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

Title & Authors
An Approximation to the Overshoot in M/En/1 Queues
Bae, Jong-Ho; Jeong, Ah-Reum; Kim, Sung-Gon;

Abstract
In this paper, we propose an approximation to the overshoot in M/$\small{E_n}$/1 queues. Overshoot means the size of excess over the threshold when the workload process of an M/$\small{E_n}$/1 queue exceeds a prespecified threshold. The distribution, $\small{1^{st}}$ and $\small{2^{nd}}$ 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/$\small{E_n}$/1 queue;overshoot;approximation;
Language
Korean
Cited by
1.
M/En/1 대기모형에서 얼랑분포의 성질을 이용한 오버슛의 분포에 대한 근사,이상기;배종호;

응용통계연구, 2015. vol.28. 1, pp.33-47
1.
Approximation on the Distribution of the Overshoot by the Property of Erlang Distribution in the M/En/1 Queue, Korean Journal of Applied Statistics, 2015, 28, 1, 33
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