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Abstract: We study message transport on a $1-d$ ring of nodes and randomly distributedhubs. Messages are deposited on the network at a constant rate. When the rateat which messages are deposited on the lattice is very high, messages startaccumulating after a critical time and the average load per node startsincreasing. The power-spectrum of the load time-series shows $1-f$ like noisesimilar to the scenario of the Internet traffic. The inter-arrival timedistribution of messages for the $1-d$ ring network shows stretched exponentialbehavior, which crosses over to power-law behavior if assortative connectionsare added to the hubs. The distribution of travel times in a related doublering geometry is shown to be bimodal with one peak corresponding to initialcongestion and another peak to later decongestion.



Author: Satyam Mukherjee, Gautam Mukherjee, Neelima Gupte

Source: https://arxiv.org/







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