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

¹ School of Systems Science, Beijing Jiaotong University - Beijing 100044, China
² Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB) - Palma de Mallorca 07122, Spain
³ Department of Transport & Planning, Faculty of Civil Engineering and Geosciences, Delft University of Technology Stevinweg1, Delft 2628 CN, The Netherlands

^(a) E-mail: erjianliu@bjtu.edu.cn
^(b) E-mail: yanxy@bjtu.edu.cn (corresponding author)

Received: 22 February 2023
Accepted: 21 June 2023

Abstract

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 . 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.