Convergence of synchronous and asynchronous greedy algorithms in a multiclass telecommunications environment

The Nash equilibrium point for optimum flow control in a noncooperative multiclass environment is studied. Convergence properties of synchronous and asynchronous greedy algorithms are investigated in the case where several users compete for the resources of a single queue using power as their performance criterion. A proof of the convergence of a synchronous greedy algorithm for the n users case is given, and the necessary and sufficient conditions for the convergence of asynchronous greedy algorithms are obtained. Another important contribution is the introduction to the literature and the extension of a not very widely known theorem for the convergence of Gauss-Seidel algorithms in the linear systems theory.>