As a file system ages, it can experience multiple forms of fragmentation. Fragmentation of the free space in the file system can lower write performance and subsequent read performance. Client operations as well as internal operations, such as deduplication, can fragment the layout of an individual file, which also impacts file read performance. File systems that allow sub-block granular addressing can gather intra-block fragmentation, which leads to wasted free space. Similarly, wasted space can also occur when a file system writes a collection of blocks out to object storage as a single large object, because the constituent blocks can become free at different times. The impact of fragmentation also depends on the underlying storage media. This article studies each form of fragmentation in the NetApp ® WAFL ® file system, and explains how the file system leverages a storage virtualization layer for defragmentation techniques that physically relocate blocks efficiently, including those in read-only snapshots. The article analyzes the effectiveness of these techniques at reducing fragmentation and improving overall performance across various storage media.

Stochastic models are often employed to study dependability of critical systems and assess various hardware and software fault-tolerance techniques. These models take into account the randomness in the events of interest (aleatory uncertainty) and are generally solved at fixed parameter values. However, the parameter values themselves are determined from a finite number of observations and hence have uncertainty associated with them (epistemic uncertainty). This paper discusses methods for computing the uncertainty in output metrics of dependability models, due to epistemic uncertainties in the model input parameters. Methods for epistemic uncertainty propagation through dependability models of varying complexity are presented with illustrative examples. The distribution, variance and expectation of model output, due to epistemic uncertainty in model input parameters are derived and analyzed to understand their limiting behavior.

In this paper, we discuss a Monte Carlo sampling based method for propagating the epistemic uncertainty in model parameters, through the system availability model. We also outline methods to compute the number of samples needed to obtain a desired confidence interval for various scenarios. We illustrate this method with a real system example and discuss the results obtained. While our example discusses confidence interval for system availability, this method can be directly applied to compute uncertainty for other dependability, performance and perform ability measures, computed by solving stochastic analytic models. We also emphasize the fact that no simulation is carried out in our method but a repeated sampling is performed over the parameter space followed by the execution of the analytic model with the final phase being the statistical analysis of the output vector.