Time-Reversibility of Stationary Markov Chains and Queueing Processes

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Published: Nov 12, 2018
Keywords:
Time-reversibility, Markov chain, invariant measure, atom, queue, waiting time, queue-length

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Hideo Ōsawa
Nihon University, College of Economics, Tokyo, Japan
Chikayoshi Shina
Nihon University, College of Science and Technology, Tokyo, Japan

Abstract

This paper considers the time-reversibility of stationary Markov chains in discrete-time with general state space and its applications to queueing processes. Ōsawa obtained the necessary and sufficient conditions for time-reversibility of Markov chains with general state space and applied these results to queueing processes. His results are introduced here and some time-reversible processes. His results are introduced here and some time-reversible processes are studied.


Keywords:  Time-reversibility, Markov chain, invariant measure, atom, queue, waiting time, queue-length


Corresponding author: E-mail: [email protected]

Article Details

Issue
Vol. 5 No. 1 (2005)
Section
Original Research Articles

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References

[1] F.P. Kelly, Reversibility and Stochastic Networks, (John Wieley & Sons, New York (1979)).
[2] A. Kolmogorov, Zur theorie der Markoffshen ketten, Mathematishe Annalen 112 (1936), 155-160.
[3] H. Ōsawa, Reversibility of Markov chains with applications to storage models, J. Appl. Prob. 22 (1985), 123-137.
[4] H. Ōsawa, Reversibility of first-order autoregressive processes, Stochastic Processes and their Applications 28 (1988), 61-69.
[5] H. Ōsawa, Discrete-time storage models with negative binomial inflow, Journal of the Operations Research of Japan 32 (1989), 218-232.
[6] H. Ōsawa, Reversibility and Markovian Storage Processes, (Doctorial Thesis, Tokyo Institute of Technology (1990)).
[7] H. Ōsawa, Quasi-reversibility of a discrete-time queue and related models, Queueing Systems 18 (1994), 133-148.
[8] H. Ōsawa and C. Shima, Reversibility of Lindley processes with discrete states, Report of the Research Institute of Science and Technology Nihon University, 44 (1999), 1-8.