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

AbstructIn this letter, the Nash equilibrium point for optimum flow control in 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. The main contributions of this letter consist of the proof of the convergence of a synchronous greedy algorithm for the n users case and the obtaining of the necessary and sufficient conditions for the convergence of asynchronous greedy algorithms. Another very important contribution of this letter 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.