A Simple Cellular Automaton Model with Limited Braking Rule

Despite its simplicity, the Nagel-Schreckenberg (NaSch) traffic cellular automaton is able to reproduce empirically observed traffic phenomena such as spontaneous traffic jam formation. Most traffic cellular automata models achieve collision-free driving by explicitly allowing for unlimited braking capabilities. However, it is rather natural to view the collision-free traffic flow as a consequence of moderate driving instead of infinite braking capabilities. Lee et al. (Phys Rev Lett 23:238702, 2004) introduced a traffic model that limits the vehicles’ acceleration and deceleration rates to realistic values. The underlying rules of motion in this model are, however, quite complicated. In this article, we introduce and analyse a modified version of the NaSch traffic model with simple rules of motion and limited braking capabilities. We achieve collision-free driving with realistic deceleration rates by the introduction of the function μ ( v t i + 1 , δ t i ) $$\mu (v_{t}^{i+1},\delta _{t}^{i})$$ which determines a vehicle’s new speed depending on the preceding vehicle’s speed v t i+1 and the distance δ t i $$\delta _{t}^{i}$$ to its predecessor. After proving that this function limits the maximum deceleration rate to realistic values and guarantees the collision-freeness at the same time, we investigate the resulting traffic dynamics.