  A multi-species generalization of the asymmetric simple exclusion process
(ASEP) is studied in ordered sequential and sub-lattice parallel updating
schemes. In this model particles hop with their own specific probabilities to
their rightmost empty site and fast particles overtake slow ones with a
definite probability. Using Matrix Product Ansatz (MPA), we obtain the relevant
algebra, and study the uncorrelated stationary state of the model both for an
open system and on a ring. A complete comparison between the physical results
in these updates and those of random sequential introduced in [20,21] is made.
