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 $1-\left|t\right|/\tau$ with a finite support $\left[-\tau ,\tau \right]$. 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 $v_{\text{max}}=1$ (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.

• Received 13 January 2010

DOI:https://doi.org/10.1103/PhysRevE.82.021107