  In this paper, we numerically study energy dissipation caused by traffic in
the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC).
Numerical results show that there is a nonvanishing energy dissipation rate Ed,
and no true free-flow phase exists in the deterministic and nondeterministic
NaSch models with OBC. In the deterministic case, there is a critical value of
the extinction rate $\beta{cd}$ below which Ed increases with increasing
$\beta$, but above which Ed abruptly decreases in the case of the speed limit
vmax>2. However, when vmax<3, no discontiguous change in Ed occurs. In the
nondeterministic case, the dissipated energy has two different contributions:
one coming from the randomization, and one from the interactions, which is the
only reason for dissipating energy in the deterministic case. The relative
contributions of the two dissipation mechanisms are presented in the stochastic
NaSch model with OBC. Energy dissipation rate Ed is directly related to traffic
phase. Theoretical analyses give an agreement with numerical results in three
phases (low-density, high-density and maximum current phase) for the case
vmax=1.
