Heavy tails in dynamic flow networks: Universal explanation of their emergence

Abstract: Overload-induced cascading failures can cause extreme disruptions in a wide range of networked systems, such as power grids, transportation networks, or financial systems. Empirical studies across domains report that the size of such disruptions often follows a Pareto- or heavy-tailed distribution. While many models reproduce this scaling behavior, they are either tailored to specific domains or based on simplified mechanisms that overlook key aspects of overload cascading behavior. Hence, a general understanding of the mechanisms driving scale-free behavior in these settings remains incomplete. In this paper, we develop a universal and analytically tractable model of overload cascading failures on flow networks, offering a new perspective on how Pareto-tailed disruptions emerge across networks. Our framework shows, under mild assumptions, that heavy-tailed disruptions can arise naturally from Pareto-tailed external inputs, and it establishes a transformation law linking the input and output tail exponents. We further identify broad conditions under which the resulting cascade cost exhibits a heavy-tailed distribution and show that the mechanism is robust across several domains, including power transmission, traffic networks, and processing systems. Our results provide a unified explanation for the emergence of scale-free failures in overload-driven systems and connect previously disparate, application-specific models under a unified framework.