There is something more fundamental than fundamental diagram

Abstract

Revealing the inherent relationships among traffic flow characteristics, fundamental diagram has long been regarded as one of the pillars of traffic flow theory since Greenshields seminal work. When it is combined with the law of (mass/vehicle) conservation, dynamic modelling of traffic flow at the macroscopic level such as LWR and others have thrived. This paper shows that fundamental diagram is only a shadow of something more fundamental, i.e., phase diagram, which is originated from first principles of physics. At the microscopic level, traffic flow can be analyzed by examining the relative motion of two vehicles in car following. When the coordinate system is fixed on the leading vehicle, the Hamiltonian of this system can be defined as the total energy of the system. Conservation of total energy is established by incorporating physical entities (vehicles) and non-physical entities (drivers), the latter of which is enabled by the field theory of traffic flow. Consequently, the Hamilton's equations stipulate a vector field that constitutes the phase diagram of the system which, in turn, specifies Hamiltonian flow swirling around some equilibrium points. When focusing on the equilibrium points, the phase diagram reduces to the fundamental diagram, during which process much information is lost. Consequently, the lost information obscures the origin of the equilibrium points and further the fundamental diagram. This research roots traffic flow theory in first principles of physics and offers an example to address the dynamics of similar systems that involve human intelligence.