Model for Instantaneous Residential Water Demands

Abstract

Residential water use is visualized as a customer-server interaction often encountered in queueing theory. Individual customers are assumed to arrive according to a nonhomogeneous Poisson process, then engage water servers for random lengths of time. Busy servers are assumed to draw water at steady but random rates from the distribution system. These conditions give rise to a time-dependent Markovian queueing system having servers that deliver random rectangular pulses of water. Expressions are derived for the mean, variance, and probability distribution of the flow rate and the corresponding pipe Reynolds number at points along a dead-end trunk line. Comparison against computer-simulated results shows that the queueing model provides an excellent description of the temporal and spatial variations of the flow regime through a dead-end trunk line supplying water to a block of heterogeneous homes. The behavior of the local flow field given by the queueing model can be coupled with water-quality models that require ultrafine temporal and spatial resolutions to predict the fate of contaminants moving through municipal distribution systems.