The semi-markov model for the ‘technological module – storage device’ structure

Simulation of physical processes
Authors:
Kopp Vadim Ya. Kartashov Aleksey L. Zamoryonov Michael V. Klyukin Valery Y.
Abstract:

The theory of semi-Markov process has been used to design the model of ‘technological module – storage device’ (TM-SD) structure. Stationary characteristics based on obtained equations were determined to find stationary distribution of the Markov embedded chain. Relying upon performed studies the stationary distribution of semi-Markov process was determined. This allowed calculation of the availability ratio of TM-SD structure and the design formula was given. The Markov restoration equations for TM-SD system with taking into account TM and SD failures were solved assuming the exponential behavior of these failures. The obtained expressions describe operating of such a system and allow substitution of TM-SD system with an equivalent element with two factor states. This result significantly simplifies the modeling problem for more complex systems. The legitimacy of using exponential distributions of random variables (error-free periods for TM and SD) was analyzed. The performed simulation modeling disclosed that the hypothesis for an exponential behavior of error-free periods for TM as a whole (and SD as well) can be accepted even in the case that TM (or SD) consists of six nodes.