On the distance between random events on a network

Journal Article

Abstract In this paper, we study several statistical properties regarding the distance between events that take place on random locations along the edges of a given network. We derive analytical expressions for the arbitrary moments of such a distance, its probability density function, its cumulative distribution function, as well as their conditional counterparts for the cases in which the position of one event is known in advance. As part of this study, we implement our developments as a callable library for the Python language, to provide potential users with a computational engine able to calculate and visualize these statistics for any given network. We test our implementation on several networks of different sizes and topologies, analyze some of interesting properties we observed in our experiments, and discuss several applications for our proposed methodology. In particular, we focus our discussion on applications aimed to help with the optimal design of emergency response systems on infrastructure networks.

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