Proportional Fair Coding for Wireless Mesh Networks

We consider multihop wireless networks carrying unicast flows for multiple users. Each flow has a specified delay deadline, and the lossy wireless links are modeled as binary symmetric channels (BSCs). Since transmission time, also called airtime, on the links is shared among flows, increasing the airtime for one flow comes at the cost of reducing the airtime available to other flows sharing the same link. We derive the joint allocation of flow airtimes and coding rates that achieves the proportionally fair throughput allocation. This utility optimization problem is nonconvex, and one of the technical contributions of this paper is to show that the proportional fair utility optimization can nevertheless be decomposed into a sequence of convex optimization problems. The solution to this sequence of convex problems is the unique solution to the original nonconvex optimization. Surprisingly, this solution can be written in an explicit form that yields considerable insight into the nature of the proportional fair joint airtime/coding rate allocation. To our knowledge, this is the first time that the utility fair joint allocation of airtime/coding rate has been analyzed, and also one of the first times that utility fairness with delay deadlines has been considered.