RAID5 Disk Arrays Research Articles

Reliability model of disk arrays RAID-5 with data striping

Within the scope of the this scientific paper, the simplified reliability model of disk arrays RAID-5 (redundant arrays of inexpensive disks) and an advanced reliability model offered by the authors taking into the consideration nonzero time of the faulty disk replacement and different failure rates of disks in normal state of the disk array and in degraded and rebuild states are discussed. The formula obtained by the authors for calculation of the mean time to data loss (MTTDL) of the RAID-5 disk arrays on basis of the advanced model is also presented. Finally, the technique of estimation of the initial reliability parameters, which are used in the reliability model, and the calculation examples of the mean time to data loss of the RAID-5 disk arrays for the different number of disks are also given.

Vacationing server model for M/G/1 queues for rebuild processing in RAID5 and threshold scheduling for readers and writers

We present two methods to obtain the mean delay cycle for the M/G/1 queueing system with the Vacationing Server Model – VSM, which starts with an arrival during a vacation and ends when the queue is emptied and a vacation starts. In the case of VSM with multiple vacations the server returning from a vacation takes another vacation if the queue is empty, otherwise it starts serving requests. The M/G/1 queue has arrivals with rate λ, mean service time x‾, so that its utilization factor is ρ=λx‾, and its mean busy period is g‾=x‾/(1−ρ). The VSM delay cycle starts with a requested whose mean service time is augmented by the mean residual vacation time: y‾=x‾+v‾r, so that the mean delay cycle is d‾v=y‾/(1−ρ). This is the method used to determine rebuild time in RAID5 disk arrays. In a second study which deals with threshold scheduling of readers and writers d‾v is obtained as the product of the mean number of requests arriving during the residual vacation time plus one (the request starting the residual vacation time) times g‾, which yields d‾v−v‾r=(1+λv‾r)×g‾ as before. The analysis of VSM for rebuild processing in RAID5 and threshold scheduling of readers and writers is provided.

Balancing disk access times in RAID5 disk arrays in degraded mode by conditionally prioritizing fork/join requests

RAID5 disk arrays with rotated parities can tolerate single disk failures by reconstructing missing blocks on demand by XORing the contents of corresponding K blocks on surviving disks by a K -way Fork/Join ( F/J ) request, which is considered completed after the K disks are accessed. F/J accesses in RAID5 are processed concurrently with interfering disk accesses. The mean response time of F/J and independent/interfering requests: R F/J / K and R Ind and the mean delay from the completion of the first to the last F/J task, known as task dispersion time: T disp / K , are performance metrics of interest. Given R F/J / K > R Ind with FCFS scheduling, it is desirable to equalize disk access times, but giving a higher nonpreemptive priority to disk accesses due to F/J requests with respect to interfering disk accesses results in R Ind & R F/J / K . We propose a continuum of conditional priority methods based on the fraction F of F/J accesses completed with FCFS scheduling. F = ∞stands for FCFS and F = 0 stands for unconditional priorities. Simulation shows that F = 1/8 with K = 8 yields R F/J / K ≈ RInd for three distributions of disk requests and in the range of F/J and independent disk requests considered. F can be varied adaptively based on measurement results to balance disk access times.

Rebuild processing in RAID5 with emphasis on the supplementary parity augmentation method[37

The rotated parity RAID5 disk array tolerates single disk failures by continuing operation by on-demand reconstruction of data blocks of the failed disk, until the systematic reconstruction of the contents of the failed disk is completed by the rebuild process on a spare disk. Supplementary Parity Augmentation (SPA), unlike the pyramid code, which has two parities covering half of the arrays disks each, extends RAID5's P parity with an additional S parity, which covers half of the disks. The extra load with respect to RAID5 of updating the S parity by one half of the disks is compensated by the more efficient on demand reconstructtion and rebuild processing when a disk fails. Although SPA has the same disk space redundancy level as RAID6, unlike RAID6 it can only deal with roughly half of all possible double disk failure cases for eight disks. For rebuild processing SPA reads half of the disks required by RAID5 and this leads to a higher Mean Time to Data Loss than RAID5, since fewer Latent Sector Errors are encountered. We review performance and reliability modeling of RAID5 arrays to provide insights into SPA's performance and reliability, which cannot be gained from numerical results alone. SPA is outperformed by the Intra-Disk Redundancy schemes combined with RAID5, which results in RAID6's reliability and RAID5 performance.

