Lexicographic Max-Min Fairness in a Wireless Ad Hoc Network with Random Access

We consider the lexicographic max-min fair rate control problem at the link layer in a random access wireless network. In lexicographic max-min fair rate allocation, the minimum link rates are maximized in a lexicographic order. For the Aloha multiple access model, we propose iterative approaches that attain the optimal rates under very general assumptions on the network topology and communication pattern; the approaches are also amenable to distributed implementation. The algorithms and results in this paper generalize those in our previous work [7] on maximizing the minimum rates in a random access network, and nicely connects to the “bottleneck-based” lexicographic rate optimization algorithm popularly used in wired networks [1].