A New Analysis of a Fluid Queue Driven By M/M/1 Queue

In this paper, we consider a fluid queue with an infinite buffer capacity which is both filled and depleted by a fluid at constant rates. These rates are uniquely determined by the number of customers in an M/M/1 queue with constant arrival and service rates. A simple series form is obtained for the joint stationary distribution of the buffer occupancy. This method is explicit where the coefficients of the series are obtained in closed form