Experimental results on matrix-analytical solution techniques-Extensions and comparisons

The matrix-analytic analysis of many stochastic models requires the solution of nonlinear matrix equations. In this paper, several iterative algorithms for solving these equations are reviewed and insights gained on their convergence behavior are reported. An extension to these algorithms based on linear extrapolation is proposed with a view towards extending the computational feasibility of the matrix-analytic techniques to even larger classes of problems. Although this proposed extension is a minor addition to the existing algorithms, it has been observed to considerably improve their efficiency especially when the convergence rates are slow. This is illustrated through several examples, for which the CPU requirements of the reviewed algorithms are compared. Finally, the matrix-geometric approach is compared to the M/G/1 approach through specific examples and the conclusions are summarized.