Traffic Flow as a Simple Fluid: Toward a Scaling Theory of Urban Congestion

Abstract

The analogy between the theory of phase transitions in simple fluids and vehicular traffic flow has long been suspected, promising a new level of understanding of urban congestion by standing on one of the firmer foundations in physics. The obstacle has been the interpretation of the thermal energy of the particle system, which remains unknown. This paper proposes the flow of cars through the network as a viable interpretation, where the fundamental diagram of traffic flow would be analogous to the coexistence curve in gas-liquid phase transitions. Through the power-law form of the coexistence curve, it was possible to formalize that the resulting network traffic model belongs to the Kardar–Parisi–Zhang universality class. The scaling relationships arising in this universality class were found to be consistent with West’s scaling theory for cities. It was shown that congestion costs (delays + fuel consumption) scaled superlinearly with city populations, possibly, and worryingly, more so than predicted by West’s theory. Implications for sustainability and resiliency are discussed.