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

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 gas-particle system, which remains unknown. This paper proposes the flow of cars through the network as a viable interpretation, where the fundamental diagram for traffic flow would be analogous to the coexistence curve in gas-liquid phase transitions. Thanks to 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 are found to be consistent with West's scaling theory for cities. It is shown that congestion costs (delays + fuel consumption) scale superlinearly with city population, possibly and worryingly more so than predicted by West's theory. Implications for sustainability and resiliency are discussed.