  This article provides a comparison of the successive lumping (SL) methodology
with the popular lattice path counting algorithm in obtaining rate matrices for
queueing models, satisfying the quasi birth and death structure. The two
methodologies are compared both in terms of applicability requirements and
numerical complexity by analyzing their performance for the same classical
queueing models.
  The main findings are: i) When both methods are applicable 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 LPCAs is that the former includes a method to compute
the steady state distribution using this rate matrix.
