Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node $i$ is proportional to $k_i^{\varphi }$, where $k_i$ is the degree of node $i$ and $\varphi$ is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter $\varphi$ leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal $\varphi$.