  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 travel displacement
distribution with exponent -2. When considering the inhomogeneities of cities'
locations and attractions, this model reproduces a power-law displacement
distribution with an exponential cutoff, as well as a scaling behavior in the
probability density of having traveled a certain distance at a certain time.
Our results agree very well with the empirical observations reported in [D.
Brockmann et al., Nature 439, 462 (2006)].
