  An extended multi-class Aw-Rascle (AR) model with pressure term described as
a function of area occupancy defined in form of proportional densities is
presented. Two vehicle classes that is; cars and motorcycles are considered
based on an assumption that proportions of these form total traffic density.
Qualitative properties of the proposed equilibrium velocity is established.
Conditions under which the proposed model is stable are determine by linear
stability analysis. To compute numerical flux, the model is discretized by the
original Roe decomposition scheme, where Roe matrix, averaged data variables
and wave strengths are explicitly derived. The Roe matrix is shown to be
hyperbolic, consistent and conservative. From the numerical results, the effect
of motorcycles proportion on the flow of vehicle classes is determined. Results
obtained remain within limits therefore, the proposed model is realistic.

Analysis of PDEs