Non-convexity issues for internet rate control with multi-class services: Stability and optimality

In this paper, we investigate the problem of distributively allocating transmission rates to users on the Internet. We allow users to have concave as well as sigmoidal utility functions that are natural in the context of various applications. In the literature, for simplicity, most works have dealt only with the concave case. However, we show that when applying rate control algorithms developed for concave utility functions in a more realistic setting (with both concave and sigmoidal types of utility functions), they could lead to instability and high network congestion. We show that a pricing based mechanism that solves the dual formulation can be developed based on the theory of subdifferentials with the property that the prices "self-regulate" the users to access the resource based on the net utility. We discuss convergence issues and show that an algorithm can be developed that is efficient in the sense of achieving the global optimum when there are many users.