Entropy‐Based Redundancy Measures in Water‐Distribution Networks

Reliability and flexibility in the face of failure conditions are implied aspects of redundancy in water‐distribution networks. Explicit and comprehensive ways to measure either the reliability or the redundancy of water‐distribution networks have not yet been developed. In this paper a measurement of the redundancy inherent in the layout of water distribution networks is developed using an axiomatic approach based upon the desired properties of such a measurement. The local redundancy at a node and the redundancy imposed by redundancies at adjacent nodes (global redundancy) are addressed by the measurement. The measurement is examined in an application to candidate layouts obtained from the solutions of a distribution layout design model. A comparison between redundancy measurements and network performance, as indicated by percentage of flow supplied under a range of link failures, demonstrates that an increase in the value of redundancy, as measured by the entropic parameter, increases the ability of the water‐distribution network to respond to failure problems in the network. The value of the measurement in design is demonstrated by its use in the least‐cost design of an example network.