Semi-Markov Estimation of Dependability of Information System for Critical Use
DOI:
https://doi.org/10.31649/1997-9266-2019-143-2-61-77Keywords:
system for critical use, dependability, controlled semi-Markov process, multi-state system, stochastic modelingAbstract
The information system for critical use (ISCU) can be classified as a complex, extensive information system operating in the software-hardware environment of a network client-server system. To estimate the dependability of the hardware component of the ISCU we can use known, approved, correct methods. At the same time, in order to estimate the dependability of the information component of the system, additional studies are required related to the specific features of the ISCU architecture and its critical use. In particular, an object-oriented description of such indicators of dependability as reliability, recoverability, and structural redundancy are necessary. Also, when modeling it is necessary to take into account the specific interpretation of the concept of a functional state for such a system. Analysis of the results of an information search has shown that the mathematical apparatus of Markov networks turns out to be optimal for the dependability estimation of the ISCU modelling from the standpoint of taking into account the architectural features of the system and the specifics of its functioning. Thus, for the first time, a complex of the controlled semi-markov models describing the dynamics of the functioning information system for critical use was proposed, in which, unlike the existing ones, the system being modeled is considered as a many states system, in which semi-markov description the states described by different distributions agree, which allows to formalize the maximum likelihood estimation function and parameters of the semi-Markov process that describes the life cycle of the ISCU, for possible types of distributions of its states, identify the Markov recovery functions and the semi-Markov transition matrix of this process and formulate expressions for calculating the indicators of the simulated system's dependability. The article synthesizes expressions for calculating the likelihood for uncensored and censored specific segments of semi-Markov processes with one and many trajectories that simulate the life cycle of the ISCU. Expressions for the maximum likelihood estimation and the parameters estimation of the original distribution class, which are basic for certain semi-Markov processes, are synthesized. Expressions are obtained for estimating such integral characteristics of the dependability of the ISCU as reliability, availability, maintainability, failure rate and the average system uptime in the formalism of the semi-Markov models obtained. This article analytically proved the correctness of the obtained estimates of the parameters of a semi-Markov process that simulates the operation of an information system for critical use. An empirical study was conducted in which the proposed methodology for estimating the dependability of efficiency of the ISCU was tested. The results of the study proved, in particular, that an analytical assessment of the reliability of the simulated system approaches the real value of this characteristic with an increase in the interval of observation of the operation of the ISCU, and the confidence interval for the reliability calculated on the basis of the proposed models covers the real value of this characteristic.
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