The oxygen order in YBa₂Cu₃O_6+x has been investigated by Monte Carlo simulation with an extension of the well known anisotropic next nearest neighbor lattice gas model, the ASYNNNI model. Our results for the widths of the structure factor at the ( 1 2,0,0) superstructure reflection are compared with recent neutron diffraction measurements. In addition we determine the effect on the materials properties of the interplay between oxygen ordering and the diffusive motion of metal-ion dopants in YBa₂Cu_3-yM_yO_6+x (M Co, Fe, Al) by Monte Carlo simulation. The simulations are performed on a massively parallel computer, the Connection Machine.