Gaps on the flow of the simplified path-preference cellular automaton model

The path-preference model is a cellular-automaton model to describe the dynamics of RNA polymerase II in transcription. The main difference from the standard traffic flow model is that it contains another preferential paths at some sites. In this paper, we propose an exact analysis for the simplest version of this model which consists on the minimal structure and removes stochastic factors. We find that the number of particles is dominant to the dynamics of this version and observed that there are not only expected phase shift but also several non-continuous gaps as the number of particles increases. By considering the behavior of limit cycles, we also determine the point where such gaps in the flow appear and the exact value of the flow.