Etaqa-MG1: an efficient technique for the analysis of a class of M/G/1-type processes by aggregation

We extend the Etaqa approach, initially proposed for the efficient numerical solution of a class of quasi-birth–death processes, to a more complex class of M/G/1-type Markov processes where arbitrary forward transitions are allowed but backward transitions must be to a single state to the previous level. The new technique reduces the exact solution of this class of M/G/1-type models to that of a finite linear system. We demonstrate the utility of our method by describing the exact computation of an extensive class of Markov reward functions that include the expected queue length or its higher moments. We also provide an algorithm that finds an appropriate state reordering satisfying our applicability conditions, if one such order exists. We illustrate the method, discuss its complexity and numerical stability, and present comparisons with other traditional techniques.