From traffic breakdown to energy flow analysis

Usually a traffic breakdown is defined as a speed drop of a certain amount within a dense traffic situation. To describe these dynamics successfully a probabilistic model is chosen where the unpredictable influences are summarized by a stochastic force creating vehicular platoons out of the metastable free flow. In this way the speed drop mentioned above is translated into an overshot of the threshold given by the critical cluster size.The vehicular flow as an open nonequilibrium system of driven or active particles has energy sources like gasoline and energy sinks like road friction. Here we investigate the flux of mechanical energy to evaluate the energy balance out of the given nonlinear dynamical system of vehicular particles.The long-time result, either fixed point or limit cycle depending on traffic density, is characterized by a certain energy value. In order to understand the traffic breakdown as transition from free flow to congested traffic we estimate the total energy per car at low and high densities and observe the energy of jam formation. This picture of energy consumption cannot be prompted by field observations directly. Nevertheless the idea of an energy picture in traffic is quite attractive and pathbreaking.