The totally asymmetric simple exclusion process (TASEP) was introduced around 1970 as a model for translation in protein synthesis and traffic flow. The inhomogeneous TASEP is a Markov chain of weighted particles hopping on a lattice, in which the hopping rate depends on the weight of the particles being interchanged. We will consider the case where the lattice is a ring, and each particle has a distinct weight, so that we can think of this model as a Markov chain on permutations. We will see that in many cases, and in particular for w an "evil-avoiding" permutation, the steady state probability of w can be expressed in terms of Schubert polynomials. Based on joint work with Donghyun Kim.