Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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An optimal policy for an infinite dam with exponential inputs of water

비의 양이 지수분포를 따르는 경우 무한 댐의 최적 방출정책 연구

  • Kim, Myung-Hwa (Department of Statistics, Sookmyung Women's University) ;
  • Baek, Jee-Seon (Methodology Division, Statistical Research institute) ;
  • Choi, Seung-Kyoung (Department of Statistics, Sookmyung Women's University) ;
  • Lee, Eui-Yong (Department of Statistics, Sookmyung Women's University)
  • 김명화 (숙명여자대학교 통계학과) ;
  • 백지선 (통계청 통계개발원 조사연구실) ;
  • 최승경 (숙명여자대학교 통계학과) ;
  • 이의용 (숙명여자대학교 통계학과)
  • Received : 2011.09.30
  • Accepted : 2011.11.07
  • Published : 2011.12.01
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Abstract

We consider an infinite dam with inputs formed by a compound Poisson process and adopt a $P^M_{\lambda}$-policy to control the level of water, where the water is released at rate M when the level of water exceeds threshold ${\lambda}$. We obtain interesting stationary properties of the level of water, when the amount of each input independently follows an exponential distribution. After assigning several managing costs to the dam, we derive the long-run average cost per unit time and show that there exist unique values of releasing rate M and threshold ${\lambda}$ which minimize the long-run average cost per unit time. Numerical results are also illustrated by using MATLAB.

본 논문에서는 댐으로 물이 복합 포아송 과정을 따라 유입되고, 댐 수위가 적정수준 ${\lambda}$를 넘어서게 되면 방출률 M으로 물을 방출하는 무한 댐 모형이 고려된다. 한번 내리는 비의 양이 지수분포를 따르는 경우, 정상상태에서 댐 수위의 확률적 성질들을 구한다. 댐 운영과 관리에 관련된 여러 비용을 고려한 후, 장시간에 걸친 단위시간당 평균 비용을 구하고, 이를 최소화하는 방출률 M과 적정수준${\lambda}$가 유일하게 존재함을 보인다. MATLAB을 이용하여 수치적인 결과도 함께 보인다.

Keywords

References

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