• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.347-357
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• 2011

In this paper, we propose an approximation to the overshoot in M/$E_n$/1 queues. Overshoot means the size of excess over the threshold when the workload process of an M/$E_n$/1 queue exceeds a prespecified threshold. The distribution, $1^{st}$ and $2^{nd}$ moments of overshoot have an important role in solving some kind of optimization problems. For the approximation to the overshoot, we propose a formula that is a convex sum of the service time distribution and an exponential distribution. We also do a numerical study to check how exactly the proposed formula approximates the overshoot.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.5 no.1
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• pp.1-10
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• 1972

Studies on the circulation and water masses in the continental shelf break region of the East China Sea are Summerized as follows : 1. The main stream of the Kuroshio flowing north-east near $29^{\circ}N\;Lat\;127^{\circ}E$ tong of the East China Sea in summer is narrow in width. Moving toward east, it becomes twice as wide in Tokora Strait, Japan. 2. In the main stream area of the Kuroshio, the surface Waters in the Upper layer (0-250m) are influenced by the coastal waters of China, and the counter current submerges under the surface water. Therefore, the mixing waters are found in its intermediate layer. 3. Water mass between Amami Island and the continental shelf of the East China Sea consists of main stream water, counter current water, gyration water and mixed water with coastal waters. 4. The maximum velocity of current in this waters was 139cm/sec. The volume transport was estimated approximately as $24.2\;\times\;10^6m^3/sec$. It was less than $33\;\times\;10^6m^3/sec$ in the region between Okinawa and continental shelf of the East China Sea. 5. Surface waters east of $29^{\circ}N\;Lat\;128^{\circ}E$ Long flows toward Amami Island, Okinawa Island, and Hachi Ju San Island, while those west of the region flow toward the Korea-strait, Cheju Island, coastal waters of Kyusyu, and the Pacific Ocean through Tokora Strait. The velocity of the current was estimated approximately as $0.3\~0.5$ miles per hour. 6. The bottom waters in the continental shelf break region flow toward the Korea Strait, Cheju Island and the coastal water of Kyusyu, while that of the continental shelf flows toward the Yellow Sea, 7, The characteristics of the Kuroshio water is changed remarkably by the mixing with the coastal water of China.