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

From global scaling to the dynamics of individual cities