Semi-Markov Reliability Model of a Computer System with Container Virtualization

Abstract

In modern cloud infrastructures and microservice architectures, ensuring high reliability, fault tolerance, and continuity of application operation is a critically important task. The primary factor reducing the efficiency of such systems is the phenomenon of software aging – the gradual degradation of system resources (memory leaks, data fragmentation) during prolonged operation, leading to a nonlinear increase in failure intensity. The complexity of reliability prediction under such conditions is обусловлена by the hierarchical dependency between the host's shared software and isolated containers, as well as the dynamic nature of recovery processes. This paper addresses the pressing problem of ensuring software reliability in a computer system with container virtualization subject to the phenomenon of software aging. The scientific novelty lies in the development of a comprehensive mathematical model based on semi-Markov processes, which accounts for the hierarchical structure of the system (host shared software and isolated containers) and enables the optimization of proactive recovery strategies. The Weibull distribution is used to describe the aging process, reflecting an increasing failure rate. A semi-Markov model of states and transitions is proposed, incorporating mechanisms of proactive container restart and migration. To reduce computational complexity, a simplified model is developed based on the assumption of negligibly low probability of secondary failures during short recovery intervals. Calculations of steady-state probabilities and availability are implemented in the Mathcad environment. The conducted numerical experiments showed that implementing a proactive recovery strategy within the interval range of 1200-2400 hours substantially improves the system availability. It is established that the error of the simplified model is negligible compared to the rigorous model. The proposed model allows determining the maximum availability value depending on the number of deployed containers and proactive container restart intervals. A comparison of the developed approach with traditional reactive recovery models confirms the advantage of proactive methods in minimizing downtime caused by error accumulation (memory leaks, resource fragmentation). The proposed model can be applied in the design of highly reliable cloud infrastructures and DevOps pipelines.