Learning Spatial Density Functions of Random Waypoint Mobility over Irregular Triangles and Convex Quadrilaterals

For the optimization and performance evaluation of mobile ad hoc networks, a beneficial but challenging act is to derive from nodal movement behavior the steady-state spatial density function of nodal locations over a given finite area. Such derivation, however, is often intractable when any assumption of the mobility model is not basic, e.g., when the movement area is irregular in shape. As the first endeavor, we address this density derivation problem for the classic random waypoint mobility model over irregular convex polygons including triangles (i.e., 3-gons) and quadrilaterals (i.e., 4-gons). By mixing multiple Dirichlet distributions, we first devise a mixture density neural network tailored for density approximation over triangles and then extend this model to accommodate convex quadrilaterals. Experimental results show that our Dirichlet mixture model (DMM) can accurately capture the irregularity of ground-truth density distributions at low training cost, markedly outperforming the classic Gaussian mixture model (GMM).