Homework, etc. Computer Science Foundations
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1 Homework, etc. 0 Chapter 12: reading, exercises Due: 10/4 NOTE: EARLIER THAN USUAL! Will be covered in depth on test (change from Monday s announcement) Prelim I: 10/6 Copyright c UMaine School of Computing and Information S 1 / 34
2 COS 140: Foundations of : Redundant Array of Independent Fall 2017 Copyright c UMaine School of Computing and Information S 2 / 34
3 The problem 0 How to store data: Reliably So that we can maximize a lot of requests by different processes So that we can maximize the amount of data transferred/second to each process Copyright c UMaine School of Computing and Information S 3 / 34
4 The problem 0 How to store data: Reliably So that we can maximize a lot of requests by different processes So that we can maximize the amount of data transferred/second to each process These are conflicting, as we ll see! Copyright c UMaine School of Computing and Information S 3 / 34
5 The problem 0 How to store data: Reliably So that we can maximize a lot of requests by different processes So that we can maximize the amount of data transferred/second to each process These are conflicting, as we ll see! We ll concentrate on disk storage Copyright c UMaine School of Computing and Information S 3 / 34
6 More About Magnetic Data layout Access time Types Example: Seagate 3.5 in. hard disk Type of external memory, like magnetic tape or optical disks (CD s) Access method: direct access 0 Copyright c UMaine School of Computing and Information S 4 / 34
7 Arrangement of Data on Mag Data layout Access time Types Example: Seagate 3.5 in. hard disk TRACKS: Concentric circles around disk Arm with read/write head (animation) 0 Copyright c UMaine School of Computing and Information S 5 / 34
8 Arrangement of Data on Mag Data layout Access time Types Example: Seagate 3.5 in. hard disk TRACKS: Concentric circles around disk Sector of interest Arm with read/write head (animation) 0 Copyright c UMaine School of Computing and Information S 5 / 34
9 Arrangement of Data on Mag (animation) TRACKS: Concentric circles around disk Data layout Access time Types Example: Seagate 3.5 in. hard disk Sector of interest Arm with read/write head DISK HEAD: Moves to appropriate track for target sector/block 0 Copyright c UMaine School of Computing and Information S 5 / 34
10 Arrangement of Data on Mag (animation) TRACKS: Concentric circles around disk Data layout Access time Types Example: Seagate 3.5 in. hard disk Sector of interest Arm with read/write head DISK HEAD: Moves to appropriate track for target sector/block 0 Once head is at right track, have to wait until disk spins to bring sector under the head Copyright c UMaine School of Computing and Information S 5 / 34
11 Arrangement of Data on Mag Data layout Access time Types Example: Seagate 3.5 in. hard disk TRACKS: Concentric circles around disk Arm with read/write head (animation) DISK HEAD: Moves to appropriate track for target sector/block 0 Sector of interest Once head is at right track, have to wait until disk spins to bring sector under the head Copyright c UMaine School of Computing and Information S 5 / 34
12 Arrangement of Data on Mag Data layout Access time Types Example: Seagate 3.5 in. hard disk TRACKS: Concentric circles around disk Arm with read/write head (animation) DISK HEAD: Moves to appropriate track for target sector/block 0 Sector of interest Once head is at right track, have to wait until disk spins to bring sector under the head CONSTANT ANGULAR VELOCITY: Disk spins at constant speed => data is more dense near center than at edges Copyright c UMaine School of Computing and Information S 5 / 34
13 Access Time for Data layout Access time Types Example: Seagate 3.5 in. hard disk 0 Seek time: time to get to the right track (either to move a single head or to find the correct head for reading and writing) Rotational latency: time for the disk to position the right sector under the head Access time = Seek time + Rotational latency Sector of interest Arm with read/write head Copyright c UMaine School of Computing and Information S 6 / 34
14 Types of Data layout Access time Types Example: Seagate 3.5 in. hard disk 0 Type: depends on how close head gets to surface Closer the head narrower head can be narrower tracks more data Closer the head increased chance of errors due (e.g.) to impurities, dust, etc. Standard disks: head floats on a cushion of air does not come in contact with the disk Floppy: head touches the disk when reading and writing Winchester: in a sealed unit so head can get closer to the disk because there are no contaminants Copyright c UMaine School of Computing and Information S 7 / 34
