Properties of volume-capacity ratio in congested complex networks

The volume-capacity ratio (v/c) is one of the most important indexes to measure the congestion of a traffic network. If v/c is very small, the traffic demand is deficient and/or the transportation supply or capacity is surplus, leading to a waste of capacity; on the contrary, a large value of v/c means that the traffic network is seriously congested. This paper investigates the properties of v/c in complex small-world and scale-free networks by introducing the congestion effects, described by link cost functions. The relationship between v/c and the degree of the node is mainly discussed. Finally, a simple strategy is presented to balance the tradeoff between traffic congestion and a waste of capacity.