Diesel $NO_x$ reduction by $NH_3$-SCR in conjunction with the effective oxidation precatalyst was analytically investigated. Physicochemical processes in regard to $NH_3$-SCR $NO_x$ reduction and catalytic NO-$NO_2$ conversion are formulated with detailed descriptions on the commanding reactions. A unified model is correctly validated with experimental data in terms of extents of $NO_x$ reduction by SCR and NO-$NO_2$ conversion by DOC. The present deterministic model based on the rate expressions of Langmuir-Hinshelwood reaction scheme finds a conversion extent directly. A series of numerical experiments concomitant with parametric analysis of the $NO_x$ reduction was conducted. $NO_x$ reduction is promoted in proportion to DOC volume ar lower temperatures and an opposite holds at lower space velocity and intermediate temperatures. $NO_x$ conversion is weakly correlated to the space velocity and the DOC volume at higher exhaust temperature. In DOC-SCR system, the $NO_x$ reduction efficiency depends on the $NH_3/NO_x$ ratio.