Autoregressive Cascades on Random Networks

TL;DR

This paper introduces a model for cascades on random networks where failures propagate based on load redistribution, identifying conditions for finite or infinite cascade propagation and analyzing phase transitions.

Contribution

It presents a novel cascade model incorporating load, degree, and failure dynamics, with analysis of phase transition thresholds on random networks.

Findings

Identifies two regimes: finite and infinite cascade propagation.

Provides bounds on the critical parameters for phase transition.

Shows the model's applicability to understanding cascade phenomena in networks.

Abstract

This paper considers a model for cascades on random networks in which the cascade propagation at any node depends on the load at the failed neighbor, the degree of the neighbor as well as the load at that node. Each node in the network bears an initial load that is below the capacity of the node. The trigger for the cascade emanates at a single node or a small fraction of the nodes from some external shock. Upon failure, the load at the failed node gets divided randomly and added to the existing load at those neighboring nodes that have not yet failed. Subsequently, a neighboring node fails if its accumulated load exceeds its capacity. The failed node then plays no further part in the process. The cascade process stops as soon as the accumulated load at all nodes that have not yet failed is below their respective capacities. The model is shown to operate in two regimes, one in which the cascade terminates with only a finite number of node failures. In the other regime there is a positive probability that the cascade continues indefinitely. Bounds are obtained on the critical parameter where the phase transition occurs.