Little's 법칙의 미시적 활용 사례

A MIrcroscopic Application of the Little's Formula

  • 윤봉규 (한국과학기술원 산업공학과) ;
  • 김남기 (한국과학기술원 산업공학과) ;
  • 채경철 (한국과학기술원 산업공학과)
  • 투고 : 19981000
  • 심사 : 19981200
  • 발행 : 1999.03.31

초록

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.

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