[Paper Review] Reliability Models for Highly Fault-tolerant Storage Systems

Jason K. Resch, Ilya Volvovski|arXiv (Cornell University)|Oct 2, 2013

Advanced Data Storage Technologies6 references3 citations

TL;DR

This paper proposes a new reliability model for highly fault-tolerant storage systems, such as RAID 6, triple replication, and k-of-n erasure codes, which outperforms existing models like Chen and Angus by accurately capturing the impact of rebuild progress and failure correlation. The key contribution is a refined Markov-based formula that significantly improves MTTDL (Mean-Time-To-Data-Loss) estimation for systems with fault-tolerance >1, especially when MTTF/MTTR ratios are low.

ABSTRACT

We found that a reliability model commonly used to estimate Mean-Time-To-Data-Loss (MTTDL), while suitable for modeling RAID 0 and RAID 5, fails to accurately model systems having a fault-tolerance greater than 1. Therefore, to model the reliability of RAID 6, Triple-Replication, or k-of-n systems requires an alternate technique. In this paper, we explore some alternatives, and evaluate their efficacy by comparing their predictions to simulations. Our main result is a new formula which more accurately models storage system reliability.

Motivation & Objective

• To address the inaccuracy of existing reliability models—particularly the Chen model—for systems with fault-tolerance greater than 1.
• To identify why common models like Chen's overestimate reliability in highly fault-tolerant systems such as RAID 6 and triple replication.
• To develop and validate a new reliability model that accounts for rebuild progress and failure dependencies in k-of-n storage systems.
• To provide a practical, accurate method for estimating MTTDL that supports efficient system design with minimal redundancy.

Proposed method

• Derives a new Markov-based reliability model that accounts for the time-dependent state transitions during disk rebuilds in fault-tolerant storage systems.
• Uses simulation to compare predictions of the new model against the Chen and Angus models under varying MTTF/MTTR ratios and fault-tolerance levels.
• Incorporates the effect of partial rebuilds on URE (Unrecoverable Read Error) exposure, reducing the expected likelihood of data loss during recovery.
• Applies a simplified version of the Angus model for systems with high MTTF/MTTR ratios, where it performs within a few percent of the full model.
• Validates the new model’s accuracy by comparing its MTTDL predictions to empirical simulation results across multiple fault-tolerance levels.
• Introduces a modified failure rate assumption that reflects the reduced exposure to UREs during rebuilds, especially in systems with high fault-tolerance.

Experimental results

Research questions

• RQ1 Why does the Chen model fail to accurately predict MTTDL for systems with fault-tolerance >1, such as RAID 6 or triple replication?
• RQ2 How does the progress of disk rebuilds affect the probability of encountering an Unrecoverable Read Error (URE) during recovery?
• RQ3 Can a Markov-based model be constructed that more accurately estimates MTTDL for k-of-n storage systems with low MTTF/MTTR ratios?
• RQ4 How do correlated disk failures impact MTTDL predictions, and can a realistic model be developed to reflect this in highly fault-tolerant systems?
• RQ5 To what extent does accounting for partial rebuild exposure reduce the expected likelihood of data loss due to UREs in high-fault-tolerance systems?

Key findings

• The Chen model overestimates MTTDL by a factor that grows factorially with fault-tolerance, making it unsuitable for systems with fault-tolerance >1.
• The Angus model provides a good approximation for systems with high MTTF/MTTR ratios, but underperforms when MTTF/MTTR is low.
• The proposed Markov-based model achieves significantly higher accuracy than both Chen and Angus models, especially in low MTTF/MTTR regimes.
• The model shows that the first (f-1)/f of the disk data is already read during the rebuild of the first failed disk, reducing exposure to UREs during subsequent failures.
• Simulations confirm that the new model’s MTTDL predictions closely match empirical results, validating its use for system design.
• The study suggests that URE exposure is not uniformly distributed across all data during rebuilds, and this should be factored into reliability models for high-fault-tolerance systems.