Relaxation dynamics in congested traffic.
We investigate the relaxation dynamics in congested traffic when starting from the "megajam" initial condition (all cars standing in one big cluster of density 1) in the framework of the traffic model proposed by Nagel and Schreckenberg. On the one hand, a simple comparison of the time evolutions of some relevant traffic quantities shows that the slowest relaxing quantity is the density of "go and stop" cars rather than the average velocity of cars. On the other hand, we find that the relaxation time diverges in the form of a power law tau approximately tau(0) p(-beta) . A simple theoretical argument predicts that the exponent " beta " is equal to 1. This prediction is consistent with the numerical result.
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