Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations

We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density $R_c.$ Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free flow.