The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The Approximation for the Auxiliary Renewal Function

보조재생함수에 대한 근사

  • Bae, Jong-Ho (Department of Information Statistics, Chungnam National University) ;
  • Kim, Sung-Gon (Department of Information Statistics, Gyeongsang National University)
  • 배종호 (충남대학교 정보통계학과) ;
  • 김성곤 (경상대학교 정보통계학과)
  • Published : 2007.07.31
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Abstract

The auxiliary renewal function has an important role in analyzng queues in which the either of the inter-arrival time and the service time of customers is not exponential. As like the renewal function, the auxiliary renewal function is hard to compute although it can be defined theoretically. In this paper, we suggest two approximations for auxiliary renewal function and compare the two with the true value of auxiliary renewal function which can be computed in some special cases.

고객의 도착간격시간과 서비스시간 중 어느 하나가 지수분포가 아닌 큐를 분석할 때 중요하게 등장하는 함수가 보조재생함수(auxiliar renewal function)이다. 재생함수와 마찬가지로 보조재생함수도 이론적으로는 정의할 수 있으나 함수값을 실제로 계산하기에는 어려움이 많아 근사값을 구하는 연구가 필요하다. 본 논문에서는 보조재생함수의 값을 근사적으로 계산하는 두 가지 방법을 보여주고 부분적으로 알려져 있는 보조재생 함수의 참값과의 비교를 통하여 두 방법을 서로 비교한다.

Keywords

References

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Cited by

  1. An Approximation to the Overshoot in M/En/1 Queues vol.24, pp.2, 2011, https://doi.org/10.5351/KJAS.2011.24.2.347
  2. 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