Time-Reversibility of Stationary Markov Chains and Queueing Processes
Article Sidebar
Main Article Content
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: cast@kmitl.ac.th
Article Details
Copyright Agreement Statement
The corresponding author has to submit Copyright Agreement form after the article is accepted for publication in order to warrant that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
The author(s) grant Current Applied Science and Technology a non-exclusive, irrevocable, royalty-free license to publish, reproduce, distribute, and archive the article in print and electronic form with effect if and when the article is accepted for publication. In the event that the article is withdrawn prior to acceptance or is declined, this agreement shall have no effect, and no party shall be bound by it.
The author(s) retain copyright of this article, including but not limited to the right to reproduce and distribute the article, to include it in a thesis or book, and to post it on an institutional or personal repository, provided that the original publication in Current Applied Science and Technology is properly cited.
References
[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.
