A note on the convergence of asynchronous greedy algorithm with relaxationin a multiclass queueing environment

In this letter, we consider the convergence of asynchronous greedy algorith m with relaxation for the Nash equilibrium in a noncooperative multiclass q ueuing environment, The process of asynchronous greedy algorithm is equival ent to the iteration of Jacobi method in solving a linear system. However, it has been proved that the algorithm converges only for some particular ra nge of queuing parameters, Here we propose the asynchronous greedy algorith m with relaxation, which is in principle equivalent to solving a linear sys tem by Jacobi method with relaxation. We propose also some relaxation param eters such that our algorithm converges very fast.