An extended master-equation approach applied to aggregation in freeway traffic

We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail. The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.