Convex Multi-commodity Flow Routing

There are many problems related to the design of networks and accommodate demands from different users subject to some constraints on users’ quality of service (QoS) and fairness through the network. The problem of resource allocation and message routing plays a determinant role in the optimization of networks performance. Our work emphasizes the message routing problem in data networks, but it also includes a broader class of convex multicommodity flow problem. We present and discuss various approaches for solving this class of large-scale convex problems. We next briefly discuss about network layer queuing and stability theorems, resulting in backpressure-based routing algorithms that are proved to be throughput-optimal. We finally show that classical subgradient search method for solving the multicommodity flow problem via convex duality theory corresponds almost exactly to a deterministic network simulation of the backpressure algorithm.