A Case for Redundant Arrays of Inexpensive Disks (RAID) David A. Patterson, Garth Gibson, and Randy H. Ka~z Computer Science Division Depar~nent of Elec~aical Engineering and Computer Sciences 571 Evans Hall University of California Berkeley, CA 94720 (pa~n@pepper.berl~eley.edu) Abs~act Increasing performance of CPUs and memories will be squandered if not matched by a similar performance increase in IIO. While the capacity of Single Large Expensive Disk (SLED) has grown rapidly, the performance improvement of SLED has been modest. Redundant Arrays of Inexpensive Disks (RAID), based on the magnetic disk technology developed for personal computers, offers an attractive alternative to SLED, promising improvements of an order of magnitude in performance, reliability, power consumption, and scalability. This paper introduces five levels of RAIDs, giving their relative costlperformance, and compares RAIDs to an IBM 3380 and a Fujitsu Super Eagle. ** No page found ** 1. Background: Rising CPU and Memory Performance The users of computers are currently enjoying unprecedented growth in the speed of computers. Gordon Bell said that between 1974 and 1984, single chip computers improved in performance by 40% per year, about twice the rate of minicomputers [Bell 84]. In the following year Bill Joy predicted an even faster growth [Joy 85]: MIPS = 2Year-1984 Mainframe and supercomputer manufacturers, having difficulty keeping pace with this rapid growth predicted by Joy's Law, cope by offering multiprocessors as their top-of-the-line product. But a fast CPU does not a fast system make. Gene Amdahl related CPU speed to main memory size using this rule [Siewiorek 8y: Each CPU instn ction per second reql ires one byte of main memory; If computer system costs are not to be dominated by the cost of memory, then Amdahl's constant suggests that memory chip capacity should grow at the same rate. Gordon Moore predicted that growth rate over 20 years ago, with the capacity of MOS DRAMs quadrupling every two to three years [Moore64]. Recently this ratio of megabytes of main memory to MIPS has been defined as alpha [Garcia 87], with Amdahl's constant meaning alpha = 1. In part because of the rapid drop of memory prices, main memory sizes have grown faster than CPU speeds and many machines are shipped today with alphas of 3 or higher. While there is no famous formula that correlates growth in main memory size to secondary memory capacity, common sense tells us that secondary memory must also keep pace. Magnetic disk technology has doubled the capacity and halved the price every three years, roughly in line with the required growth rate[Myers86], and in practice between 1967 and 1979 the disk capacity of the average IBM data processing system more than kept up with its main memory capacity [Stevens81] . Capacity is not the only memory characteristic that must grow rapidly to maintain system balance, since the speed with which instructions and data are delivered to a CPU also determines its ultimate performance. The speed of main memory has kept pace for two reasons: (1) The invention of caches, showing that a small buffer can be managed automatically to contain a substantial fraction of memory references; and (2) The SRAM technology, used to build caches, whose speed has improved at the rate of 40% to 100% per year. In contrast to primary memory technologies, the performance of single large expensive magnetic disks (SLED) has improved at a modest rate. These mechamcal devices are dominated by the seek and the rotation delays: from 1971 to 1981, the raw seek time for a high-end IBM disk improved by only a factor of two while the rotation time did not change[Harker81]. Greater density means a higher transfer rate when the information is found, and extra heads can reduce the average seek time, but the raw seek time only improved at a rate of 7% per year. There is no reason to expect a faster rate in the near future. To maintain balance, computer systems have been using even larger main memories to buffer some of the VO activity. This may be a fine solution for applications whose VO activity has locality of reference and for which volatility is not an issue, but applications such as transaction-processing (characterized by a high rate of random requests for small pieces of data) or large simulations running on supercomputers (characterized by a low number of requests for massive amounts of data) are facing a serious performance limitation. 2. The Pending I/O Crisis What is the impact of improving the performance of some pieces of a problem while leaving others the same? Amdahl's answer is now known as Amdahl's Law [Amdahl67]: 1 ~1-f) + f/k where: S = the effective speedup; f = fraction of work in faster mode; and k = speedup while in faster mode. Suppose that some current applications spend 10% of their time in I/O. Then when computers are 10X faster--according to Bill Joy in just over three years--then Amdahl's Law predicts effective speedup will be only SX. When we have computers 100X faster--via evolution of uniprocessors or by multiprocessors--this application will be less than 10X faster, wasting 90% of the potential speedup. While we can imagine improvements in software file systems via buffering for near term VO demands, we need innovation to avoid an VO crisis. . A Solution: Arrays of Inexpensive Disks Rapid improvements in capacity of large disks have not been the only target of disk designers, since personal computers have cr~ated a market for inexpensive magnetic disks. These lower cost disks have lower performance as well as less capacity. Table I below compares the top-of-the-line IBM 3380 model AK4 mainframe disk, Fujitsu M2361A "Super Eagle" minicomputer disk, and the Conner Peripherals CP 3100 personal computer disk. Characterist~cs IBM Fujitsu Conners 3380 v. 2361 v. 3380 M2361A CP3100 CP3100 CP3100 (>I means3100be~ter) Disk diameter (inches) 14 10.5 3.5 4 3 Formatted Data Capacity (MB)7500 600 100 .01 .2 Price/MB(controller incl.)