• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.13.1-13
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• 2003

The Markovian arrival process with marked transitions (MMAP) is useful in modeling input processes of stochastic system with several types. Especially, the MMAP can be used to model the phenomena where the correlation of different types is considered. In this talk we discuss modeling issues for the queue with three types of customers; ordinary customers, negative customers and disasters which are correlated by using MMAP. We also present the recent results and further studies.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.3
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• pp.32-37
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• 2004

This paper investigates the mathematical model of multi-server retrial queueing system with the Batch Markovian Arrival Process (BMAP), the Phase type (PH) service distribution and the finite buffer. The sufficient condition for the steady state distribution existence and the algorithm for calculating this distribution are presented. Finally, a formula to solve loss probability in the case of complete admission discipline is derived.

• Proceedings of the Korean Society for Quality Management Conference
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• 2007.04a
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• pp.461-465
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• 2007

The BMAP/M/N/O queueing system operating in Markovian random environment is investigated. The stationary distribution of the system is calculated. Loss probability and other performance measures are calculated. Numerical experiments which show the necessity of taking into account the influence of random environment and correlation in input flow are presented.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.271-275
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• 2005

Queueing models are good models for fragments of communication systems and networks, so their investigation is interesting for theory and applications. Theses queues may play an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, in this paper we illustrate that the batch size distribution affects the loss probability, which is the main performance measure of a finite buffer queues.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.115-117
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• 2002

In this paper, we obtain an explicit formula of the Laplace transform of the forward recurrence time at finite time t > 0 in an alternating renewal process, by adopting a Markovian approach. As a consequence, we obtain the first two moments of the forward recurrence 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 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.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.277-292
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• 2006

We consider a single-server queue with service time distribution of phase type where positive customers, negative customers and disasters arrive according to a Markovian arrival process with marked transitions (MMAP). We derive simple formulae for the stationary queue length distributions. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions under the combinations of removal policies and service disciplines are also obtained by using the absorption time distribution of a Markov chain.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.611-625
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• 1999

We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.985-1004
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• 2016

We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.