A stable recursion for the steady state vector in markov chains of m/g/1 type

For the matrix analogues of Markov chains of the M/G/1 type, we derive a stable recursive scheme to compute the steady state probability vector. This scheme, which is the natural generalization of a clever device attributed to P.J. Burke in the M/G/1 case, is substantially superior to the Gauss-Seidel iterative scheme.