$18-$10 $20-$17 $10-$7 1-2.5 1.7-3 Ml l~ Rated (hours) 30,000 20,000 30,000 1 1.5 MTTF in practice (hours) 100,000 ? ? ? ? No. Actuators 4 1 1 .2 Maximum I/O's/secondlActuator 50 40 30 .6 .8 Typical VO's/second/Actuator 30 24 20 .7 .8 Maximum I/O's/second/box 200 40 30 .2 .8 Typical VO's/second/box 120 24 20 .2 .8 Transfer Rate (MB/sec) 3 2.5 1 .3 .4 Power/box (W) 6,600 640 10~ 660 64 Volume (cu. ft.) 24 3.4 .03 800 11 Table I. Comparison of IBM 3380 disk model AK4 for mainframe computers, ~he Fujitsu M2361A "Super Eagle" disk for minicomputers, and the Conners Peripherals CP 3100 disk for personal computers. By "Maximum IIO'slsecond" we mean the maximum number of average seeks and average rotates for a single sector access. Cost and reliability information on the 3380 comes from widespread experience fIBM 87I [Gawlick87] and the information on the Fujitsu from the manual [Fujitsu 87], while some numbers on the new CP3100 are based on speculation. The price per megabyte is given as a range to allow for different prices for volume discount and different mark-up practices of the vendors. ~l~e 8 watt maximum power of the CP3100 was increased to 10 watts to allow for the inefficiency of ar extemal power supply (since the other drives contain their own power supplies). One surprising fact is that the number of VOs per second per actuator in an inexpensive disk is within a factor of two of the large disks. In several of the remaining metrics, including price per megabyte, the inexpensive disk is superior or equal to the large disks. The small size and low power are even more impressive since disks such as the CP3100 contain full track buffers and most functions of the traditional mainframe controller. Small disk manufacturers can provide such functions in high volume disks because of the efforts of standards committees in defining higher level peripheral interfaces, such as the ANSI X3.131-1986 Small Computer Synchronous Interface (SCSI). Such standards have encouraged companies like Adaptec to offer SCSI interfaces as single chips, in turn allowing disk companies to embed mainframe controller functions at low cost. Figure 1 compares the traditional mainframe disk approach and the small computer disk approach. The same SCSI interface chip embedded as a controller in every disk can also be used as the direct memory access (DMA) device at the other end of the SCSI bus. Mainframe Small Computer ~ r~ LMemory | | Channel | Controller ~ < SCSI Figure 1. Comparison of organizations for typical mainframe and small computer disk interfaces. Single chip SCSI interfaces such as the Adaptec AIC-500 allow the srnall computer to use a single chip to be the DMA interface as well as provide an embedded controller for each disk. (The price per megabyte shown in Table I includes everything in the dotted boxes.) Such characteristics lead to the proposal of building VO systems as arrays of inexpensive disks, either interleaved for the large transfers of supercomputers or independent for the many small transfers of transaction processing. Using the information in Table I, 75 inexpensive disks potentially have 12 times the VO bandwidth of the IBM 3380 and the same capacity, with lower power consumption and cost. 4. Caveats We cannot explore all issues associated with such arrays in the space available for this paper, so we concentrate on the price-performance and reliability.~ We characterize the transaction-processing workload to evaluate performance of a collection of inexpensive disks, but remember that such a collection is just one hardware component of a complete tranaction-processing system (TPS). While designing a complete TPS based on these ideas is enticing, we will resist that temptation in this paper. Cabling and packaging, certainly an issue in the cost and reliability of an array of many inexpensive disks, is also beyond this paper's scope. 5. And Now The Bad News: Reliability The unreliability of disks forces computer systems managers to make backup versions of all information every night in case of failure. What would be the impact on reliability of having a hundredfold increase in disks? Assuming a constant failure rate--that is, an exponentially distributed time to failure--and that failures are independent--both assumptions made by disk manufacturers when calculating the Mean Time To Failure (Ml~F)--the reliability of an array of disks is: M7TF of a Single Disk MITF of a Disk Array N~er of Disks in the Array Using the information in Table I, the MTTF of 100 CP 3100 disks is 30,000/100 = 300 hours, or less than 2 weeks. Compared to the 30,000 hour (> 3 years) Ml-rF of the IBM 3380, this is dismal. If we consider scaling the array to 1000 disks, then the Ml-rF is 30 hours or about one day, requiring an adjective worse than dismal. Without fault tolerance, large arrays of inexpensive disks are too unreliable to be useful. tOur reasoning is that if there are no advantages in price performance or terrible disadvantages in reliabili~, then there is n, need to exl~lore further. 6. A Better Solution: Redundant Arrays of Inexpensive Disks To overcome the reliability challenge, we must make use of extra disks containing redundant information to recover the original information when a disk fails. Our acronym for these Redundant Arrays of Inexpensive Disks is RAID. To simplify the explanation of our final proposal and to avoid confusion with previous work, we give the taxonomy of five different organizations of disk arrays, beginning with mirrored disks and progressing through a variety of alternatives with differing performance and reliability. We refer to each organization as a RAID level. Reliabili~. Our basic approach will be to break the arrays into reliability groups, with each group having extra "check" disks containing the redundant information. When a disk fails we assume that within a short time the failed disk will be replaced and the information will be reconstructed on to the new disk using the redundant information. This time is called the mean time to repair (MTIR). The MTTR can be reduced if the