Extreme fluctuations in noisy task-completion landscapes on scale-free networks

TL;DR

This paper investigates the behavior of extreme fluctuations in noisy task-completion landscapes on scale-free networks, revealing that extreme fluctuations grow logarithmically with system size and follow Gumbel statistics, ensuring practical synchronization.

Contribution

It provides a detailed analysis of extreme fluctuations in scale-free networks, combining large-scale simulations with mean-field theory to understand their statistical properties.

Findings

Extreme fluctuations grow logarithmically with system size.

Extreme fluctuations follow Gumbel distribution under certain conditions.

Synchronization remains practically feasible despite fluctuations.

Abstract

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.