takes multiple vacations up to a random maximum number. This is an extension of both Choudhury[7] and Zhang and Tian [11]. A few mistakes in Zhang and Tian are corrected and meaningful interpretations are supplemented.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.3
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• pp.483-486
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• 2022

Real time data exchange and information transmission are becoming more and more important these days. The concept of age of information (AoI) was proposed to quantify the freshness of information about the status of a remote source system. The AoI is defined as the amount of time that a packet experiences since it was generated at the source up to now. This paper analyses the age of information for a discrete time Geo/Geo/1/1 status updating system. The stationary probability distribution for peak AoI is obtained. Freshness ratio of information is also derived. Some numerical results obtained by the analysis are presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.1
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• pp.53-60
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• 2007

We consider the discrete-time $Geo^x/G/1$ queues under N-policy with multiple vacations (a single vacation) and setup time. In this queueing system, the server takes multiple vacations (a single vacation) whenever the system becomes empty, and he begins to serve the customers after setup time only if the queue length is at least a predetermined threshold value N. Using the heuristic approach, we derive the mean waiting time for both vacation models. We demonstrate that the heuristic approach is also useful for the discrete-time queues.

• The Journal of Engineering Research
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• v.1 no.1
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• pp.31-40
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• 1997

We first describe an approximation method for fitting a k-state MMBP to the departure process of a D-BMAP/Geo/1/K queue. The fitting model is them used in a simple decomposition algorithm to analyze a tandem configuration of finite capacity queue with cell loss.

• 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.

• The Journal of the Korea Contents Association
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• v.18 no.3
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• pp.34-40
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• 2018

In this study, the optimal buffer size is calculated for seamless video playback on a mobile device. Buffer means the memory space for multimedia packet which arrives in mobile device for video play such as VOD service. If the buffer size is too large, latency time before video playback can be longer. However, if it is too short, playback service can be paused because of shortage of packets arrived. Hence, the optimal buffer size insures QoS of video playback on mobile devices. We model the process of buffering into a discret-time queueing model. Mean busy period length and mean waiting time of Geo/G/1 queue with N-policy is analyzed. After then, we uses the main performance measures to present numerical examples to decide the optimal buffer size on mobile devices. Our results enhance the user satisfaction by insuring the seamless playback and minimizing the initial delay time in VOD streaming process.