|
On Markovian and rational arrival processes. II
V. A. Naumova, K. E. Samouylovbc a Service Innovation Research Institute, 8A Annankatu, Helsinki 00120, Finland
b Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
c 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
Abstract:
This article is the second part of the review carried out within the framework of the RFBR project No. 19-17-50126. 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 the 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. 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.
Keywords:
Markov chain, Markovian arrival process, Markov additive process, MAP, MArP.
Received: 02.07.2020
Citation:
V. A. Naumov, K. E. Samouylov, “On Markovian and rational arrival processes. II”, Inform. Primen., 14:4 (2020), 37–46
Linking options:
https://www.mathnet.ru/eng/ia695 https://www.mathnet.ru/eng/ia/v14/i4/p37
|
|