On the dual relationship between Markov chains of GI/M/1 and M/G/1 type
P. G. Taylor and B. Van Houdt
Source: Adv. in Appl. Probab. Volume 42, Number 1
(2010), 210-225.
Abstract
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 type.
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Keywords: Matrix-analytic models; quasi-birth-and-death process; processes of GI/M/1 type; processes of M/G/1 type
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1269611150
Digital Object Identifier: doi:10.1239/aap/1269611150
Zentralblatt MATH identifier: 05717824
Mathematical Reviews number (MathSciNet): MR2666925
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