system includes extra disks to act as "hot" standby spares; when a disk fails, a replacement disk is switched in electronically. Periodically the human operator replaces all failed disks. Here are some other terms that we use: D = total number of disks with data (not including the extra check disks); G = number of data disks in a group (not including the extra check disks); nG = D/G = number of groups; C = number of check disks in a group; rC = C/G = ratio of check disks per group to data disks per group; S = slowdown caused by waiting for all disks in a group to finish a read or write of a sector vsO average access time of a sector for single disk. In general, 1 < S < 2. For synchronous disks~ there is no slowdown, so S = 1. As mentioned above we make the same assumptions that the disk manufacturers make--that the failures are exponential and independent. (An earthquake or power surge is a situation where an array of disks might not fail independently.) Since these reliability predictions will be very high, we tWith synchronous disks the spindles of all disks in the g~up ate synchronous so that the cortesponding sectors of a group disks pass under the heads simultaneously. want to emphasize that the reliability is only of the the disk-head assemblies with this failure model, and not the whole software and electronic system. In addition, in our view the pace of technology means extremely high MTTF are "overkill"--for independent of expected lifetime, users will replace obsolete disks. For example, how many people are still using 20 year old disks? The general M l-l ~ calculation for RAID is given in two steps. First, the group Ml~ is: MTrFDisk MlTFGroup = C+ C Probability of another failure in a group before repairing fhe dead disk As more formally derived in the appendix, the probability of a second failure before the first has been repaired is: M7TR MlTR Probabilify of Another Failure MlTFDisk/(No. Disks-l) M~TFDisk/(G+C~l) The intuition behind the formal calculation in the appendix comes from trying to calculate the average number of second disk failures during the repair time for X single disk failures. Since we assume that disk failures occur at a uniform rate, this average number of second failures during the repair time for X first failures is X ~MTTR M7TF of remaining disks in ~he group The average number of second failures for a single disk is then MITR MlTFD&k I No. of remaining disks in the group The Ml-rF of the remaining disks is just the Ml-rF of a single disk divided by the number of good disks in the group, giving the same formula as the "Probability of Another Failure" above. The second step is the reliability of the whole system, which is approximately (since MTrFGro~p iS not quite distributed exponentially): MT~FGroup M~TFRAID = Plugging it all together, we get: 8 - M~TFDisk MTrFDisk 1 (M~FDisk) MlTFRA~D = ~ * -- = G+C (G+C-l)*MlTR nG (G+C)*nG * (G+C-l)*MlTR (M~FDisk) M~FRAlD (D+C*nG )*(G+C-l)~MTIR Since the formula is the same for each level, we make the abstract numbers concrete using these parameters as appropriate: D=100 total data disks, G=10 data disks per group, MlTFDisk = 30~000 hours, M~R = 1 hour, with the check disks per group C determined by the RAID level. Reliability Overhead Cost. This is simply the extra check disks, expressed as a percentage of the number of data disks D. As we shall see below, the cost varies with RAID level from 100% down to 4%. Useable Storage Capacity Percentage. Another way to express this reliability overhead is in terms of the percentage of the total capacity of data disks and check disks that can be used to store data. Depending on the organization, this varies from a low of 50% to a high of 96%. Performance. Since supercomputer applications and transaction-processing systems have different access patterns and rates, we need different metrics to evaluate both. For supercomputers we count the number of reads and writes per second for large blocks of data, with large defined as getting at least one sector from each data disk in a group. During large transfers all the disks in a group act as a single unit, each reading or writing a portion of the large data block m parallel. A better measure for database systems is the number of individual reads or writes per second. Since transaction-processing systems (e.g., debits/credits) use a read-modify-write sequence of disk accesses, we include that metric as well. Ideally during small transfers each disk in a group can act independently, either reading or writing independent information. For both the large and small transfer calculations we assume the minimum user request is 512 bytes, that the size of a sector is also 512 bytes, and that there is enough work to keep every device busy. Figure 2 shows the ideal operation of large and small disk accesses in a RAID. (a) Single Large or "Grouped"Read (b) Several Small orlnd~vidual Reads and Writes (I read spread over G dlsks) (G reads andlor writes spread over G d~sks) Figure 2. Large transfer vs. small transfers in a group of G disks. As shown in Figure 1, the controllersfor inexpensive SCSI disks such as the CP3100 are embedde~ in the dlsks thernselves. The six performance metrics are then the number of reads, writes, and read-modify-writes per second for both large (grouped) or small (individual) transfers. Rather than give absolute numbers for each metric, we calculate them relative to a single disk. In this paper we focus on VO rate and ignore latency as a performance metric. Effective Performance Per Disk. The cost of disks can be a large portion of the cost of a database system, so the I/O performance per disk--factoring in the overhead of the check disks--suggests the cost/performance of a system. This is the bottom line for a RAID. 7. First Level RAID: Mirrored Disks Mirrored disks are a traditional approach for improving reliability of magnetic disks. This is the most expensive option since all disks are duplicated (G=l and C=l), and every write to a data disk is also a write to a check disk. The optimized version of mirrored disks, used by Tandem, doubles the number of controllers so that reads can occur in parallel. Table II shows the metrics for a Level 1 RAID assuming this optimization. 