  Two measurements are employed to quantitatively investigate the scaling
properties of the spatial distribution of urban facilities, the K function by
number counting and the variance-mean relationship with the method of expanding
bins. The K function and the variance-mean relationship are both power
functions. It means that the spatial distribution of urban facilities are
scaling invariant. Further analysis of more data (which includes 8 types of
facilities in 37 major Chinese cities) shows that the exponents of the power
function do not have systematic variations across facilities and cities, which
suggests the possibility that the scaling rule is universal. A double
stochastic process (DSP) model is proposed such that the two empirical results
can both be embedded. Simulation of DSP yields better agreement with the urban
data than of the correlated percolation model.
