  In this work we construct the stationary measure of the N species totally
asymmetric simple exclusion process in a matrix product formulation. We make
the connection between the matrix product formulation and the queueing theory
picture of Ferrari and Martin. In particular, in the standard representation,
the matrices act on the space of queue lengths. For N >2 the matrices in fact
become tensor products of elements of quadratic algebras. This enables us to
give a purely algebraic proof of the stationary measure which we present for N
=3.
