The Totally Asymmetric Simple Exclusion Process (TASEP) is a simple stochastic model for particles moving in a lattice with very rich behavior. We will examine the case when the lattice is on a ring, where the steady-state distribution is given combinatorially using multiline queues. In this talk, we will describe some additional weighting parameters on multiline queues, give a determinant formula for certain words, and prove the commutativity conjecture of Arita et al. This is joint work with Erik Aas and Darij Grinberg.