  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.

Physics and Society;Disordered Systems and Neural Networks