The distribution of the content of finite dams

Abstract

We shall consider the following model of finite dams: In the time interval (0, ∞) water is flowing into a dam (reservoir) in accordance with a random process. Denote by χ(u) the total quantity of water flowing into the dam in the time interval (0, u). The capacity of the dam is a finite positive number m. If the dam becomes full, the excess water overflows. If the dam is not empty, there is a continuous release at a constant unit rate. Denote by η(t) the content of the dam at time t.