A comparative analysis of the successive lumping and the lattice path counting algorithms

This article provides a comparison of the successive lumping (SL) methodology developed in [19] with the popular lattice path counting [24] in obtaining rate matrices for queueing models, satisfying the specific quasi birth and death structure as in [21], [22]. The two methodologies are compared both in terms of applicability requirements and numerical complexity by analyzing their performance for the same classical queueing models considered in [21]. The main findings are: i) When both methods are applicable the SL based algorithms outperform the lattice path counting algorithm (LPCA). ii) There are important classes of problems (e.g., models with (level) non-homogenous rates or with finite state spaces) for which the SL methodology is applicable and for which the LPCA cannot be used. iii) Another main advantage of successive lumping algorithms over lattice path counting is that the former includes a method to compute the steady state distribution using this rate matrix.