10 - M7TF Exceeds Useful Product Lifehme (4,500,000 hrs or > 500 years) Total Nurnber of Disks 2D Overhead Cost 100% Useable Storage Capacity 50% IIOslSec vs. Single Disk Full RAID PerDisk Large (or Grou~7ed) Readslsec 2D/S 1 .OO/S Large(orGrou~ed) Writeslsec D/S .SO/S Large (or Grou~7ed) R-M-Wlsec 2D/3S.33lS Small (orIndividual)Readslsec 2D lo00 Small (orIndlvidual) Writeslsec D .50 Small (orIndividual)R-M-Wlsec 2D/3 .33 Table ~. Characterisncs of Level 1 RAID. Here we assume that writes are not slowed by waiting for the second write to complete because the slowdown for writing 2 disks is minor compared to the slowdown S for writing a whole group of 10 to 25 d~sks. Unlike a "pure" mirrored scheme with ~wo disks per controller that is invisible to the software, we assume an optimized scheme with a controller per disk that allows parallel reads to both disks giving full disk bandwid~h for large reads and allowinR the reads of the read-modlfy-writes can occur in parallel. Since we construct these RAIDs from asynchronous disks, all large accesses must suffer a slowdown (S) relative to the average access time of a single access to a single disk since they wait for a collection of disks to finish reading or writing. Since a Level 1 RAID has only one data disk in its group, we assume that the large transfer requires the same number of disks acting in concert as found in groups of the higher level RAIDs: 10 to 25 disks. Duplicating all disks can mean doubling the cost of the database system or using only 50% of the disk storage capacity. Such largess inspires the next levels of RAID. 8. Second Level RAID: Hamming Code for Error Correction The history of main memory organizations suggests a way to reduce the cost of reliability. With the introduction of 4K and 16K DRAMs, computer designers discovered that these new devices were subject to losing information due to alpha particles. Since there were many single bit DRAMs in a system and since they were usually accessed in groups of 16 to 64 chips at a time, system designers added redundant chips to correct single errors and to detect double errors in a group. This increased the number of memory chips by 12% to 38%--depending on the size of the group--but it significantly improved reliability. As long as all the data bits in a group are read or written together, there is no impact on performance. However, reads of less than the group size require reading the whole group to be sure the information is correct, and writes to a portion of the group mean three steps: I ) a read step to get all the rest of the data; 2) a rnodify step to merBe the new and old information; 3) a write step to write the full group, including the check information. Since we have scores of disks in a RAID and since some accesses are to groups of disks, we can mimic the DRAM solution by bit-interleaving the data across the disks of a group and then add enough check disks to detect and correct a single error. A single parity disk can detect a single error, but to correct an error we need enough check disks to identify the disk with the error. For a group size of 10 data disks (G) we need 4 check disks (C) in total, and if G = 25 then C = 5 [HammingS0]. To keep down the cost of redundancy, we will assume the group size will vary from 10 to 25. Since our individual data transfer unit is just 512 bytes and the sector size is also 512 bytes, bit-interleaved disks mean that a large transfer for this RAID must be at least G*512 bytes. Like DRAMs, reads to a smaller amount still implies reading a full sector from each of the bit-interleaved disks in a group, and writes of a single unit involve the read-modify-write cycle to all the disks. Table m shows the me~ics of this Level 2 RAID. A~F Exceeds Useful Lifetime G=10 G=25 (494,500 hrs (103,500 hrs or >50 years) or 12 years) Total Number of Disks 1.40D 1.20D Overhead Cost 40% 20% Useoble Storage Capacity 71% 83% IIOs/Sec FulI RAID PerDisk PerDisk (vs. Single Disk) LZ L2IL1 L~ L2IL1 LargeReadslsec D/S .71/S71% .86/S86% Large Writeslsec D/S .71/S143% .86/S172% Large R-M-Wlsec D/2S .36/S107% .43/S129% Small Readslsec D/SG .07/S6% .03/S3% Small Writes/sec D/2SG .04/S6% .02/S3% Small R-M-Wlsec Dt2SG .04/S9% .02/S4% Table III. Characteristics of a Level 2 RAID. The L21LI column gives the % performance of level 2 in terms of level I (>100% means L2 is faster). As long as the transfer unit is large enough to spread over all the data disks of a group, the large IIOs get the full bandwidth of each disk, divided by S to allow all disks in a group to complete. (y the disks in a group are synchronized, then S = 1.) R-M-Wlsec is further divided by 2 to allow for both the read and write. Level I large reads are faster because data is duplicated on the extra level I disks so all disks do reads. Small IIOs still require accessing all the disks in a group, so only DIG small IIOs can happen at a time, again divided by S to allow a group of disks to finish. Small writes are the same as small R-M-W because the full sectors must be read before new data can be written onto part of each sector. - 12 - For large writes, the level 2 system has the same performance as level 1 even though it uses fewer check disks, and so on a per disk basis it outperforms level 1. For small data transfers the performance is dismal either for the whole system or per disk; all the disks of a group must be accessed for a small transfer, limiting the maximum number of simultaneous accesses to DIG. We also must include the slowdown factor S since the access must wait for all the disks to complete. Thus level 2 RAID is desirable for supercomputers but inappropriate for transaction processing systems, with increasing group size increasing the disparity in performance per disk for the two applications. In recognition of this fact, Thinking Machines Incorporated