Analysis of a two-stage finite buffer flow controlled queueing model by a compensation method

The exact analysis of a two-stage finite buffer Markovian queueing model with blocking and window flow control is considered. The state distribution and mean performance measures are obtained by applying a so-called compensation method. This reduces the problem to that of (1) finding the Green’s function for a related bivariate homogeneous Markov process defined on an unrestricted two-dimensional state space and (2) solving a relatively small system of linear equations involving the Green’s function. The method is a rank-reducing real-domain technique that transforms the two-dimensional problem into one dimension. The method of analysis is computationally efficient and facilitates parametric analysis with respect to the choice of buffer size and flow control policy.