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We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenbergmodel on a finite system of length L with open boundary conditions and parallelupdates. We find numerically that in both the high and low density regimes theautocorrelation function of the system density behaves like 1-|t|/tau with afinite support [-tau,tau]. This is in contrast to the usual exponential decaytypical of equilibrium systems. Furthermore, our results suggest that in facttau=L/c, and in the special case of maximum velocity 1 (corresponding to thetotally asymmetric simple exclusion process) we can identify the exactdependence of c on the input, output and hopping rates. We also emphasize thatthe parameter tau corresponds to the integrated autocorrelation time, whichplays a fundamental role in quantifying the statistical errors in Monte Carlosimulations of these models.

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