Stochastic multi-value cellular automata models for bicycle flow

In this paper, the stochastic randomization is introduced in two different multivalue cellular automata (CA) models in order to model the bicycle flow. It is shown that with the randomization effect considered, the multiple states in the deterministic multi-value CA models disappear and the unique flow-density relations (fundamental diagrams) exist. The fundamental diagrams, the spacetime plots of the two models, are studied in detail. It is found that the transition from free flow to congested flow is smooth in one model while it is of second order in the other model. The comparison of the results of the two models indicates that in the bicycle flow, the priority of the movement should be given to slow bicycles in order to reach a larger maximum flow rate.