On the Dual Relationship between Markov Chains of Gi/m/1 and M/g/1 Type

In 1990 Ramaswami proved that, given a Markov renewal process of M/G/1– type, one can construct a Markov renewal process of GI/M/1–type such that the matrix transforms G(z, s) for the M/G/1–type process and R(z, s) for the GI/M/1–type process satisfy a duality relationship. In his 1996 PhD thesis, Bright used time reversal arguments to show that it is… (More)