A class of ‘onto’ multifunctions

A convex valued, upper continuous multifunction with pointed closed convex domain is proved to be onto, if there is a selection with certain coercive properties and if the selection for each point lies in the affine hull of the smallest face of the domain containing the point. The proof uses a piecewise affine homotopy construction. The authors apply the ‘onto’ theorem to an approximation of a network of servers and shows that arbitrary congestion levels can be realized with appropriate arrival levels.