Non-skip-free M/G/1-type Markov chains and Laurent matrix power series Original Research Article

Non-skip-free Markov chains of the M/G/1 type are revisited in functional form. The problem of the computation of the steady state vector is reduced to inverting a Laurent matrix power series A(z) which is singular for z=1. This problem is related to the Wiener–Hopf factorization and to solving matrix equations. A way for removing the singularity is presented and some algorithms for inverting a Laurent matrix power series are shown. A generalization of Ramaswamiʹs formula is derived from the Wiener–Hopf factorization of A(z).