A continuous storage model with alternating random input and output

Abstract

A stochastic model of a finite dam with alternating input and output is considered. Corresponding to a release rate of unity, and exponential nature of input and output, a renewal equation is set up for the probability frequency function governing the water level in the first wet period. The resulting equation is solved by Laplace Transform Technique to obtain the probability density function governing the time to first emptiness. The probability density function governing the water level of the dam for subsequent emptiness is also deduced.