• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.343-350
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• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.419-438
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• 1995

We investigate a tansient diffusion approximation of queue size distribution in $M^{X}/G^{Y}/c$ system using the diffusion process with elementary return boundary. We choose an appropriate diffusion process which approxiamtes the queue size in the system and derive the transient solution of Kolmogorov forward equation of the diffusion process. We derive an approximation formula for the transient queue size distribution and mean queue size, and then obtain the stationary solution from the transient solution. Accuracy evalution is presented by comparing approximation results for the mean queue size with the exact results or simulation results numerically.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.383-396
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• 2013

We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.3
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• pp.179-186
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• 1993

We derive the arbitrary time point system size distribution of M/ $G^{B}$1 queue in which late arrivals are not allowed to join the on-going service. The distribution is given by P(z) = $P_{4}$(z) $S^{*}$ (.lambda.-.lambda.z) where $P_{4}$ (z) is the probability generating function of the queue size and $S^{*}$(.theta.) is the Laplace-Stieltjes transform of the service time distribution function. We also derive the distribution of the service siez at arbitrary point of time. time.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.275-282
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• 2010

This paper analyzes a discrete-time bulk-service queue with probabilistic bulk size, where the service process is interrupted by a Markov chain. We study the joint probability generating function of system occupancy and the state of the Markov chain. We derive several performance measures of interest, including average system occupancy and delay distribution.

• 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 the Korean Operations Research and Management Science Society
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• v.25 no.2
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• pp.59-66
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• 2000

In this paper we propose an approximation analysis for the system size distribution of the M/G/c system which is transform-free,. At first we borrow the system size distribution from the Markovian service models and then introduce a newly defined parameter in place of traffic intensity. In this step we find the distribution of the number of customers up to c. Next we concentrate on each waiting space of the queue separately rather than consider the entire queue as a whole. Then according to the system state of the arrival epoch we induce the probability distribution of the system size recursively. We discuss the effectiveness of this approximation method by comparing with simulation for the mean system size.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-236
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• 1995

The purpose of this paper is to provide a transient diffusion approximation of queue size distribution for M/G/m/N system. The M/G/m/N system can be expressed as follows. The interarrival times of customers are exponential and the service times of customers have general distribution. The system can hold at most a total of N customers (including the customers in service) and any further arriving customers will be refused entry to the system and will depart immediately without service. The queueing system with finite capacity is more practical model than queueing system with infinite capacity. For example, in the design of a computer system one of the important problems is how much capacity is required for a buffer memory. It its capacity is too little, then overflow of customers (jobs) occurs frequently in heavy traffic and the performance of system deteriorates rapidly. On the other hand, if its capacity is too large, then most buffer memories remain unused.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.715-733
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• 1995

We present a transient queue size distribution for $M/G/m/N$ queue with state dependent arrival rates, using the diffusion process with piecewise constant diffusion parameters, with state space [0, N] and elementary return boundaries at x = 0 and x = N. The model considered here contains not only many basic model but the practical models such as as two-node cyclic queue, repairmen model and overload control in communication system with finite storage buffer. For the accuracy check, we compare the approximation results with the exact and simulation results.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.2
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• pp.1-12
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• 1997

We consider an M/M/2 queue with two servers placed in series. System performance measures that we present in closed expressions are the first and the second moments for the system size, the queue walting time and the sojourn time. We also present an algorithm for computing the queue waiting time distribution function based on the randomization method. As an application, we analyze the double tollbooth system and compare its performance with the conventional single tollbooth system's.