Analytic solution of a finite dam governed by a general input

Abstract

A stochastic model of a finite dam in which the epochs of input form a renewal process is considered. It is assumed that the quantities of input at different epochs and the inter-input times are two independent families of random variables whose characteristic functions are rational functions. The release rate is equal to unity. An imbedding equation is set up for the probability frequency governing the water level in the first wet period and the resulting equation is solved by Laplace transform technique. Explicit expressions relating to the moments of the random variables representing the number of occasions in which the dam becomes empty as well as the total duration of the dry period in any arbitrary interval of time are indicated for negative exponentially distributed inter-input times.