Extreme events in Nagel-Schreckenberg model of traffic flow on complex networks

The Nagel-Schreckenberg vehicular traffic model is extended to analyse a system of vehicles moving on a scale-free network to study extreme events in them. The dependence of the free-flow and congestion states on the density of vehicles is determined. In particular, a free-flow state at low vehicular density is observed and it gradually transitions to a congested state at higher density. Using detrended fluctuation analysis, it is shown that the flux of vehicles are long range correlated in a regime of low density. At higher densities, the flux becomes uncorrelated. We study the recurrence interval distribution for extreme events and the probability for its occurrence at low and high vehicular density regimes. It is shown that the occurrence probability for extreme events is independent of the degree of the node or the threshold used for defining extreme events