MATHEMATICAL MODEL FOR CALCULATING RELIABILITY INDICES OF SCALABLE COMPUTER SYSTEMS WITH SWITCHING TIME

Abstract

The main feature of scalable computer systems is modularity. Increasing performance in
such systems is achieved by increasing the same type of elements, elementary machines (EM, for
example, a computing node). As a result of failures, the system performance is changed. Thus,
scalability of computer systems (CS), on the one hand, increases performance, but on the other
hand, computer resource growth exacerbates the problem of reliability and increases the complexity
of organizing effective functioning. Analysis of reliability and potential capabilities of computing
systems is still an urgent problem. For quantitative analysis of the functioning of scalable
computing systems, robustness indices related to reliability are used. For example, indices of potential
robustness of CS take into account the fact that all operable elementary machines are used
in solving tasks, the number of which (EM) changes over time as a result of failures and recoveries.
When analyzing reliability, models based on the theory of Markov processes and Queuing
theory (QT) are popular in the theory of computing systems. Most QT analytical models do not
consider the switching time (reconfiguration) in a separate parameter, due to the complexity of thesolution. Usually, models are simplified by the fact that the recovery time and switch combined in a
single parameter. Analytical solutions of a system of differential equations with three parameters
(failure, recovery, and switching) for calculating reliability and potential robustness are obtained on
the example of the QT model. This allows the user to determine whether the switching time should be
taken into account. Also it is shown that solutions of the three-parameter model are reduced to solutions
of the two-parameter model if the switching time is not taken into consideration.