• Journal of Korea Society of Industrial Information Systems
• /
• v.21 no.6
• /
• pp.1-12
• /
• 2016

In this paper, we consider a general discrete-time queueing system with D-BMAP(discrete-time batch Markovian arrival process) and D-policy. An idle single server becomes busy when the total service times of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state workload distribution is derived in the form of generating function. Mean workload is derived as a performance measure. Simulation is also performed for the purpose of verification and a simple numerical example is shown.

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

• Journal of the Korean Institute of Intelligent Systems
• /
• v.13 no.3
• /
• pp.293-299
• /
• 2003

This paper discusses a design of intelligent controller with time delay for Internet-based remote control. The finite Markovian process is adopted to model the input delay of the overall control system. It is assumed that the zero and hold devices are used for control input. The Takagi-Sugeno (T-S) fuzzy system with uncertain input delay is utilized to represent nonlinear plant. The continuous-time T-S fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretized T-S fuzzy system is represented by a discrete-time T-S fuzzy system with jumping parameters. The robust stochastic stabilizibility of the jump T-S fuzzy system is derived and formulated in terms of linear matrix inequalities (LMIs). An experimental results is provided to visualize the feasibility of the proposed method.

• Nuclear Engineering and Technology
• /
• v.54 no.1
• /
• pp.275-282
• /
• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Journal of Korea Society of Industrial Information Systems
• /
• v.12 no.2
• /
• pp.16-23
• /
• 2007

Tandem queueing systems well suit for modeling many telecommunication systems. Recently, very general $BMAP/G/1/N/1{\to}{\bullet}/PH/1/M-1$ type tandem queues were constructively studied. In this paper we illustrate application of the obtained results for optimization of a buffer pool design.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.13.1-13
• /
• 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
• /
• v.9 no.3
• /
• pp.32-37
• /
• 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 Korea Society of Information Technology Applications Conference
• /
• 2005.11a
• /
• pp.271-275
• /
• 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.

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

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