Cellular automata (CA) models have been widely used to simulate traffic flow on highways and road networks, in particular the Nagel-Schreckenberg (NS) model. Together with car-following and continuum models, they represent the three most popular classes of traffic models.

In this talk, we will investigate a bottleneck simulation of road traffic on a loop, using the NS model. Three types of stationary wave solutions emerge. They consist of:

1. two shock waves at the bottleneck boundaries,
2. one shock wave at the boundary and one on the 'open' road, and
3. the trivial solution, i.e. homogeneous uniform flow.

These solutions are selected dynamically from a range of kinematically possible solutions. This is similar in fashion to the wave selection in a bottleneck simulation of the optimal-velocity (OV) car-following model, a coupled system of ODEs. It is also one of the strongest indications to-date that CA and OV models share certain underlying dynamics, although the former are discrete in space and time while the latter are continuous.