Not sure what you mean by "quantized market" (discrete-time auction?). But the opening and closing sessions at the NYSE run at human timescales (twice per day), and most of the daily volume is traded at open and close iirc.

edit: "Across Wall Street, less trading is taking place at 3 p.m. or, in fact, most any time but the opening minutes and the final half hour." http://www.wsj.com/articles/traders-pile-in-at-the-close-143...