Effect of Car Length in the Biham-Middleton-Levine Traffic Model

Abstract

The Biham-Middleton-Levine (BML) model is the simplest cellular automaton model of traffic in idealized networks of streets in cities. Three phases (i.e., free flow phase, jam phase, and intermediate stable phase in which free flow coexists with jam) are observed in the model. This paper studies the influence of car length on the average velocity $\bar{\upsilon}$ and on the structure of the intermediate stable phase. It is shown that when the car length ϖ > 1, there appears a density range ρ _c2 < ρ < ρ _c1 in which all the three phases could coexist. More interestingly, when the car length ϖ > 1, the structure of the intermediate stable state qualitatively changes. There appear more than two stripes in each direction. However, the average velocity of the phase essentially does not change.

This work is partially supported by National Basic Research Program of China (No. 2006CB705500), the NSFC (No. 10872194 and 11072239), and the FANEDD.