Origin of the scaling law in human mobility: Hierarchy of traffic systems

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which a random walker will generate a power-law-like travel displacement distribution with tunable exponent, and display a scaling behavior in the probability density of having traveled a certain distance at a certain time. The simulation results, analytical results, and empirical observations reported in D. Brockmann et al. [Nature (London) 439, 462 (2006)] agree very well with each other.