Are Markov Models Effective for Storage Reliability Modelling?

TL;DR

This paper demonstrates that with careful approximations and advanced modeling techniques, continuous-time Markov chains can effectively model storage system reliability, overcoming traditional limitations like the memoryless property and non-exponential failure distributions.

Contribution

The authors introduce a method to accurately model storage reliability using CTMCs by incorporating non-exponential distributions and state-space reduction, challenging the notion that simulation is the only viable approach.

Findings

CTMC models can approximate non-exponential failure distributions.

The proposed approach reduces computational cost compared to simulation.

Results closely match those obtained from simulation.

Abstract

Continuous Time Markov Chains (CTMC) have been used extensively to model reliability of storage systems. While the exponentially distributed sojourn time of Markov models is widely known to be unrealistic (and it is necessary to consider Weibull-type models for components such as disks), recent work has also highlighted some additional infirmities with the CTMC model, such as the ability to handle repair times. Due to the memoryless property of these models, any failure or repair of one component resets the "clock" to zero with any partial repair or aging in some other subsystem forgotten. It has therefore been argued that simulation is the only accurate technique available for modelling the reliability of a storage system with multiple components. We show how both the above problematic aspects can be handled when we consider a careful set of approximations in a detailed model of the system. A detailed model has many states, and the transitions between them and the current state captures the "memory" of the various components. We model a non-exponential distribution using a sum of exponential distributions, along with the use of a CTMC solver in a probabilistic model checking tool that has support for reducing large state spaces. Furthermore, it is possible to get results close to what is obtained through simulation and at much lower cost.