Bounds and Error bounds for unsolvable CT Markov chains

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Abstract

An approach is presented to compare two Markov Chains, particularly Continuous-Time Markov Chains (CTMC) such as to model Queueing Networks (QN). Here one may typically think of one CTMC or QN to be a solvable modification (e.g. a product form QN) of the other one, say the original, which is of practical interest but unsolvable. The approach is essentially based upon evaluating performance measures by cumulative reward structures and analytically bounding so-called bias-terms, also known as relative gains or fundamental matrix elements. A general comparison and error bound result will be provided. The approach, referred to as Markov Reward approach, is related to Stochastic Dynamic programming and
• may lead to analytic error bounds for the discrepancy, and
• may still apply while stochastic comparison fails
To motivate and illustrate the approach, the presentation will contain an instructive finite tandem queue example and a practical result for a real-life application of an Operation Theater-Intensive care unit system. Some remaining questions for research will be addressed briefly.
Original languageEnglish
Title of host publication15th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017)
EditorsCharalambos Tsitouras, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos, Theodore Simos
Place of PublicationUnited States
PublisherAIP Publishing LLC
Pages1-5
Number of pages5
Volume1978
Edition1
ISBN (Electronic)9780735416901
ISBN (Print)978-0-7354-1690-1
DOIs
Publication statusPublished - 10 Jul 2018
Event15th International Conference on Numerical Analysis and Applied Mathematics 2017 - The MET Hotel, Thessaloniki, Greece
Duration: 25 Sep 201730 Sep 2017
Conference number: 15
http://icnaam.org/sites/default/files/Leaflet_ICNAAM_2017.pdf

Publication series

NameINTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)
ISSN (Print)0094-243X

Conference

Conference15th International Conference on Numerical Analysis and Applied Mathematics 2017
Abbreviated titleICNAAM 2017
CountryGreece
CityThessaloniki
Period25/09/1730/09/17
Internet address

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    van Dijk, N. M. (2018). Bounds and Error bounds for unsolvable CT Markov chains. In C. Tsitouras, T. Simos, T. Simos, T. Simos, T. Simos, & T. Simos (Eds.), 15th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017) (1 ed., Vol. 1978, pp. 1-5). [190008] (INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)). United States: AIP Publishing LLC. https://doi.org/10.1063/1.5043835