Two-level solution method for Markov chain modelling transfer lines with unreliable servers and finite buffers

Transfer lines with inter-stage buffers and unreliable servers are often modelled by means of Markov chains. Because of the large number of states, solving the steady-state equations of the chain is not a trivial task. This paper proposes a two-level iterative scheme for computing the steady-state probability distribution. In the framework of non-negative matrix theory some general results are proved which guarantee the convergence of the proposed procedure. Moreover, numerous numerical experiments are given, which show that the two-level iterative scheme enjoys a very good rate of convergence. The method also works suitably for solving the steady-state probability equation of chains modelling systems with more than three stages