15 Example: Seagate 3.5 in. hard disk Data layout Access time Types Example: Seagate 3.5 in. hard disk 0 (Eric Gaba Wikimedia Commons user: Sting) Copyright c UMaine School of Computing and Information S 8 / 34
16 Performance Issues for External Memory Performance issues Transfer capacity Request rate 0 Reliability Speed Transfer capacity - how much data can be read from or written to the disk in a given amount of time I/O request rate - how many reads or writes can be Cost accomplished in a given amount of time Copyright c UMaine School of Computing and Information S 9 / 34
17 How to Measure Speed: Transfer Capacity Performance issues Transfer capacity Request rate Amount of data that can be read from or written to the disk per second Important large amount of data/request Depends on: buses, disk device, other factors 0 Copyright c UMaine School of Computing and Information S 10 / 34
18 How to Measure Speed: I/O Request Rate Performance issues Transfer capacity Request rate Number of requests/second that are serviced by disk (reads or writes) Important many requests generated per second 0 Copyright c UMaine School of Computing and Information S 11 / 34
19 What Hopes to Accomplish Purpose Architecture Data distribution Improve performance through parallelism. increase speed increase reliability But: extra disks (for parallelism) higher cost. 0 Copyright c UMaine School of Computing and Information S 12 / 34
20 Architecture of Purpose Architecture Data distribution 0 Disk 1 Disk 2 Disk 3 Disk 4 Several disks in the array Different levels specify how disks are used Each level: addresses different issue(s) Order of levels not significant Copyright c UMaine School of Computing and Information S 13 / 34
21 Distributing Data on the Purpose Architecture Data distribution 0 Logical disk: Abstraction of real disks Think of single virtual disk on which data is stored Divide data unto equal-length chunks called strips Put strips on real disks in (e.g.) round-robin fashion Stripe: all the strips at correspondign locations on the disks Copyright c UMaine School of Computing and Information S 14 / 34
22 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
23 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
24 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
25 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
26 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
27 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
28 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
29 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4...and so on... Logical Disk Copyright c UMaine School of Computing and Information S 15 / 34
30 Distributing Data on the Purpose Architecture Data distribution Disk 1 Disk 2 Disk 3 Disk 4 Each color shows a stripe of strips at the same location in each of the disks. Logical Disk There are many more strips on the logical disk that will be distributed to disks in the same way. This small example is just for illustration. Copyright c UMaine School of Computing and Information S 16 / 34
31 Level 0 0 Level 0 Cost Logical Disk Disk 1 Disk 2 Disk 3 Disk 4 Simply stripe data onto multiple disks. Distribution of data puts system and user data on all strips Copyright c UMaine School of Computing and Information S 17 / 34
32 0 benefits No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size 0 Level 0 Cost Copyright c UMaine School of Computing and Information S 18 / 34
33 0 benefits 0 Level 0 Cost No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size Effect on transfer rate? Copyright c UMaine School of Computing and Information S 18 / 34
34 0 benefits 0 Level 0 Cost No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size Effect on transfer rate? Supposes r multiple disks strips for request transfer rate increase Ideallyr = S: transfer rate increased up tontimes Copyright c UMaine School of Computing and Information S 18 / 34
35 0 benefits 0 Level 0 Cost No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size Effect on transfer rate? Supposes r multiple disks strips for request transfer rate increase Ideallyr = S: transfer rate increased up tontimes Effect on request rate? Copyright c UMaine School of Computing and Information S 18 / 34
