• Journal of Communications and Networks
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• v.7 no.1
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• pp.87-92
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• 2005

This paper presents basic queueing analysis contributing to teletraffc theory, with commonly accessible mathematical tools. This paper studies queueing systems with bulk arrivals. It is assumed that the number of arrivals and the expected number of arrivals in each bulk are bounded by some constraints B and (equation omitted), respectively. Subject to these constraints, convexity argument is used to show that the bulk-size probability distribution that results in the worst mean queue performance is an extremal distribution with support {1, B} and mean equal to A. Furthermore, from the viewpoint of security against denial-of-service attacks, this distribution remains the worst even if an adversary were allowed to choose the bulk-size distribution at each arrival instant as a function of past queue lengths; that is, the adversary can produce as bad queueing performance with an open-loop strategy as with any closed-loop strategy. These results are proven for an arbitrary arrival process with bulk arrivals and a general service model.

• 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 Operations Research and Management Science Society
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• v.26 no.4
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• pp.47-53
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• 2001

We demonstrate that the arrival time approach of Chae et al. [4], originally proposed for continuous-time queues, is also useful for discrete-time queues. The approach serves as a simple alternative to finding the probability generating functions of the queue lengths for a variety of discrete-time single-server queues with bulk arrivals and bulk services.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9B
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• pp.783-792
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• 2003

We consider a finite-buffer discrete-time queueing system with fixed-size bulk-service discipline: Geo/ $G^{B}$1/K＋B. The main purpose of this paper is to present a performance analysis of this system that has a wide range of applications in Asynchronous Transfer Mode (ATM) and other related telecommunication systems. For this purpose, we first derive the departure-epoch probabilities based on the embedded Markov chain method. Next, based on simple rate in and rate out argument, we present stable relationships for the steady-state probabilities of the queue length at different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of number of packets in the system at three different epochs and the loss probability. The numerical results are presented for a deterministic service-time distribution - a case that has gained importance in recent years.s.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.491-507
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• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.247-255
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• 2002

The objective of this paper is to clarify the decomposition property for $M^{X}$/G/1 queues with generalized vacations so that the decomposition property is better understood and becomes more applicable. As an example model, we use the $M^{X}$/G/1 queue with setup time. For this queue, we correct Choudhry's (2000) steady-state queue size PGF and derive the steady-state waiting time LST. We also present a meaningful interpretation for the decomposed steady-state waiting time LST.

• The KIPS Transactions:PartC
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• v.18C no.6
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• pp.433-440
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• 2011

In this paper, we propose a new scheduling method that can guarantee reliable jitter by minimizing the queue length variation in the streaming service provisioning such as IPTV and VoD. The amount of traffic to be delivered within a certain time is very fluid because MPEG-4 and H.264 encoders use VBR(Variable Bit Rate) for delivering video streaming traffic. This VBR characteristic increases the end-to-end propagation delay variation when existing scheduling methods are used for delivering video frames. Therefore, we propose the new scheduling method that can minimize change rate of queue length by adaptively controling service rate taking into account the size of bulk incoming packets and arrival rate for bulk streaming traffic. Video frames can be more reliably transmitted through the minimization of the queue length variation using the proposed method. We use the queueing model and also carry out OPNET simulation to validate the proposed method.