Keywords: storage systems, queueing networks, stochastic modelling.

The efficient operation of public and private enterprises worldwide depends critically on the reliability and performance of their data storage infrastructure. Redundant array of inexpensive disks (RAID) systems form fundamental components of almost all non-trivial modern storage infrastructures because they provide the ability to synthesise several physical storage devices into a single logical unit with potentially higher levels of performance and, or reliability than can be provided by any constituent device alone. Nevertheless, realised performance can vary dramatically according to the selected RAID configuration and I/O workload. Performance models provide a low-cost means to help system designers and engineers select the most appropriate RAID components and corresponding configurations capable of delivering a required level of quality of service.

In this context, this chapter presents a review of recently developed analytical techniques for predicting the cumulative distribution of I/O request response time in zoned hard disks and RAID systems made up of zoned hard disks. The ability to reason about full distributions (and derived measures such as percentiles) rather than just means of the response time (as has been the focus of much related work) is critical to fulfil modern service level agreements (SLAs). RAID levels 0, 01, 10 and 5 and a variety of workload types are supported.

The models are constructed in a bottom-up hierarchical manner. At the lowest level, an individual drive is modelled as an M/G/1 queue in which the arrival process corresponds to I/O requests arriving at the disk and the service process corresponds to the time to position the disk head and transfer the data. A RAID system is then abstracted as a fork-join queueing network comprising several M/G/1 queues, each of which represents one disk drive in the array. We derive an analytical approximation for the distribution of I/O request response time in such a system, taking into account the I/O request patterns associated with particular request types and request sizes under different RAID levels. The models are also extended to take into account modern scheduling algorithms that reorder queueing requests in order to minimise disk head positioning time.

Throughout, in order to improve, validate and gain insight into the analytical models, we compare the analytical predictions not only against simulation models which we develop but also against measurements taken from real disk drives and RAID devices.

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