Clustering of Cars in Cellular Automaton Model of Freeway Traffic

Abstract

A cellular automaton (CA) model is presented to simulate the clustering (or aggregation) process of cars in traffic flow on a highway. The CA model is an extended version of the one-dimensional asymmetric simple-exclusion model taking into account the variation of car velocity which depends on the distance between a car and the car ahead. Using computer simulation, it is found that clustering (or aggregation) of cars occurs in our model. The mean distance ⟨l⟩ between cars scales as ⟨l⟩≈t^0.37±0.02 where t is time. Similarly, the mean cluster size ⟨s⟩ of cars scales as ⟨s⟩≈t^0.37±0.02. It is shown that the cumulative cluster-size distribution N_s is not a power-law type but an exponential function N_s≈⟨s⟩⁻¹ e^{−1.72s⁄⟨s⟩}.