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http://dx.doi.org/10.5351/KJAS.2011.24.2.347

An Approximation to the Overshoot in M/En/1 Queues  

Bae, Jong-Ho (Department of Statistics, Chungnam National University)
Jeong, Ah-Reum (National Research Foundation of Korea)
Kim, Sung-Gon (Department of Statistics, University of Seoul)
Publication Information
The Korean Journal of Applied Statistics / v.24, no.2, 2011 , pp. 347-357 More about this Journal
Abstract
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.
Keywords
M/$E_n$/1 queue; overshoot; approximation;
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Times Cited By KSCI : 1  (Citation Analysis)
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