Multirate multicast service provisioning I: an algorithm for optimal price splitting along multicast trees

In this two-part paper we present a general framework for addressing the optimal rare control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users' utility functions. Specifically, we propose a market-based mechanism that satisfies the informational constraints imposed by the decentralization of information in multirate multicast service provisioning, and achieves an optimal solution to the corresponding centralized optimization problem. In Part I we discover properties of an optimal solution to the centralized problem. Based on these properties, we develop a distributed algorithm that determines how link prices are split among users whose connections along a multicast tree share the same link.