  We analytically study the one-dimensional Asymmetric Simple Exclusion Process
(ASEP) with open boundaries under sublattice-parallel updating scheme. We
investigate the stationary state properties of this model conditioned on
finding a given particle number in the system. Recent numerical investigations
have shown that the model possesses three different phases in this case. Using
a matrix product method we calculate both exact canonical partition function
and also density profiles of the particles in each phase. Application of the
Yang-Lee theory reveals that the model undergoes two second-order phase
transitions at critical points. These results confirm the correctness of our
previous numerical studies.
