Lexicographic Max-Min Fair Rate Allocation in Random Access Wireless Networks

We consider the lexicographic max-min fair rate control problem at the link layer in a random access wireless network. In the lexicographic max-min fair rate allocation, the minimum link rates in the network are maximized in a lexicographic order. For the Aloha multiple access model, we propose iterative approaches that attain optimal rates under very general assumptions on the network topology and communication pattern; the approaches are also amenable to a distributed implementation. The approach and result in this paper generalize those in the work of X. Wang and K. Kar (2004) on maximizing the minimum link rate in a random access network, and nicely connect to the "bottleneck-based" lexicographic max-min rate optimization algorithm popularly used in wired networks by D. Bertsekas and R. Gallagher (1992)