Computation of the expected value and variance of the average annual yield for a stochastic simulation of rainwater tank clusters

The problem of obtaining a detailed understanding of the behavior of a cluster (or a collection) of rainwater tanks is complex and can only be solved by simulation. If the collection of houses is very large, a tractable solution can only be obtained by stochastic simulation in which the parameters defining the houses and tanks are sampled from probability distributions. An important output from the rainwater tank simulation is the average annual yield of the cluster and it is of interest to know its expected value and variance for planning of urban water systems. This paper carries out a theoretical calculation of the expected value and variance of the average annual yield as functions of cluster size and presents an experimental confirmation of these results.