A hybrid algorithm for queueing systems

In this paper, we propose a hybrid algorithm based on [12] for solving linear systems of equations. The hybrid algorithm combines the evolutionary algorithm and the successive over-relaxation (SOR) method. The evolutionary algorithm allows the relaxation parameter w to be adaptive in the SOR method. We prove the convergence of the hybrid algorithm for strictly diagonal dominant linear systems. We then apply it to solve the steady-state probability distributions of Markovian queueing systems. Numerical examples are given to demonstrate the fast convergence rate of the method.