  We propose a new exact solution algorithm for closed multiclass product-form
queueing networks that is several orders of magnitude faster and less memory
consuming than established methods for multiclass models, such as the Mean
Value Analysis (MVA) algorithm. The technique is an important generalization of
the recently proposed Method of Moments (MoM) which, differently from MVA,
recursively computes higher-order moments of queue-lengths instead of mean
values.
  The main contribution of this paper is to prove that the information used in
the MoM recursion can be increased by considering multiple recursive branches
that evaluate models with different number of queues. This reformulation allows
to formulate a simpler matrix difference equation which leads to large
computational savings with respect to the original MoM recursion. Computational
analysis shows several cases where the proposed algorithm is between 1,000 and
10,000 times faster and less memory consuming than the original MoM, thus
extending the range of multiclass models where exact solutions are feasible.
