Properties of transportation dynamics on scale-free networks

In this work, we study the statistical properties of transportation dynamics considering congestion effects, based on the standard Barabási–Albert scale-free model. In terms of user equilibrium (UE) condition, congestion effects can be described by cost function. Simulation results demonstrate that the cumulative load distribution exhibits a power-law behavior with Pl∼l-(γ-1)Pl∼l-(γ-1), where l   is the flow loaded on the node and γ≈2.7γ≈2.7 which is much bigger than that obtained in many networks without considering congestion effects. That is, there exist fewer heavily loaded nodes in the network when considering congestion effects. Furthermore, by numerically investigating overload phenomenon of the heaviest loaded link removal in transportation networks, a phase-transition phenomenon is uncovered in terms of the key parameter characterizing the node capacity.