• 대한산업공학회지
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• 제8권2호
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• pp.15-21
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• 1982

This paper offers an alternative to the common probability generating function approach to the solution of steady state equations when a Markovian queue has a multivariate state space. Identifying states and substates and grouping them into vectors appropriately, we formulate a two - dimensional Markovian queue as a Markov chain. Solving the resulting matrix equations the transition point steady state probabilities (SSPs) are obtained. These are then converted into arbitrary time SSPs. The procedure uses only probabilistic arguments and thus avoids a large and cumbersome state space which often poses difficulties in the solution of steady state equations. For the purpose of numerical illustration of the approach we solve a Markovian queue with one server and two classes of customers.

• 품질경영학회지
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• 제28권4호
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• pp.99-105
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• 2000

This paper attempts to apply Markove chain theory to literary works. the objective of this paper is to show the trend of authors and his works by way of Markovian Models. In this introductory research, it is useful to make simple criteria as virtue and evil, good and bad, justice and injustice, positive and negative, man and woman, etc. Markovian transition matrixes which are derived by M.L.E. and A.U.E are almost same. In case of Hamlet, we are able to know the author of Hamlet or his works are inconsistent and fickle.

• 대한산업공학회지
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• 제42권1호
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• pp.30-37
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• 2016

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers' service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

• 산업공학
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• 제24권4호
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• pp.323-329
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• 2011

We develop a stochastic model to predict the score of a soccer match. We describe the scoring process of the soccer match as a markovian arrival process (MAP). To do this, we define a two-state underlying Markov chain, in which the two states represent the offense and defense states of the two teams to play. Then, we derive the probability vector generating function of the final scores. Numerically inverting this generating function, we obtain the desired probability distribution of the scores. Sample numerical examples are given at the end to demonstrate how to utilize this result to predict the final score of the match.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.553-568
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• 1999

This paper is of concern to queueing analysis of the dynamic rate leaky bucket(LB) scheme in which the token generation interval changes according to the buffer state at a token generation epoch. Cell arrivals are assumed to follow a Markovian arrival process (MAP) which is weakly dense in the class of the stationary point processes. By using the embedded Markov chain method we obtain the probability distribution of the system state at a token generation epoch and an arbitrary time. Some simple numerical examples also are provided to show the effects of the proposed LB scheme.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.1045-1053
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• 2003

Markovian EWMA control chart for simultaneously monitoring mean vector of the several correlated quality characteristics is investigated. Properties of multivariate Shewhart chart and EWMA chart are evaluated for matched FSI (fixed sampling interval) and VSI(variable sampling interval) scheme. We obtained VSI EWMA chart is more efficient than Shewhart chart for small or moderate shifts. And, we obtained stablized numerical results with Markov chain method when the number of transient state is greater than 100.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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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.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2004년도 품질경영모델을 통한 가치 창출
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• pp.499-502
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• 2004

Multi-server Markovian retrial model with heterogeneous servers is analyzed. Arriving customers constitute the MMAP(Marked Markovian Arrival Process). Distribution of the primary customers among the servers is performed randomly depending on the type of a customer and the number of the server. Customers from the orbit have the exponential service time distribution with a parameter depending on the server only. The choice of the server for a retrial is made randomly as well. Multidimensional continuous time Markov chain describing operation of the model is investigated by means of reducing to asymptotically quasi-toeplitz Markov chaius.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제4권4호
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• pp.560-574
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• 2010

In this paper, the relationship between the energy efficiency and spectrum efficiency in a two-cell cellular network is obtained, and the impact of multi-antenna on the energy efficiency of cellular network is analyzed and modeled based on two-state Markovian wireless channels. Then, the energy efficiency of multi-cell cellular networks with co-channel interference is investigated. Simulation results verify the proposed model and the energy-spectrum efficiency tradeoffs in cellular networks with multi-antenna and co-channel interference.

• Industrial Engineering and Management Systems
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• 제15권2호
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• pp.131-142
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• 2016

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.