Empirical analysis and modeling of the allometric scaling of urban freight systems

Heavy trucks which undertake the majority of freight volume play an important
role in urban freight systems. By analyzing heavy truck trip data, we find a superlinear scaling
relationship for heavy truck trips and a sublinear scaling relationship for heavy truck numbers
relative to urban population size. Although these allometric scaling relationships that widely
appear in nature and social systems have been explained by many models, a simple model that
can cover a wide range of scaling exponents in these systems is still lacking. Here, we develop a
partially mixing city operation model by quantifying the mixability of the urban population to
explain why the superlinear and sublinear scaling exponents are in the range of 1 and 1 ± 1/3.
This simple model not only helps us understand the mechanism of allometric scaling of urban
freight systems, but also provides a new framework for other superlinear and sublinear scaling
relationships in cities