• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.147-154
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• 1997

An infinite dam with a compound Poisson input having exponential jumps is considered. As an output policy, we adopt the $P_{\lambda}$$^{M}$ Policy. After assigning costs to the dam we obtain the long-rum average cost per unit time of operating the dam and find the optimal values of .lambda. and M which minimize the long-run average cost.t.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.65-71
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• 2003

We consider the finite dam with compound Poisson inputs which is called M/G/1 finite dam. We assign some costs related to operating the dam and calculate the long-run average cost per unit time. Then, we find the optimal dam capacity under which the average costs is minimized.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.159-167
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• 2004

We present a simple approach to finding the stationary workload of M/G/1 queues having generalized vacations and exhaustive service discipline. The approach is based on the level crossing technique. According to the approach, all that we need is the workload at the beginning of a busy period. An example system to which we apply the approach is the M/G/1 queue with both multiple vacations and D-policy.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.123-128
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• 2004

A finite dam under $P_{\lambda,;,T}^M-policy$ is considered, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. Explicit expression is deduced for the stationary distribution of the level of water. And the long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty which is a function of the level of water in the reservoir.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1089-1096
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• 2011

We consider an infinite dam with inputs formed by a compound Poisson process and adopt a $P^M_{\lambda}$-policy to control the level of water, where the water is released at rate M when the level of water exceeds threshold ${\lambda}$. We obtain interesting stationary properties of the level of water, when the amount of each input independently follows an exponential distribution. After assigning several managing costs to the dam, we derive the long-run average cost per unit time and show that there exist unique values of releasing rate M and threshold ${\lambda}$ which minimize the long-run average cost per unit time. Numerical results are also illustrated by using MATLAB.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.491-507
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• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.