Traffic Flow Prospectives: From Fundamental Diagram to Energy Balance

Congestion modeling is a topic under consideration in traffic flow theory since Greenshields' study of traffic capacity in 1934. There are several levels of investigation dealing with different categories. Microscopic car-following dynamics, mesoscopic stochastic theories of car cluster formation as well as macroscopic fluid-dynamical models study traffic states characteristics, given by speed, flow and density, shown in the fundamental diagram. By this relationship speed and flow can be represented as a function of density, usually as a steady state dependence, but also as function of time since traffic states change continuously. Distinguishing a collection of similar traffic states as phases, the phenomenon of phase transition from (nearly) free flow to stop-and-go traffic is the emergence of a random fluctuation (e.g., of speed) developing into a vehicular congestion known as breakdown. Usually a traffic breakdown is defined as a speed drop of a certain amount within a dense traffic situation. It has always a reason but the reason is hard to analyze. To describe these dynamics successfully a probabilistic model is chosen where the unpredictable influences are summarized by a stochastic force creating vehicular platoons (called vehicular clusters) out of the metastable free flow. This spontaneous formation of a new traffic phase is modeled as a stochastic cluster emergence process. A car cluster being a vehicular platoon larger than a predefined critical number of participating (or bounded) vehicles. In this way the speed drop mentioned above is translated into an overshot of the threshold given by the critical cluster size.