Traffic Flow Prospectives: From Fundamental Diagram to Energy Balance

Congestion modeling is a topic considered in traffic flow theory since Greenshields’ study of traffic capacity in 1934. Several levels of investigation deal with different categories: microscopic car-following dynamics, mesoscopic stochastic theories of car cluster formation (for queuing description, see Wang et al.), as well as macroscopic fluid-dynamical models study the characteristics of traffic states, 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 because 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 certain amount of speed drop in a dense traffic situation. It always has 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 is a vehicular platoon larger than a predefined critical number of participating (or bounded) vehicles. Using this definition, the speed drop is translated into an overshot of the threshold given by the critical cluster size.