Effective delivering capacity in traffic dynamics based on scale-free network

We investigate the percentage of delivering capacities that are actually consumed in a typical traffic dynamics where the capacities are uniformly assigned over a scale-free network. Theoretical analysis, as well as simulations, reveal that there are a large number of idle nodes under both free and weak congested state of the network. It is worth noting that there is a critical value of effective betweenness to classify nodes in the congested state, below which the node has a constant queue size but above which the queue size increases with time. We also show that the consumption ratio of delivering capacities can be boosted to nearly 100% by adopting a proper distribution of the capacities, which at the same time enhances the network efficiency to the maximum for the current routing strategy.