36 0 benefits 0 Level 0 Cost No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size Effect on transfer rate? Supposes r multiple disks strips for request transfer rate increase Ideallyr = S: transfer rate increased up tontimes Effect on request rate? Supposer s disk active per strip multiple requests handled at once increased request rate Ideallyr = s: request rate increased up tontimes Copyright c UMaine School of Computing and Information S 18 / 34
37 0 benefits 0 Level 0 Cost No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size Effect on transfer rate? Supposes r multiple disks strips for request transfer rate increase Ideallyr = S: transfer rate increased up tontimes Effect on request rate? Supposer s disk active per strip multiple requests handled at once increased request rate Ideallyr = s: request rate increased up tontimes So which? Copyright c UMaine School of Computing and Information S 18 / 34
38 0 benefits 0 Level 0 Cost No effect on reliability Letr = average request size,s = strip size,n = # of disks, S = ns = stripe size Effect on transfer rate? Supposes r multiple disks strips for request transfer rate increase Ideallyr = S: transfer rate increased up tontimes Effect on request rate? Supposer s disk active per strip multiple requests handled at once increased request rate Ideallyr = s: request rate increased up tontimes So which? Depends on system characteristics, goals Copyright c UMaine School of Computing and Information S 18 / 34
39 level 0 cost Ifndisks were going to be used anyway no additional cost If not, thennsmall disks likely more expensive than 1 large disk 0 Level 0 Cost Copyright c UMaine School of Computing and Information S 19 / 34
40 Level 1 0 Level 1 Cost When to use Disk 1 Disk 2 Disk 3 Disk Disk 5 Disk 6 Disk 7 Disk 8 Two sets of disks, mirror images of each other. Copyright c UMaine School of Computing and Information S 20 / 34
41 level 1 benefits 0 Level 1 Cost When to use Reliability Data completely redundantly stored Disk fails: read from/write to copy Transfer rate, request rate Same arguments as for 0 re: strip size vs. request size Additionally: If disk busy, can read from duplicate speeds Could handle up to2 requests of 0 ifs = r Could makes = 1 2r all disks involved, up to2times request rate of 0 Writes must be done to both disks, but they can be done in parallel. Copyright c UMaine School of Computing and Information S 21 / 34
42 cost If needndisks worth of data, need2n disks I.e., doubles cost 0 Level 1 Cost When to use Copyright c UMaine School of Computing and Information S 22 / 34
43 So what is good for? Critical data for which a failure cannot be tolerated and where the cost is not a problem. Additional transfer or request rates 0 Level 1 Cost When to use Copyright c UMaine School of Computing and Information S 23 / 34
44 Level 2 0 Level 2 Benefit Costs Idea: use some additional space to store an error-correcting code When an error occurs (on read or write), use that to fix it Uses a Hamming code (we ll study this later) For corresponding bit locations on each data disk, create Hamming code Hamming code requires aboutlog 2 n additional bits forn data bits extra disks needed Copyright c UMaine School of Computing and Information S 24 / 34
45 benefit Reliability Correction of 1-bit errors on read or write Reconstruct data if one disk fails. 0 Level 2 Benefit Costs Copyright c UMaine School of Computing and Information S 25 / 34
46 costs 0 Level 2 Benefit Costs Block A Bit 1 Synchronized disks, write penalty (to compute ECC) May need a large number of disks or a large number of reads/writes per disk Block B Bit 1 Block C Block A Bit 1 Bit 38 Block B Bit (d) Block C Bit 38 Disk # Data bit # c c 1 c c c c , 32-bit data blocks Copyright c UMaine School of Computing and Information S 26 / 34
47 What is Level 2 Good For? 0 Not commercially implemented Would be good if many single-disk errors......but unlikely and......disks themselves use ECC! If are really worried about data, use Level 1. Level 2 Benefit Costs Copyright c UMaine School of Computing and Information S 27 / 34
48 Level Disk 1 Disk 2 Disk 3 Disk 4 Disk 5 Level 3 Parity Cost Use Single extra disk stores a parity bit. Strip size: byte or word, access disks in parallel (synchronized) Copyright c UMaine School of Computing and Information S 28 / 34
49 What is a Parity Bit? 0 Level 3 Parity Cost Use Consider # 1s in data: s Add an extra bit: Set to make total # 1s even even parity Set to make total # 1s odd odd parity E.g., even parity: Copyright c UMaine School of Computing and Information S 29 / 34
