Title
On the dual relationship between Markov chains of GI/M/1 and M/G/1 type
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Sheffield ,
Subject
Mathematics
Source (journal)
Advances in applied probability. - Sheffield, 1969, currens
Volume/pages
42(2010) :1 , p. 210-225
ISSN
0001-8678
1475-6064
ISI
000277002600010
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/5566d4/4453.pdf
E-info
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000277002600010&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000277002600010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000277002600010&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
Handle