Copyright © 2012 Kazuhiro Tobita and Takashi Nagatani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the traffic states and fundamental diagram of vehicular traffic controlled by a series of traffic lights using a deterministic cellular automaton (CA) model. The CA model is not described by a set of rules but is given by a difference equation. The vehicular traffic varies highly with both signal’s characteristics and vehicular density. The dependence of fundamental diagram on the signal’s characteristics is derived. At a low value of cycle time, the fundamental diagram displays the typical trapezoid, while it shows a triangle at a high value of cycle time. The dynamic transitions among distinct traffic states depend greatly on the signal’s characteristics. The dependence of the transition points on the cycle time split and offset time is found.