Performance of Two-Disk Failure-Tolerant Disk Arrays

RAID5 disk arrays use the rebuild process to reconstruct the contents of a failed disk on a spare disk, but this process is unsuccessful if latent sector failures are encountered or a second disk failure occurs. The high cost of data loss has led to two-disk failure-tolerant (2DFT) arrays: RAID6, EVENODD, row-diagonal parity (RDP), and RM2. RAID6 uses Reed-Solomon (RS) codes, whereas the latter three use parity encoding. This paper is concerned with the performance from the viewpoint of disk accesses, which, with an appropriate choice of symbol sizes, is the same for RAID6, EVENODD, and RDP, rather than the computational cost (number of XOR operations). We compare the performance of 2DFTs with each other, as well as RAIDO and RAID5 in normal and degraded operating modes. We derive cost functions for processing discrete disk accesses. The mean response time can be obtained analytically with Poisson arrivals and first-come, first-served (FCFS) scheduling. A simulation is used for validation, calibrating the approximate fork-join response analysis, and shortest-access-time-first (SATF) scheduling. The response time for read requests in RAID6 and RM2 is higher than RAID5 and RAIDO and increases with the fraction of write requests. When there is a single disk failure, RM2 outperforms RAID6 since it has a smaller parity group size than RAID6, but RAID6 outperforms RM2 with two disk failures because of its costlier recovery process. Disk loads in RM2 and RAID6 in degraded mode are unbalanced, and a solution based on pseudorandom permutations is proposed for this purpose

Analysis of Rebuild Processing in RAID5 Disk Arrays

RAID5 tolerates single disk failures by exclusive-ORing (XORing) the blocks corresponding to a requested block on the failed disk to reconstruct it. This results in increased loads on surviving disks and degraded disk response times with respect to normal mode operation. Provided a spare disk is available, a rebuild process systematically reads successive disk tracks, XORs them to recreate lost tracks and writes them onto a spare disk, thus returning the system to its original state. Rebuild time is important since RAID5 disk arrays with a single disk failure are susceptible to data loss if a second disk fails. According to the vacationing server model (VSM), rebuild read requests on surviving disks are given a lower priority than external user requests, so as to have less impact on their response time. Given that disk loads are balanced due to striping, rebuild time can be approximated by the time to read the contents of any one of the surviving disks. The analysis of the M/G/1 queueing model of VSM, given in this article, is more accurate and yet simpler than a previous analysis, but it also takes into account the effect of disk zoning explicitly. We also present a heuristic method to estimate rebuild time, which can be combined with the new analysis. The ability to quickly and accurately estimate rebuild time is useful in computing the reliability of RAID5 systems, especially during design tradeoff studies. The accuracy of the various analyses to estimate rebuild time are checked against detailed simulation results.

Shortcut method for reliability comparisons in RAID

Given that the reliability of each disk in a disk array during its useful lifetime is given as r = 1 − ϵ with ϵ ≪ 1, we show that the reliability of a RAID disk array tolerating all possible n − 1 disk failures can be specified as R ≈ 1 − a n ϵ n , where a n is the smallest nonzero coefficient in the corresponding asymptotic expansion, e.g., for n-way replication R = 1 − ϵ n . We compare the reliability of several mirrored disk organizations, which provide tradeoffs between reliability and load balancedness (after disk failure) by comparing their a 2 values, which can be obtained via a partial reliability analysis taking into account a few disk failures. We next use asymptotic expansions to compare the reliability of hierarchical RAID disk arrays, which combine replication and rotated parity disk arrays (RAID5 and RAID6). Finally, we argue that the mean time to data loss in systems with repair is related to the reliability without repair. As part of this discussion we show how to estimate the mean time to data loss in RAID5 and RAID6 disk arrays without resorting to transient analysis.

RAID5 performance with distributed sparing

Distributed sparing is a method to improve the performance of RAID5 disk arrays with respect to a dedicated sparing system with N+2 disks (including the spare disk), since it utilizes the bandwidth of all N+2 disks. We analyze the performance of RAID5 with distributed sparing in normal mode, degraded mode, and rebuild mode in an OLTP environment, which implies small reads and writes. The analysis in normal mode uses an M/G/1 queuing model, which takes into account the components of disk service time. In degraded mode, a low-cost approximate method is developed to estimate the mean response time of fork-join requests resulting from accesses to recreate lost data on the failed disk. Rebuild mode performance is analyzed by considering an M/G/1 vacationing server model with multiple vacations of different types to take into account differences in processing requirements for reading the first and subsequent tracks. An iterative solution method is used to estimate the mean response time of disk requests, as well as the time to read each disk, which is shown to be quite accurate through validation against simulation results. We next compare RAID5 performance in a system (1) without a cache; (2) with a cache; and (3) with a nonvolatile storage (NVS) cache. The last configuration, in addition to improved read response time due to cache hits, provides a fast-write capability, such that dirty blocks can be destaged asynchronously and at a lower priority than read requests, resulting in an improvement in read response time. The small write penalty is also reduced due to the possibility of repeated writes to dirty blocks in the cache and by taking advantage of disk geometry to efficiently destage multiple blocks at a time.

