zbMATH — the first resource for mathematics

Semi-Markov models of renewal systems and queueing systems. (Polumarkovskie modeli vosstanavlivaemykh sistem i sistem massovogo obsluzhivaniya.) (Russian) Zbl 0778.60064
Kishinev: Shtiintsa. 276 p. (1991).
Some problems of the reliability theory and the queueing theory are considered. They are described with the help of finite systems of stepped semi-Markov processes. To analyse such a system the authors transform it to a multi-dimensional Markov process extending its phase space with continuous time components. The book consists of 5 chapters. The first one is devoted to general ideas and theorems of the semi-Markov theory. The authors attract the special attention to precise and approximate evaluation of stationary probabilities and expectations of such a system. In the second chapter characteristics of superpositions of semi-Markov processes are investigated. Chapters 3 and 4 are dedicated to the analysis of technical systems with reserve elements. Semi-Markov components of the complex process describing such a system depend on the structure of the system, on the reserving and maintenance policy. In the last chapter some stationary characteristics of \(GI/G/2/0\), \(GI/G/1/\infty\) and other queueing systems are examined.

60K15 Markov renewal processes, semi-Markov processes
60-02 Research exposition (monographs, survey articles) pertaining to probability theory