Load Distribution In Congested Scale-Free Networks

In this work, we study the effects of scale-free topology and congestion on load distribution. Congestion effect can be described by link cost functions, which map link flows into travel times. Two different kinds of link's practical capacity (it is similar to link's capacity for transport) which is a parameter in link cost functions, i.e., uniform case and nonuniform case, are investigated. After introducing the effect of congestion, load distribution is typically discussed in Barábasi–Albert and Goh scale-free networks. In the uniform case, for Barábasi–Albert scale-free networks, we recover a power-law behavior for load distribution with a larger exponent, as compared with the distribution of betweenness centrality; for Goh scale-free networks, we also recover a power-law behavior and its exponent approaches to the exponent of degree distribution. While in the nonuniform case, the power-law behavior for load distribution may not always be conserved in both Barábasi–Albert and Goh scale-free networks. That is to say, different kinds of load distributions are obtained under different conditions. It may shed some light to study traffic dynamics on scale-free networks.