Littles 법칙의 미시적 활용 사례

Abstract

The Littles formula, , 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 Littles formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Littles formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Littles 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 Littles formula.