Extreme fluctuations in noisy task-completion landscapes on scale-free networks.
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.
Guclu
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Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, MS-B258, Los Alamos, New Mexico 87545, USA.
Korniss
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Toroczkai
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