Jamming mechanism on the scale-free network with heterogeneous node capacity

To understand how the jamming on real communication networks depends on node capacity, we study the traffic model with heterogeneous node capacity. In this model, each movable packet takes a biased random walk and the capacity of a node with degree k is given as C(k) ∼ k^x with a tunable parameter x. Each packet disappears when it arrives at the preassigned target node. We analytically and numerically show that the transition from the free-flow phase to the jammed phase occurs when the balance between the packet generations and removals is broken. The balance breaking condition for the jamming is analytically determined by the competition between C(k) and the average number of packets on a node of degree k, m_f(k), in the free-flow phase. Based on the analytic arguments, we find that there exist three different jamming patterns depending on C(k). The analytic conjectures for jamming patterns are verified by numerical simulations.