Quadratic algebras in traffic flow models

The basic features of traffic flow problems can be modelled via the asymmetric simple exclusion process. It is explained how quadratic algebras can be used to obtain the stationary state of the model in a matrix-product form, from which the quantities of interest can be calculated. In particular, we focus on the role of diffusion algebras in this context and discuss results about their construction and classification, as well as their implications on traffic flow models.