Utility maximization for communication networks with multipath routing

In this paper, we study utility maximization problems for communication networks where each user (or class) can have multiple alternative paths through the network. This type of multi-path utility maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path flow control problem, the optimal quality-of-service (QoS) routing problem, and the optimal network pricing problem. We develop a distributed solution to this problem that is amenable to online implementation. We analyze the convergence of our algorithm in both continuous-time and discrete-time, and with and without measurement noise. These analyses provide us with guidelines on how to choose the parameters of the algorithm to ensure efficient network control.