Semi-markov model of processing requests to the cloud storage

Abstract

This paper presents a semi-Markov model as an important part of the computer-aided manufacturing and a modular system of cloud storage, which affects the functioning of the whole process. The residence times of the system in states and the probability of system transitions are determined. There is a stationary distribution of the embedded Markov chain. The residence times of the system in states with allowance for repeated hits are determined by the theorem on the distribution functions of the residence times of the system in states with allowance for repeated hits. When using the trajectory method, the distribution function of the time for the complete processing of the read request by such a system is determined. A comparison of the expectation time complete processing the read request obtained in this study and obtained by the known formula for determining from the literature the expectation residence time in the subset of the system states.