  A numerical method based on Matrix Product Formalism is proposed to study the
phase transitions and shock formation in the Asymmetric Simple Exclusion
Process with open boundaries and parallel dynamics. By working in a canonical
ensemble, where the total number of the particles is being fixed, we find that
the model has a rather non-trivial phase diagram consisting of three different
phases which are separated by second-order phase transition. Shocks may evolve
in the system for special values of the reaction parameters.
