A Quasi-Reversibility Approach to the Insensitivity of Generalized Semi-Markov Processes
1989 ◽
Vol 3
(3)
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pp. 405-415
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Keyword(s):
This paper is concerned with a certain property of the stationary distribution of a generalized semi-Markov process (GSMP) known as insensitivity. It is well-known that the so-called Matthes' conditions form a necessary and sufficient algebraic criterion for insensitivity. Most proofs of these conditions are basically algebraic. By interpreting a GSMP as a simple queueing network, we are able to show that Matthes' conditions are equivalent to the quasi-reversibility of the network, thus obtaining another simple proof of the sufficiency of these conditions. Furthermore, we apply our method to find a simple criterion for the insensitivity of GSMP's with generalized routing (in a sense that is introduced in the paper).
2004 ◽
Vol 41
(3)
◽
pp. 746-757
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Keyword(s):
1970 ◽
Vol 7
(02)
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pp. 388-399
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2003 ◽
Vol 40
(4)
◽
pp. 1060-1068
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