The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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An Approximation to the Overshoot in M/En/1 Queues

M/En/1 큐에서 Overshoot에 대한 근사

  • Received : 20100800
  • Accepted : 20101100
  • Published : 2011.04.30
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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.

본 논문은 M/$E_n$/1 큐에서 overshoot에 대한 근사식을 제안한다. overshoot은 큐의 작업부하량과정이 어떤 한계점을 처음으로 초과한 순간에 그 초과량을 의미하는데, overshoot의 분포 및 1차, 2차 적률은 큐의 최적화문제를 푸는데 중요한 역할을 한다. 본 논문에서는 그동안 이루어진 overshoot의 분포에 대한 이론적인 결과를 바탕으로 하여 overshoot의 분포를 고객의 서비스시간의 분포와 지수분포의 선형결합으로 표현하는 근사식을 제안한다. 그리고 제안된 근사식의 정확성을 확인하기 위하여 시뮬레이션을 통해 구한 overshoot의 분포와 비교한다.

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References

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Cited by

  1. Approximation on the Distribution of the Overshoot by the Property of Erlang Distribution in the M/En/1 Queue vol.28, pp.1, 2015, https://doi.org/10.5351/KJAS.2015.28.1.033