Source: Adv. in Appl. Probab.
Volume 42, Number 1
In 1990, Ramaswami proved that, given a Markov renewal process of M/G/1 type,
it is possible to 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 possible to define a different dual for
positive-recurrent and transient processes of M/G/1 type and GI/M/1 type. Here
we compare the properties of the Ramaswami and Bright dual processes and show
that the Bright dual has desirable properties that can be exploited in the
design of algorithms for the analysis of Markov chains of GI/M/1 type and M/G/1
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