Equilibrium allocation and pricing of variable resources among user-suppliers

We propose a novel model of resource sharing schemes that provide each user with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability and user demands. At equilibrium, if it exists, all users optimize their utility and resource demand equals supply, i.e., the marginal increase in user utility due to higher return on variable resources is balanced by the marginal decrease in utility due to their variability. We show how an equilibrium might be approached using a simple price adjustment rule that does not require any knowledge on the part of the network about user utilities. We further show that at equilibrium every user holds strictly positive amounts of variable bandwidth and variable buffer, and in the same ratio. We characterize the equilibrium prices to lie in a hyperplane that can be computed by the network without having to know user utilities. We illustrate with an example how this characterization might significantly speed up convergence towards an equilibrium.