On The Critical Packet Injection Rate Of A Preferential Next-Nearest Neighbor Routing Traffic Model On Barabasi-Albert Networks

Recently, Yin et al. [Eur. Phys. J. B 49, 205 (2006)] introduced an efficient small-world network traffic model using preferential next-nearest neighbor routing strategy with the so-called path iteration avoidance (PIA) rule to study the jamming transition of internet. Here we study their model without PIA rule by a mean-field analysis which carefully divides the message packets into two types. Then, we argue that our mean-field analysis is also applicable in the presence of PIA rule in the limit of a large number of nodes in the network. Our analysis gives an explicit expression of the critical packet injection rate $R_c$ as a function of a bias parameter of the routing strategy $\alpha$ in their model with or without PIA rule. In particular, we predict a sudden change in $R_c$ at a certain value of $\alpha$. These predictions agree quite well with our extensive computer simulations.