Search and topology aspects in transport on scale-free networks

Using a recently proposed model Physica A 332 (2004) 566 of information transport on complex networks we study the role of network substrates on the statistics of queuing times and correlations in traffic streams. When navigation with an enlarged information horizon is applied the waiting time distribution on structured networks has a power-law tail which can be parametrized by 1/(1-q), where the respective value of the non-extensivity parameter q increases systematically with increasing graph complexity. The corresponding distribution on the small-world graph appears to be a stretched-exponential function that cannot be classified within the same scheme. We further demonstrate by looking at the anti-persistence in flow time-series and the transit time distributions, how traffic efficiency increases with an extended information horizon. A horizon of two layers approaches the critical horizon on the correlated cyclic scale-free graph, suggesting that the mechanisms of signaling over two-to-three layers ensure efficient transport processes on networks with this organizational complexity.