Traffic Properties for Stochastic Routing on Scale-Free Networks

For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters alpha and delta, this model controls degree-dependent hopping of packets and forwarding of packets with higher performance at more busy nodes. Through a theoretical analysis and numerical simulations, we derive the condition for the concentration of packets at a few hubs. In particular, we show that the optimal alpha and delta are involved in the trade-off between a detour path for alpha < 0 and long wait at hubs for alpha > 0; In the low-performance regime at a small delta, the wandering path for alpha < 0 better reduces the mean travel time of a packet with high reachability. Although, in the high-performance regime at a large delta, the difference between alpha > 0 and alpha < 0 is small, neither the wandering long path with short wait trapped at nodes (alpha = -1), nor the short hopping path with long wait trapped at hubs (alpha = 1) is advisable. A uniformly random walk (alpha = 0) yields slightly better performance. We also discuss the congestion phenomena in a more complicated situation with packet generation at each time step.