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An iterative approximation scheme for repetitive Markov processes
Date
1999-09-01
Author
Tüfekçi, Tolga
Güllü, Refik
Metadata
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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Repetitive Markov processes form a class of processes where the generator matrix has a particular repeating form. Many queueing models fall in this category such as M/M/1 queues, quasi-birth-and-death processes, and processes with M/G/1 or GI/M/1 generator matrices. in this paper, a new iterative scheme is proposed for computing the stationary probabilities of such processes. An infinite state process is approximated by a finite state process by lumping an infinite number of states into a super-state. What we call the feedback rate, the conditional expected rate of flow from the super-state to the remaining states, given the process is in the super-state, is approximated simultaneously with the steady state probabilities. The method is theoretically developed and numerically tested for quasi-birth-and-death processes. It turns out that the new concept of the feedback rate can be effectively used in computing the stationary probabilities.
Subject Keywords
Statistics, Probability and Uncertainty
,
Statistics and Probability
,
General Mathematics
URI
https://hdl.handle.net/11511/64381
Journal
JOURNAL OF APPLIED PROBABILITY
DOI
https://doi.org/10.1239/jap/1032374624
Collections
Department of Industrial Engineering, Article
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T. Tüfekçi and R. Güllü, “An iterative approximation scheme for repetitive Markov processes,”
JOURNAL OF APPLIED PROBABILITY
, pp. 654–667, 1999, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64381.