Energy dissipation in the Nagel-Schreckenberg model with open boundary condition

In this paper, we numerically investigate energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Boundary results in excess energy dissipation. The effects of the stochastic boundary conditions on energy dissipation are discussed. The behaviors of energy dissipation in different traffic phase are distinct. As an order parameter, energy dissipation rate E <Subscript> d </Subscript> characterizes the phase transition behaviors well. It is shown that there is no true free-flow state in nondeterministic NaSch model with OBC. We refer to this non-true free-flow state as quasi-free-flow (QFF) phase in which there are interactions between vehicles caused by stochastic braking but no backward moving jam exists. In the maximum current phase, E <Subscript> d </Subscript> is minimal thus the social payoff is maximal. Energy dissipation profiles in QFF, jammed and maximum current phase are presented. Theoretical analyses are in good agreement with numerical results for the case v <Subscript>max</Subscript>=1. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014