  We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg
model on a finite system of length L with open boundary conditions and parallel
updates. We find numerically that in both the high and low density regimes the
autocorrelation function of the system density behaves like 1-|t|/tau with a
finite support [-tau,tau]. This is in contrast to the usual exponential decay
typical of equilibrium systems. Furthermore, our results suggest that in fact
tau=L/c, and in the special case of maximum velocity 1 (corresponding to the
totally asymmetric simple exclusion process) we can identify the exact
dependence of c on the input, output and hopping rates. We also emphasize that
the parameter tau corresponds to the integrated autocorrelation time, which
plays a fundamental role in quantifying the statistical errors in Monte Carlo
simulations of these models.