announced a Level 2 RAID this year for its Connection Machine supercomputer called the "Data Vault," with G = 32 and C = 8, including one hot standby spare [Hillis 87]. Before improving small data transfers, we concentrate once more on lowering the costO 9c Third Level RAID: Single Check Disk Per Group Most check disks in the level 2 RAID are used to determine which disk failed, for only one redundant paIity disk is needed to detect an error. These extra disks really are redundant since most disk controllers can already if a disk a failed: either through special signals provided in the disk interface or the extra checking information at the end of a sector to detect and correct soft errors. The information on the failed disk is reconstructed by calculating the parity of the remaining good disks and then comparing bit-by-bit to the parity calculated for the original full group. When these two parities agree, the failed bit was a 0; otherwise it was a 1. If the check disk is the failure9 just read all the data disks and store the group parity in the replacement disk. Reducing the check disks to one per group (C=l) reduces the overhead cost to between 4% and 10% for the group sizes considered here. The performance for the third level RAID system is the same as the Level 2 RAID, but the effective performance per disk increases since it needs fewer check disks. This reduction in total disks also increases reliability, but since it is still larger than the useful lifetime of disks, this is a minor point. The single advantage of a level 2 system is that the extra check information associated with each sector to correct soft errors is not needed, increasing the capacity per disk by perhaps 10%. Table IV summarizes the third level RAID characteristics and Figure 3 compares the sector layout and check disks for levels 2 and 3. 13 - MTIF Exceeds Useful Lifetime G=10 G=25 (820,000 hrs (346,000 hrs or >90 years) or 40 years) Total Number of Disks 1.10D 1.04D Overhet~d Cost 10% 4% UseableStorageCapacity 91% 96% IIOslSec Full RAlD PerDisk PerDisk (vs. Single Disk) ~3 L,3lL2 L~ L3ll2 LargeReads/sec D/S .91/S 127% .96/S 112% Large Writeslsec D/S .91/S 127% .96/S 112% Large R-M-Wlsec D~2S .45/S 127% .48/S 112% Small Readslsec D/SG .09/S 127% .04/S 112% Sm~ll Writeslsec D/2SG .05/S 127% .02/S 112% Small R-M-Wlsec D~2SG .05/S 127% .02/S 112% Table IV. Characteristics of a Level 3 RAID. The L3/L2 column gives the % performance of L3 in terms of L2 (>100% rneans L3 is faster). The performance for the full systerns is the same in RAID levels 2 and 3, but since their are fewer check disks the performance per disk improves. Once again if the dlsks in a group are synchronized, then S = 1. Last year Park and Balasubramanian proposed a third level RAID system without suggesting a particular application [Park86]. Our data suggests it is a much better match to supercomputer applications than to transaction processing systems. This year two disk manufacturers have announced level 3 RAIDs for such applications using synchronized 5.25 inch disks with G=4 and C=l: a new model from Maxtor and the Micropolis 1804 [Maginnis 87]. This third level has brought the reliability overhead cost to its lowest level, so in the last two levels we improve performance of small accesses without changing cost or reliability. 10. Fourth Level RAID: Independent Reads and Writes Spreading a transfer across all disks within the group has the following advantage: ù Large or grouped transfer time is reduced because transfer bandwidth of the entire array can be exploited. But it has the following disadvantages as well: ù Reading/writing to a disk in a group requires reading/writing to all the disks in a group; levels 2 and 3 RAIDs can perform only one VO at a time per group. ù If the disks are not synchronized, you do not see average rotational delays; the observed delays should move towards the worst case, hence the S factor in the equations above. la aCI~y ~ c 4 T ~ U ts ~ b~ c~ dl b3~ c Level 2 Level 3 Level 4 aO ~ aC i~ aO Sector 0 bO _ bO _ al DataDisk1 cO ~ cn ~ a2 dO IIIIl_ IIIIl a3 ~ al ~ a ~ bO ~ D Sector O bl ~7 b] r7~ bl ~ _~ A Data Disk 2 cl ~ c: ~ b2 ~1 C T dl 11111 d] ~ b3 n a, ~ a ~ cO ~ SectorO b2 77 b: _ cl ~ 1~1 S DataDisk3 c2 ~ c ~ c2 ~ ~ S d2 ~ d ~ c3 a3 ;\\~1 a ~ 1 dO . 11111 ~ _ O Sector O b3 ;~ b 1~5 dl . ,. . ,. 4 DataDisk4 c3 ~ c: ~// d2 . . __ ......................... d3. mI.I ..... d mI.I ...... d3 . ~ . . .. O aECCO~ ECCa ~ ECCO bECCO~ ECCb ~ ECCl SectorO ~ 7~ 1 5 Check Disk S cECCO~ ECCc ~ ECC2 CA~ ~ C dECCOmml ECCd mml ECC3 ~ H aECCl~l C p~y (Only one check (Each transfer unit is K bECCl ~ I disk in level 3. placed into a single sector. Sector O ~ Check info is Note that the check info D Check Disk 6 cECCl ~A calculated over is now calculated over dECCl ~ each transfer unit.) a piece of each transfer S aECC2~3 unit-) bECC2 Sector O Check Disk 7 cECC2 dECC2 Figure 3. Comparison of location of data and check information in sectors for RAID levels 2, 3, and 4 for G=4. Not shown is the small amount of check information per sector added by the disk controller to detect and correct soft errors within a sector. 