Keynote

Marked Markov Processes and Their Applications

Prof. Vladimir V. Rykov(Russia)

It appears that A.N. Kolmogorov was the first to use the term "processes with discrete random intervention (PDRI)." This terminology has been adopted by Yu.A. Rozanov [1], A.N. Shiryaev [2], and several other authors. However, references to the first mention of this term and its definition (even informal) could not be found. A conceptually similar notion is used by several foreign authors under the name "Discrete Event System (DES) modeling" [3]. As a mathematical framework for studying such systems, Generalized Semi-Markov Processes (GSMP) have been proposed [4]. These processes enable the analysis of many real-world stochastic systems. However, their structure is sufficiently complex and does not always allow for practical numerical analysis or result visualization. This talk formalizes the PDRI concept and proposes its mathematical model as Marked Markov Processes (MMP) in the specific case when intervention times are generated by a sequence of independent and identically distributed random variables. Examples are provided demonstrating the application of MMPs to describe various systems in queuing theory, reliability theory, inventory control, warranty analysis, and other fields, along with results of their numerical analysis.

References:

Yu.A. Rozanov. Introduction to the Theory of Random Processes. Nauka, 1982.
A.N. Shiryaev. Fundamentals of Stochastic Financial Mathematics. Vol. 1. Facts. Models. FAZIS, Moscow, 1998.
P. Haas (2002) Stochastic Petri Nets: Modeling, Stability, Simulation. Springer Series in Operations Research. Springer, 2002. 509p.
Glynn P.W. A GSMP formalism for discrete event systems // Proceedings of the IEEE. 1989. Vol. 77, No. 1. Pp. 14-23. DOI: 10.1109/5.21067

About the speaker

Prof. Vladimir V. Rykov

Russia

RUDN University,
Department of Applied Informatics and Probability Theory
Professor
Russian State University of Oil and Gas (Gubkin University),
Department of Applied Mathematics
Professor

Vladimir V. Rykov - doctor of science, professor, graduated from the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University in 1960, PhD from the Central Economics and Mathematics Institute in 1964 and his doctorate at Moscow State University in 1990.

Since 1973, Associate Professor, then Professor of the Russian State University of Oil and Gas (Gubkin University)- Department of Applied Mathematics, since 1990 - Professor of People’s Friendship University (RUDN University)- Department of Probability Theory and Mathematical Statistics (1990-2014), from 2014 to the present - Professor of the Department of Applied Informatics and Probability Theory.

His main research interests are controlled stochastic systems and networks (including especially controlled queueing systems), reliability theory and risk theory.

V.V. Rykov is the author of more than 250 widely known scientific works in Russian and foreign publications, several monographs, reviews, textbooks, he is also the editor of collections of works and conference materials,

V.V. Rykov is the editor-in-chief of the journal “Reliability: Theory & Applications” (Gnedenko Forum), a member of the editorial board of the journals “Automation and Telemechanics” and “Automatic Control and Computer Sciences”, a guest editor of the special issue “Stochastic Modeling and Applied Probability” of the journal “Mathematics”, as well as a permanent member of the organizing committees and participant in a series of major international conferences, including DCCN and others.