1210.7562 (Hideaki Ujino et al.)

Exact Solutions and Flow--Density Relations for a Cellular Automaton
Variant of the Optimal Velocity Model with the Slow-to-Start Effect    [PDF]

Hideaki Ujino, Tetsu Yajima

A set of exact solutions for a cellular automaton, which is a hybrid of the optimal velocity and the slow-to-start models, is presented. The solutions allow coexistence of free flows and jamming or slow clusters, which is observed in asymptotic behaviors of numerically obtained spatio-temporal patterns. An exact expression of the flow--density relation given by the exact solutions of the model agrees with an empirical formula for numerically obtained flow--density relations.

View original: http://arxiv.org/abs/1210.7562