• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1101-1103
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• 2006

For a broad class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process) arrivals, we present a distributional Little's law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue for example, we illustrate how to utilize this relation to get the desired distribution of the number of customers.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.827-837
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• 1998

We consider the M/G/1 queue with instantaneous feed-back. The probabilities of feedback are determined by the state of the underlaying Markov chain. by using the supplementary variable method we derive the generating function of the number of customers in the system. In the analysis it is required to calculate the matrix equations. To solve the matrix equations we use the notion of Ex-tended Laplace Transform.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.803-811
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• 2011

We present an algorithmic solution for the stationary distribution of the M/M/c retrial queue in which the retrial times of each customer in orbit are of phase type distribution of order 2. The system is modeled by the level dependent quasi-birth-and-death (LDQBD) process.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.1
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• pp.67-75
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• 1992

In this paper, by using perturbation analysis method, We find the sensitivity of the mean busy cycle with respect to means interrival time in M/M/1 Queue. We show that the Perturbation analysis estimate can be expressed as a sum of the infinitesimal perturbation analysis (IPA) estimate and the effect caused by changes in transition probabilities, thus explaining why IPA estimates are not consistent in general.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.647-653
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• 2010

We consider an M/M/1 retrial queue with collision and impatience. It is shown that the generating functions of the joint distributions of the server state and the number of customers in the orbit at steady state can be expressed in terms of the confluent hypergeometric functions. We find the performance characteristics of the system such as the blocking probability and the mean number of customers in the orbit.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.805-814
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• 1999

We consider an MMPP/G/1/K finite queue with two-level threshold overload control. This model has frequently arisen in the design of the integrated communication systems which support a wide range applications having various Quality of Service(QoS) requirements. Through the supplementary variable method, se derive the queue length distribution.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.505-511
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• 2007

In this paper, we examine the Markov chain $\{X_k,\;N_k;\;k=0,\;1,...$. We show that the marginal steady state distribution of Xk is discrete phase type. The implication of this result is that the queue length distribution of phase type for large number of examples where this Markov chain is applicable and shows a queueing application by matrix geometric methods.

• Journal of the Korean Statistical Society
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• v.34 no.1
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• pp.39-47
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• 2005

We adopt the P/sub λ, T//sup M/ policy of dam to introduce a service policy with alternating service rates for a Poisson arrival queue, in which the service rate alternates depending on the number of customers in the system. The stationary distribution of the number of customers in the system is derived and, after operating costs being assigned to the system, the optimization of the policy is studied.

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.83-91
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• 1996

We first obtain the departure process of a D-BMAP/Geo/1/K queue. The departure process is then exactly characterized by a k-state MMBP in order to capture the burstiness and correlation of the departure process.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.319-330
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• 2002

We consider BMAP/G/1 queueing system with N-policy and multiple vacations. We derive the vector generating functions of the queue length in a factorized form and interpret the factorization. We also derive the mean queue length.