Traffic gridlock on complex networks

Here we study how a traffic jam spreads on complex networks when driven by an increasing flux between certain initial and final points. For that purpose, we developed two new traffic models based on vehicular traffic and applied them on the Apollonian network and the Swiss road network. The first model is an electrical analog, using ohmic and non-ohmic resistors which is a classical approach in Physics while the second one which we call the herding model, is based on human driving behavior. For both models, we study the sequence of clogged roads up to the traffic gridlock and display the fragilities of the network. In the electrical model, by increasing the external potential, resistors burn out, as the voltage drop between the ends increases above a certain threshold. Analyzing both models, we observed some power-law functions that occur only near a traffic gridlock as well as the dependence on topological features of the network and influence on flux and the robustness in Apollonian networks of different generations.