Performance of RAID5 disk arrays with read and write caching

In this paper, we develop analytical models and evaluate the performance of RAID5 disk arrays in normal mode (all disks operational), in degraded mode (one disk broken, rebuild not started) and in rebuild mode (one disk broken, rebuild started but not finished). Models for estimating rebuild time under the assumption that user requests get priority over rebuild activity have also been developed. Separate models were developed for cached and uncached disk controllers. Particular emphasis is on the performance of cached arrays, where the caches are built of Non-Volatile memory and support write caching in addition to read caching. Using these models, we evaluate the performance of arrayed and unarrayed disk subsystems when driven by a database workload such as those seen on systems running any of several popular database managers. In particular, we assume single-block accesses, flat device skew and little seek affinity. With the above assumptions, we find six significant results. First, in normal mode, we find there is no difference in performance between subsystems built out of either small arrays or large arrays as long as the total number of disks used is the same. Second, we find that if our goal is to minimize the average response time of a subsystem in degraded and rebuild modes, it is better to use small arrays rather than large arrays in the subsystem. Third, we find the counter-intuitive result that if our goal is to minimize the average response time of requests to any one array in the subsystem, it is better to use large arrays than small arrays in the subsystem. We call this the best worst-case phenomenon. Fourth, we find that when no caching is used in the disk controller, subsystems built out of arrays have a normal mode performance that is significantly worse than an equivalent unarrayed subsystem built of the same drives. For the specific drive, controller, workload and system parameters we used for our calculations, we find that, without a cache in the controller and operating at typical I/O rates, the normal mode response time of a subsystem built out of arrays is 50% higher than that of an unarrayed subsystem. In rebuild mode, we find that a subsystem built out of arrays can have anywhere from 100% to 200% higher average response time than an equivalent unarrayed subsystem. Out fifth result is that, with cached controllers, the performance differences between arrayed and equivalent unarrayed subsystems shrink considerably. We find that the normal mode response time in a subsystem built out of arrays is only 4.1% higher than that of an equivalent unarrayed system. In degraded (rebuild) mode, a subsystem built out of small arrays has a response time 11% (13%) higher and a subsystem built out of large arrays has a response time 15% (19%) higher than an unarrayed subsystem. Our sixth and last result is that cached arrays have significantly better response times and throughputs than equivalent uncached arrays. For one workload, a cached array with good hit ratios had 5 times the throughout and 10 to 40 times lower response times than the equivalent uncached array. With poor hit ratios, the cached array is still a factor of 2 better in throughput and a factor of 4 to 10 better in response time for this same workload. We conclude that 3 design decisions are important when designing disk subsystems built out of RAID level 5 arrays. First, it is important that disk subsystems built out of arrays have disk controllers with caches, in particular Non-Volatile caches that cache writes in addition to reads. Second, if one were trying to minimize the worst response time seen by any user, one would choose disk array subsystems built out of large RAID level 5 arrays because of the best worst-case phenomenon. Third, if average subsystem response time is the most important design metric, the subsystem should be built out of small RAID level 5 arrays.

Comparing rebuild algorithms for mirrored and RAID5 disk arrays

Several disk array architectures have been proposed to provide high throughput for transaction processing applications. When a single disk in a redundant array fails, the array continues to operate, albeit in a degraded mode with a corresponding reduction in performance. In addition, the lost data must be rebuilt to a spare disk in a timely manner to reduce the probability of permanent data loss. Several researchers have proposed and examined algorithms for rebuilding the failed disk in a disk array with parity. We examine the use of these algorithms to rebuild a mirrored disk array and compare the rebuild time and performance of the RAID5 and mirrored arrays. Redirection of Reads provides comparable average response times and better rebuild times than Piggybacking for a mirrored array, whereas these two algorithms perform similarly for a RAID5 array. In our experiments comparing the two architectures, a mirrored array has more disks than a RAID5 array and can sustain 150% more I/Os per second during the rebuild process. Even if the size of the RAID5 array is increased to match the mirrored array, the mirrored array reduces response times by up to 60% and rebuild times by up to 45%.