An iterative approximation scheme for repetitive Markov processes

Date

1999-09-01

Author

Tüfekçi, Tolga
Güllü, Refik

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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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Citation Formats

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.