Stochastic modeling of residential drinking water demand using the Neyman-Scott scheme

Residential water demand is highly unsteady and stochastic. This has motivated the development, in the last few years, of methods that model it as series of rectangular pulse:3 following a Poisson process (PRP methods). In order to generate the demand series, these methods require several basic parameters of the instantaneous water demand, such as frequency of water use, and intensity and duration of stochastic demand pulses, each of them defined by its mean, variance, and probability distribution. Known procedures for obtaining those parameters are generally based on direct observation of the instantaneous water demand by registering it every second at selected homes during periods of at least several days. That direct technique turns out to be impractical, however, because of the enormous amount of data generated and processed, olus the need of special equipment for carrying out water demand studies. A new method for estimating the necessary parameters for simulating instantaneous water demand from (e.g. one minute) meter readings at time intervals that are greater than 1 second is presented in this paper. The proposed method considers some principles from the Neyman-Scott (N-S) process, such as the disaggregation of the accumulated water volume, based on a comparison between the statistical moments of the observed greater interval demand series and the theoretical moments of the instantaneous water demand. An objective function expressing the relation between both the theoretical and the observed moments is formulated and minimized by a non linear orogramming technique. The intensity, duration and frequency or arrival rate of the instantaneous demand oulses are thus obtained. Using these results, instantaneous water demand series, or demand series with any averaging interval, can be generated. The method is validated by comparing the generated demand series with observed demand series.