A complete understanding of the microscopic dynamics of a monolayer of identical spheres moving on a substrate must encompass the effects of collisions and the substrate on the particles. We begin from first principles by considering collections of spherical frictional particles that roll and slip on a flat horizontally vibrated substrate. We present a numerical model which accounts for the substrate motion, collisional and surface frictional dissipation and their influence on particle dynamics for a quasi 2-dimensional dilute granular gas. In such systems, the ratio of the substrate acceleration to the particlesubstrate static frictional force (Kondic, Phys Rev. E (1999)) dominates the individual particle dynamics and the collision dynamics. This model is an extension of a previous numerical model which accounted for the influence of the collisional and substrate dissipation on a quasi two-dimensional cooling granular gas (Dutt Behringer, Phys. Rev. E (2004)). We willpresent results from our numerical experiments which highlight the progression of dynamical variables and fluctuation velocity distributions as a function of the initial conditions and the driving acceleration.