Eur. Phys. J. B (2014) 87: 4
https://doi.org/10.1140/epjb/e2013-40506-4

Regular Article

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

¹ Department of Physics, Jinan University, Guangzhou 510632, P.R. China
² Department of Applied Physics, Northwestern Polytechnical University, Xi’an 710072, P.R. China
³ Department of Physics, Fudan University, Shanghai 200433, P.R. China

^a e-mail: wzhangph@gmail.com

Received: 20 May 2013
Published online: 7 January 2014

Abstract

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_d 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_d 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_max = 1.