IS02: Heavy-Tailed Phenomena in Networks

Organizer: Bert Zwart (CWI Amsterdam)

Emergence of heavy-tailed cascades in flow networks through a unified stochastic overload framework.

Agnieszka Janicka

From power blackouts to traffic jams and financial crises, cascading failures pose a persistent threat to networks. These events rarely remain isolated — an initial failure can propagate through the system, leading to widespread disruption. Notably, across domains, the associated costs often follow heavy-tailed distributions. Our work provides a mathematically rigorous modeling framework that explains the emergence of this phenomenon. In this talk, I will present our stochastic, multi-commodity model for overload cascading failures — events triggered when flows exceed component capacities. Flows and resources are allocated optimally, following the principle of minimum energy dissipation. This formulation offers a flexible, yet analytically tractable framework applicable across diverse systems. Our results suggest that, despite domain-specific complexities, a common underlying driver — exogenous heavy-tailed inputs — may be responsible for the heavy-tailed nature of cascade costs. We derive probabilistic results that characterize when and why these costs inherit the input’s tail behavior. In particular, we show that large costs arise with high probability when a single location exhibits disproportionately high resource requirements — a phenomenon reminiscent of the catastrophe principle. The analysis also relies on continuity and scale-invariance properties of the cascade cost function, which we establish for several broad classes of modeling choices. This work deepens our understanding of cascading failures in complex systems and provides a unifying framework for analyzing large-scale disruptions, laying the groundwork for resilience analysis and policy design.