• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.83-100
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• 2000

Many queueing systems such as M/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers and MAP/M/$\infty$ queue can be modeled by a level dependent quasi-birth-death(LDQBD) process with linear transition rates of the form ${\lambda}_k$={\alpga}{+}{\beta}k$ at each level $\kappa$. The purpose of this paper is to propose an algorithm to find transient distributions for LDQBD processes with linear transition rates based on the adaptive uniformization technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results.

• 대한수학회논문집
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• 제10권4호
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• pp.975-980
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• 1995

We suggest an improvement of the algorithm in [2] for calculating the transient solutions for continuous time Markov chain with countable state space.

• 대한산업공학회지
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• 제17권1호
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• pp.117-126
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• 1991

When {X(t), t ${\geq}$ 0} is a Markov process representing time-varying system states, we develop efficient bounding methods for some time-dependent performance measures. We use the discretization technique for stochastically monotone Markov processes and a combination of discretization and uniformization for Markov processes with the stochastic convexity(concavity) property. Sufficient conditions for stochastic monotonocity and stochastic convexity of a Markov process are also mentioned. A simple example is given to demonstrate the validity of the bounding methods.