15 - This fourth level RAID improves performance of small transfers through parallelism--the ability to do more than one VO per group at a time. We no longer spread the individual transfer information across several disks, but keep each individual unit in a single disk. The virtue of bit-interleaving is the easy calculation of the Hamming code needed to detect or correct errors in level 2. But recall that in the third level RAID we can rely on the disk controller to detect errors within a single disk sector. Hence if we store an individual transfer unit in a single sector, we can detect errors on an individual read without accessing any other disk. Figure 3 shows the different ways the information is stored in a sector for RAID levels 2, 3, and 4. By storing a whole transfer unit in a sector, reads can be independent and operate at the maximum rate of a disk yet still detect errors. Thus the primary change between level 3 and 4 is that we interleave data between disks on a sector level rather than at the bit level. At first thought you might expect that an individual write to a single sector still involves all the disks in a group since (1) the check disk must be rewritten with the new parity data and (2) the rest of the data disks must be read to be able to calculate the new parity data Recall that each parity bit is just a single exclusive or of all the corresponding data bits in a group. In level 4 RAID, unlike level 3, the parity calculation is much simpler since if we know the old data value and the old parity value as well as the new data value, we can calculate the new parity information as follows: new parity = (old data xor new data ) xor old panty In level 4 a small write then uses 2 disks to perform 4 accesses--2 reads and 2 writes--while a small read involves only one read on one disk. Table V summarizes the fourth level RAID characteristics. Note that all small accesses improve--dramatically for the reads--but the small read-modify-write is still so slow relative to a level 1 RAID that its applicability to transaction processing is doubtful. Before proceeding to the next level we need to explain the performance of small writes in Table V (and hence small read-modify-writes since they entail the same operations in this RAID). The formula for the small writes divides D by 2 instead of 4 because 2 accesses can proceed in parallel: the old data and old parity can be read at the same time and the new data and new parity can be written at the same time. The performance of small writes is also divided by G because the single check disk in a group must be read and written with every small write in that group, thereby 16 - limiting the number of wIites that can be performed at a hme to the number of groups. ~'he check disk is the bottleneck. and the final level RAID removes this botdeneck. MTIF Exceeds Useful Lifetime G=10 G=25 (820,000 hrs (346,000 hrs or >90 years) or 40 years) Total Nurnber of Disks 1.10D 1.04D Overhead Cost 10% 4% Useable Storage Ca~acity 91% 96% IIOslSec FulI RAlD PerDisk PerDisk (vs. Single Disk) L~ L41L3 L~ L4IL3 LargeReadslsec D/S .91/S 100% .96/S 100% Large Writeslsec D/S .91/S 100% .96/S 100% Large R-M-Wlsec Dns .45/S 100% .48/S 100% Small Readslsec D .91 1200% .96 3000% Small Writeslsec DnG .05 120% .02 120% Small R-M-Wlsec DnG .05 120% .02 120% Table V. Characteristics of a Level 4 RAID. The UIL3 column gives the % performance of L4 in terms of L3 (>100% means U is faster). Small reads improve because they no longer tie up a whole group at a time. Small writes and R-M-Ws improve some because we make the same assumptions as we made in Table II: the slowdown for two related llOs can be ignored because only two dtsks are involved. If the disks in a group are synchronized, large IIOs are faster because S = I . 11. Fifth Level RAID: Spread datatparity over all disks (no single check disk) While level 4 RAID achieved parallelism for reads, writes are still limited to one per group since every write to a group must read and write the check disk. The fimal level RAID distnbutes the data and check information per sector across all the dislcs--including the check disks. Figure 4 compares the location of check information in the sectors of disks for levels 4 and 5 RAIDs. The performance impact of this small change is large since RAID level S can support multiple individual writes per group. For example, suppose in Figure 4 above we want to write sector 0 of disk 2 and sector 1 of disk 3. As shown on the left Figure 4, in RAID level 4 these writes must be sequential since both sector 0 and sector 1 of disk 5 must be written. However, as shown on the right, in RAID level 5 the writes can proceed in parallel since a write to sector 0 of disk 2 still invr~lve.~ ~ write to disk S bllt a write to sector 1 of disk 3 involves a write to disk 4. 17 - 4DataDisks CheckDisk 5Disks(containingDataandChecks) sø n n n n ~ SO [~ sl [~ sl [l [1 [~ [ s2 [~ 3 s2 [~ s3 3 [~ s3[~ s4 [~ 3 s4 s5 [~ 3 ss[ ...... ... ... ... : ... ...... ... ... ... ... (a) Check inforrnation for Level 4 RAID (b) Check information for Level S RAID for G=4 and C=l . The sectors are for G=4 and C=l . The sectors are shown shown below the disks. (The checked areas below the disks, with the check inforrnation indicate the check information.) Writes to and data spread evenly through all the disks. s0 of disk 2 and sl of disk 3 imply Writes to s0 of disk 2 and sl of disk 3 still writes to s0 and sl of dis~ 5. The check imply 2 writes, but they can be split across disk (5) becomes the write bottleneck. 2 disks: to s0 of disk 5 and to sl of disk 4. Figure 4. Location of check inforrnation per sector for Level 4 RAID vs. Level 5 RA-D. These changes bring RAID level 5 near the best of both worlds: small read-modify-writes now perform close to the speed per disk of a level 1 RAID while keeping the large transfer performance per disk and high useful storage capacity percentage of the RAID levels 3 and 4. Spreading the data across all disks even improves the performance of small reads, since there is one more disk per group that contains data. Table VI summarizes the characteristics of this RAID. Keeping in mind the caveats given earlier, a Level 5 RAID appears very attractive if you want to do just supercomputer applications, or just transaction processing when storage capacity is limited, or if you want to do both supercomputer applications and transaction processing. 