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

H. Guclu, G. Korniss, Z. Toroczkai
Guclu, H., G. Korniss, and Z. Toroczkai. "Extreme fluctuations in noisy task-completion landscapes on scale-free networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 17.2 (2007): 026104-026104.
Publication Date: 
June, 2007

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.