Cascading traffic jamming in a two-dimensional Motter and Lai model

We study the cascading traffic jamming on a two-dimensional random geometric graph using the Motter and Lai model. The traffic jam is caused by a localized attack incapacitating circular region or a line of a certain size, as well as a dispersed attack on an equal number of randomly selected nodes. We investigate if there is a critical size of the attack above which the network becomes completely jammed due to cascading jamming, and how this critical size depends on the average degree $\langle k\rangle$ of the graph, on the number of nodes $N$ in the system, and the tolerance parameter $\alpha$ of the Motter and Lai model.