Multi-scaling mix and non-universality between population and facility density

Abstract: The distribution of facilities is closely related to our social economic activities. Recent studies have reported a scaling relation between population and facility density with the exponent depending on the type of facility. In this paper, we show that generally this exponent is not universal for a specific type of facility. Instead by using Chinese data we find that it increases with Per Capital GDP. Thus our observed scaling law is actually a mixture of some multi-scaling relations. This result indicates that facilities may change their public or commercial attributes according to the outside environment. We argue that this phenomenon results from the unbalanced regional economic level and suggest a modification for previous model by introducing consuming capacity. The modified model reproduces most of our observed properties.