18 - M~F Exceeds Useful Lifetime G=10 G=25 (820,~00 hrs (346,000 hrs or >90 years) or 40 years) Total N~unber of Disks 1.10D 1.04D Overhead Cost 10% 4% UseableStorageCapacity 91% 96% IIOs/Sec FullRAlD PerDisk PerDisk (vs. Single Disk) L5 L5lL~ L5 L5lL4 LargeReadslsec D/S .91/S 100% .96/S100% ~rge Writeslsec D/S .91/S 100% .96/S100% Large R-M-Wlsec DQS .45/S 100%o48/S 100% Small Readslsec (l+rc)D 1.00 110% 1.00 104% Srn~ll Wnteslsec (l+rc)D/4 .25 550% .25 1300% Sm~ll R-M-Wlsec (l+rc)D/4 .25 550% .25 1300% Table VI. Characteristics of a Level 5 RAID. The LSIL4 column gives the % performance of L5 in terms of L4 (~100% means L5 is faster)O Because reads can be spread over all disks, including wha~ were check disks in level 4, all small l/Os improve ~y a factor of 1 + rc (rC is the ratio of check disks to data disks: C/G.) Small writes and R-M-Ws improve because they are no longer constrained by group size, getting the full disk bandwidth for the 4 I/O's associated with these accesses. We again make the sarne assurnptions as we made in Tables II and V: the slowdown for two related I/Os can be ignored because only two disks are involved. If the disks in a group are synchronized, then S = I and so large I/Os are faster. 12. Discussion Before concluding the paper, we wish to note a few more interesting points about RAIDs~ The first is that while the schemes for disk stnpping and pari~y support were presented as if they were done by hardware, there is no necessity to do so. We just give the method, and the decision between hardware and software solutions is strictly one of cost and benefit. For example, in cases where disk buffering is effective, there is no extra disks reads for level 5 small writes since the old data and old parity would be in main memory, so software would give the best perforrnance as well as the least cost. In this paper we have assumed the transfer unit is a multiple of the sector, which again is no~ fundamental to the ideas. As the size of the smallest transfer unit grows as large as a full track the performance of RAIDs improves significantly because of the full track buffer in every disk~ For example, if every disk begins transferring to its buffer as soon as it reaches the next sector, then S is actually less than 1 since there would be no rotational delay. With transfer units the size of a track, it is not even clear if synchronizing the disks in a group improves RAID performanceO 19 - 13. Conclusion This paper makes two separable points: the advantages of building VO systems from personal computer disks and the advantages of five different disk array organizations, independent of disks used in those array. The later point starts with the traditional mirrored disks to achieve acceptable reliability, with each succeeding level improving ù the effectil~e perforrnance per diskfor supercornputer applications (characterized by a small number of requests per second for a massive amounts of information each time), ù the transaction-processing perforrnance (characterized by a large number of read-modify-writes to a small amount of information each time), or ù the l~seable storage capacity, or possibly all three. Figure S shows the performance improvements per disk for each level RAID. The highest performance per disk comes from either Level 1 or Level 5. In transaction-processing situations using no more than 50% of storage capacity, then the choice is mirrored disks (Level 1). However, if the situation calls for using more than 50% of storage capacity, or for supercomputer applications, or for combined supercomputer applications and transaction processing, then Level 5 looks best. 20 - 12.00 - 1 1.36 1 1.36 1 1.36 ù 100% o ~ i~i7-50 ~30% 60% /sec . j ~ ~ 50~ø 20% o oo ~1 , ~, ~, ~, ~1 1; 10 /; Level 1 Level 2 Level 3 Lev61 4 Level 5 E~l Grouped Read-Modify- E~l Individual Read-Modify- -- Useable Storage Capacity Writes/disk/sec Writes/disk/sec _ Figure 5O Plot of Large (Crouped) and Small (Individual) Read-Modify-Writes per second per disk and useable storage capacity for all five levels of RAID (D=100, G=10, I/O=30/sec. S=1.2). To scale performance to other speed disks, simply multiply these numbers by the ratio to 30 I/O's/sec. Let us return to the first point, the advantages of building VO system from personal computer disks. Compared to traditional Single Large Expensive Disks (SLEDs), Redundant Arrays of Inexpensive Disks (RAID) offer significant advantages for the same cost. Table VII compares a level 5 RAID using 100 inexpensive data disks with a group size of 10 to the IBM 3380. As you can see, a level 5 RAID offers a factor of roughly 10 improvement in performance, reliability, and power consumption and a factor of 3 reduction in size over this SLED. Table VII also compares a level S RAID using 10 inexpensive data disks with a group size of 10 to a Fujitsu M2361A "Super Eagle". In this comparison RAID offers roughly a factor of S improvement in performance, power consumption, and size with more than two orders of magnitude improvement in (calculated) reliability. - Characteris~ics RAID SL SLED RAID RAID SL SLED RAID (100,10) (IBMv. SLED (10,10) (Fujitsu v. SLED (CP3100)33~0)(>I better(CP3100) M2361A) (>I better forRAlD) forRAlD) Formatted Data Capacity (MB)10,000 7,500 1.33 1,000 600 1.67 Price/MB (controllerincl.) $11-$8 $18-$10 2.2-.9 $11-$8 $20-$17 2.5-1.5 Rated MTTF (hours) 820,00030,000 27.3 8,200,000 20,000 410 MTTF in practice (hours) ? 100,000 ? ? ? ? No. Actuators 110 4 22.5 11 1 11 Max VO's/Actuator 30 50 .6 30 40 .8 Max Grouped RMW/box 1250 100 12.5 125 20 6.2 Max Individual RMW/box 825 100 8.2 83 20 4.2 Typ I/O's/Actuator 20 30 .7 20 24 .8 Typ Grouped RMW/box 833 60 13.9 83 12 6.9 Typ Individual RMW/box 550 60 9.2 55 12 4.6 Volume/Box (cubic feet) 10 24 2.4 1 3.4 3.4 Power/box (W) 1100 6,600 6.0 110 640 5.8 MinimumExpansionSize(MB) 100-1000 7,500 7.5-75 100-1000 600 0.6-6 Table VII. Companson of IBM 3380 disk model AK4 to Level S RAID using 100 Conners & Associates CP 3100s disks and a group size of 10 and a comparison of the Fujitsll M2361A "Super Eagle" to a level 5 RAID using 10 inexpensive data disks with a group size of 10. Numbers greater than I in the comparison columns favor the RAID. RAIDs offer the further advantage of modular growth over SLEDs. Rather than being limited to 7,500 MB per increase for $100,000 as in the case of the IBM 3380, RAIDs can grow at either the group size (1000 MB for $11,000) or, if partial groups are allowed, at the disk size (100 MB for $1,100). The flip side of the coin is