Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model

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-vertical bar t vertical bar/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 upsilon(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.