From global scaling to the dynamics of individual cities

Abstract: Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of urban datasets displays apparent nonlinear behaviors whose statistical validity and meaning were recently the focus of many debates. We discuss here another aspect which is the implication of such scaling forms on individual cities and how they can be used for predicting the behavior of a city when its population changes. We illustrate this discussion on the case of delay due to traffic congestion with a dataset for 101 US cities in the range 1982-2014. We show that the scaling form obtained by agglomerating all the available data for different cities and for different years displays indeed a nonlinear behavior, but which appears to be unrelated to the dynamics of individual cities when their population grow. In other words, the congestion induced delay in a given city does not depend on its population only, but also on its previous history. This strong path-dependency prohibits the existence of a simple scaling form valid for all cities and shows that we cannot always agglomerate the data for many different systems. More generally, these results also challenge the use of transversal data for understanding longitudinal series for cities.