Description
In [1] [2], we proposed a family of distributed scheduling and rate control algorithms to achieve the maximal throughput in a general class of networks with interference constraints, as well as approaching the optimal fairness among different data flows. These algorithms were inspired by CSMA (Carrier Sense Multiple Access). In this paper, we analyze and prove the convergence of such a scheduling algorithm and the queue stability it guarantees, with properly-chosen step sizes and adjustment periods. Convergence of other algorithms in [1] [2] can be proved similarly.