Path survival reliabilities as measures of reliability for lifeline utility networks

Abstract

Lifeline utility networks have been studied extensively within the domain of network reliability due to the prevalence of natural hazards. The reliability of these networks is typically investigated through graphs that retain their structural characteristics. This paper introduces novel connectivity-based reliability measures tailored for stochastic graphs with designated source vertices and failure-probability-weighted edges. In particular, the per-vertex path survival reliability quantifies the average survival likelihood of single-source paths from a vertex to any source. A consolidated per-graph reliability measure is also presented, incorporating graph density and the shortest distance to a source as regulating elements for network comparison. To highlight the advantages of the proposed reliability measures, a theoretical discussion of their key properties is presented, along with a comparison against standard reliability measurements. The proposal is further accompanied by an efficient calculation procedure utilizing the zero-suppressed binary decision diagram, constructed through the frontier-based search, to compactly represent all single-source paths. Finally, the path survival reliabilities are calculated for a set of real-world networks and demonstrated to provide practical insights.