Random Walks and Extreme Events on Complex Networks

Abstract

Dynamics on complex networks, such as traffic on roads or information packets on network of routers, display a variety of collective and emergent properties. Of practical interest are congestion and extreme events phenomena, which ultimately control the smooth functioning of networks. To get a deeper understanding of these phenomena, we employ a continuous-time random walk model with probabilistic routing protocol for traffic flows in complex networks such that it contains the most relevant characteristics of real-world systems. We study the collective behavior through phase transitions in congestion and individual behavior of nodes through extreme events. We observe that increasing the outgoing flux enlarges the free- flow region in the parameter space. Moreover, a degree-dependent outflux can completely eradicate the congested state in the parameter space. In accordance with the previous results for a parameter-free model, we see that in most cases, small degree nodes are more prone to experience extreme events than the hubs. We also notice a striking relation between the flux fluctuations and extreme event probability on nodes.