A molecular dynamics stimulation of alkali sulfate-zinc sulfate melts and glasses is presented. Oxygen coordinations of Zn2+, Na+, and K+ cations have been found to be nearly six, eight, and twelve respectively. The radial distribution function has been calculated and compared with the same reported from experimental X-ray diffraction work. Several important aspects of a modified random close packing model described earlier to account for the behavior of sulfate glasses have been confirmed by the present molecular dynamics simulation. Diffusion coefficients of various ions have been evaluated from mean squared displacement data and occurrence of the mixed alkali effect has been noted. A surprising spatial correlation of dissimilar alkali ions has been observed and it is suggested that it provides support for a structural origin of mixed alkali effect in ionic glasses.