Informatics and Applications
2020, Volume 14, Issue 3, pp 13-19
ON MARKOVIAN AND RATIONAL ARRIVAL PROCESSES. I
- V. A. Naumov
- Ê. Å. Samouylov
Abstract
This article is the first part of a review carried out within the framework of the RFBR project No. 1917-50126. The purpose of this review is to get the interested readers familiar with the basics of the theory of Markovian arrival processes to facilitate the application of these models in practice and, if necessary, to study them in detail. In the first part of the review, the properties of general Markovian arrival processes are presented and their relationship with Markov additive processes and Markov renewal processes is shown. In the second part of the review, the important for applications subclasses of Markovian arrival processes, i. e., simple and batch arrival processes of homogeneous and heterogeneous arrivals, are considered. After that, it is shown how the properties of Markovian arrival processes are associated with the product form of stationary distributions of Markov systems. In conclusion, matrix-exponential distributions and rational arrival processes are discussed that expand the capabilities of Markovian arrival processes for modeling complex systems, while preserving the convenience of analyzing them using computations.
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[+] About this article
Title
ON MARKOVIAN AND RATIONAL ARRIVAL PROCESSES. I
Journal
Informatics and Applications
2020, Volume 14, Issue 3, pp 13-19
Cover Date
2020-09-30
DOI
10.14357/19922264200302
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov chain; Markovian arrival process; Markov additive process; MAP; MArP
Authors
V. A. Naumov  and Ê. Å. Samouylov  , 
Author Affiliations
Service Innovation Research Institute, 8A Annankatu, Helsinki 00120, Finland
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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