Reply to “Comment on ‘Cellular automata model simulating traffic interactions between on-ramp and main road’ ”

Abstract

We agree with the argument presented in the previous Comment in which the characteristics of a phase diagram are dictated by the prescribed asymmetric rules of on-ramp. We further point out that the existence of the four regions for ${v}_{\mathrm{max}}>1$ is due to the rule in the case of ${t}_{a}{=t}_{b}$ and the rule that two cars can occupy the same site successively in one time step. We argue that the existence of the stable limit cycles in region IV is the property of the deterministic on-ramp system, and it is not the cause of the formation of region IV.