that RAIDs also make sense in systems considerably smaller than SLEDs. Small incremental costs also makes hot standby spares practical to further reduce M l-l K and thereby increase the MI~F of a large system. For example, a 1000 disk level 5 RAID with 5% standby spares and a group size of 10 would still have a calculated MTTF of 90 years. A final comment concems the temptation to design a complete transaction processing system from either a Level 1 or Level 5 RAID. The drastically lower power per megabyte of inexpensive disks allows systems designers to consider battery backup for the whole disk array--the power needed for 110 PC disks is less than two Fujitsu Super Eagles. Another application would be to use a few such disks copy the contents of battery backed-up main memory in the event of an extended power failure. RAIDs offer a cost effective option to meet the challenge of exponential growth in the processor and memory speeds. With advantages in cost-performance, reliability, power consumphon, and modular growth, we expect RAIDs to replace SLEDs in future VO systems. There are, however, several open issues that may bare on the prachcality of RAIDs: ù What is the impact of a RAID on latency? ù What is the impact on MTIF calculations of non-exponential failure assumptions for individual disks? ù What will be the real lifetime of a RAID vs. calculated MTIF using the independentfailure model? ù How would synchronized disks affect performance of level 4 and S RAlDs? ù How do you schedule IIO to level S RA Ds to maximize write parallelism? ù Can information be automatically redistributed over 100 to 1000 disks to reduce contention? ù Will disk controller design limit RAID performance? ù How should 100 to 1000 disks be constructed and physically connected to the processor? ù What is the impact of cabling on cost, performance, and reliability? ù Where should a RAlD be connected to a CPU so as not to limit performance? Memory bus? I/O bus? Cache? ù What is the role of solid state disks and WORMs in a RAID? ù What is ~he impact of RAlDs of "parallel access" disks (access to every surface under the readlwr~te head in parallel)? ~cknowledgements We wish to acknowledge the following people who participated in the discussions from which these ideas emerged: Michael Stonebraker, John Ousterhout, Doug Johnson, Ken Lutz, Anapum Bhide, Gaetano Boriello, Mark Hill, David Wood, and students in SPATS seminar offered at U. C. Berkeley in Fall 1987~ We also wish to thank the following people who gave comments useful in the preparation of this paper: Anapum Bhide, Pete Chen, Ron David, Dave Ditzel, Fred Douglis, Dieter Gawlick, Jim Gray, Mark Hill, Doug Johnson, Joan Pendleton, Martin Schulze, and Herve Touati. This work was supported by the National Science Foundation under grant ~ MIP-87---. - 23 - References [Bell 84] C.G. Bell, "The Mini and Micro Industries," IEEE Computer, Vol. 17, No. 10 (October 1984), pp. 14-30. [Joy 85] B. Joy, presentation at ISSCC '85 panel session, February 1985. [Siewiorek 82] D.P. Siewiorek, C.G. Bell, and A. Newell, Computer Structures: Principles and Examples, p. 46. [Moore 65] G. Moore, 1965. [Garcia 87] H. Garcia-Molina and A. Park, "Performance Through Memory," Department of Computer Science, Princeton University, Technical Report, January 1987. [Myers 86] W. Myers, "The Competitiveness of the United States Disk Industry," IEEE Computer, Vol. 19, No. 11 (January 1986), pp. 85-90. [Stevens 81] L.D. Stevens, "The Evolution of Magnetic Storage," IBM Journal of Research and Development, Vol. 25, No. 5, September 1981, pp. 663-675. [Harker 81] J.M. Harker et al., "A Quarter Century of Disk File Innovation," IBM Journal of Research and Development, Vol. 25, No. 5, September 1981, pp. 677-689. [Amdahl 67] G.M. Amdahl, "Validity of the single processor approach to achieving large scale computing capabilities," Proceedings AFIPS 1967 Spring Joint Computer Conference Vol. 30 (Atlantic City, New Jersey April 1967), pp. 483-485. [IBM 87] "IBM 3380 Direct Access Storage Introduction," IBM GC 26-4491-0, September 1987. [Gawlick 87] D. Gawlick, private communication, November,1987. [Fujitsu 87] "M2361A Mini-Disk Drive Engineering Specifications," (revised) Feb., 1987, B03P-4825-00OlA. [Hamming 50] R. W. Hamming, "Error Detecting and Correcting Codes," The Bell System Technical Journal, Vol XXVI, No. 2 (April 1950), pp. 147-160. [Hillis 87] D. Hillis, private communication, October, 1987. [Park86] A. Park and K. Balasubramanian, "Providing Fault Tolerance in Parallel Secondary Storage Systems," Department of Computer Science, Princeton University, CS-TR-057-86, November 7, 1986. [Maginnis 87] N.B. Maginnis, "Store More, Spend Less: Mid-range Options Abound9" Computerworld, November 16, 1987, p. 71. - 24 - Appendix: Reliability Calculation Using probability theory we can calculate the Ml-rFGroUp. We first assume independent and exponential failure rates. Our model uses a biased coin with the probability of heads being the same probability that a second failure will occur within the MTI R of a first failure. Since disk failures are exponential: Probability(at least one of the remaining disks failing in MTTR) = [ 1 - (e~M~PDisk)(G+C~1) ] In all practical cases MTTFDisk MTrR << G+C and since (1 - e~X) is approximately X for 0 < X << 1: Probability(at least one of the remaining disks failing in MTI R) = MTTR~(G+C- l)/Ml'rFD,sk Then that on a disk failure we flip this coin: heads => a system crash, because a second failure occurs before the first was repaired; tails => recover from error and continue. Then MTTFGroUp = Expected[Time between Failures] * Expected[no. of flips until first heads~ Expected[Time between Failures] Probability(heads) MTTFDisk (G+C)~(M~R~(G+C-I)/MTTFDisk) (Ml l~Disk)2 MTTFGroup (G+Cl~(G+C-1~MTIR Group failure is not precisely exponential in our model, but we have validated this simplifying assumption for the practical case of M~TR << MTTF/(G+C), making the Ml~F c)f the whole cvstem just MTTFGroup divided by the number of groups, nG