50 What is a Parity Bit? 0 Level 3 Parity Cost Use Consider # 1s in data: s Add an extra bit: Set to make total # 1s even even parity Set to make total # 1s odd odd parity E.g., even parity: Copyright c UMaine School of Computing and Information S 29 / 34
51 What is a Parity Bit? 0 Level 3 Parity Cost Use Consider # 1s in data: s Add an extra bit: Set to make total # 1s even even parity Set to make total # 1s odd odd parity E.g., even parity: Copyright c UMaine School of Computing and Information S 29 / 34
52 What is a Parity Bit? 0 Level 3 Parity Cost Use Consider # 1s in data: s Add an extra bit: Set to make total # 1s even even parity Set to make total # 1s odd odd parity E.g., even parity: Copyright c UMaine School of Computing and Information S 29 / 34
53 What is a Parity Bit? 0 Level 3 Parity Cost Use Consider # 1s in data: s Add an extra bit: Set to make total # 1s even even parity Set to make total # 1s odd odd parity E.g., even parity: Store both data and parity bit Copyright c UMaine School of Computing and Information S 29 / 34
54 How is the Parity Bit Used? 0 Level 3 Parity Cost Use When writing: compute, store parity bit When reading: Know if parity supposed to be even or odd Compute parity: if not correct error How to compute? Remember homework asking about odd # of 1s in a number? For even parity, can just XOR the bits Copyright c UMaine School of Computing and Information S 30 / 34
55 How is the Parity Bit Used? 0 Level 3 Parity Cost Use When writing: compute, store parity bit When reading: Know if parity supposed to be even or odd Compute parity: if not correct error How to compute? Remember homework asking about odd # of 1s in a number? For even parity, can just XOR the bits xor xor xor xor xor xor xor 0 1 Copyright c UMaine School of Computing and Information S 30 / 34
56 benefits 0 Level 3 Parity Cost Use Reliability Detect errors; can try re-reading If disk drive fails reduced mode Every read will parity error But now know which bit is wrong! Transfer rate due to small strip size Request rate: no change Copyright c UMaine School of Computing and Information S 31 / 34
57 costs Need only 1 extra disk 0 Level 3 Parity Cost Use Copyright c UMaine School of Computing and Information S 32 / 34
58 costs Need only 1 extra disk Have to access it every read, write... 0 Level 3 Parity Cost Use Copyright c UMaine School of Computing and Information S 32 / 34
59 costs 0 Need only 1 extra disk Have to access it every read, write......but small strip size, probably won t have multiple requests needing it at same time Level 3 Parity Cost Use Copyright c UMaine School of Computing and Information S 32 / 34
60 costs 0 Need only 1 extra disk Have to access it every read, write......but small strip size, probably won t have multiple requests needing it at same time Can only catch single-bit errors how bad is that? Level 3 Parity Cost Use Copyright c UMaine School of Computing and Information S 32 / 34
61 costs 0 Level 3 Parity Cost Use Need only 1 extra disk Have to access it every read, write......but small strip size, probably won t have multiple requests needing it at same time Can only catch single-bit errors how bad is that? Modern disk drives are very good maybe 1 error per10 14 bits read Copyright c UMaine School of Computing and Information S 32 / 34
62 costs 0 Level 3 Parity Cost Use Need only 1 extra disk Have to access it every read, write......but small strip size, probably won t have multiple requests needing it at same time Can only catch single-bit errors how bad is that? Modern disk drives are very good maybe 1 error per10 14 bits read P(error) in a 4 KB read: about Copyright c UMaine School of Computing and Information S 32 / 34
63 costs 0 Level 3 Parity Cost Use Need only 1 extra disk Have to access it every read, write......but small strip size, probably won t have multiple requests needing it at same time Can only catch single-bit errors how bad is that? Modern disk drives are very good maybe 1 error per10 14 bits read P(error) in a 4 KB read: about P(2 errors) in a 4KB read= ( ) Copyright c UMaine School of Computing and Information S 32 / 34
64 costs 0 Level 3 Parity Cost Use Need only 1 extra disk Have to access it every read, write......but small strip size, probably won t have multiple requests needing it at same time Can only catch single-bit errors how bad is that? Modern disk drives are very good maybe 1 error per10 14 bits read P(error) in a 4 KB read: about P(2 errors) in a 4KB read= ( ) I.e., , or 1 in 10,000,000,000,000,000,000 Copyright c UMaine School of Computing and Information S 32 / 34
65 What is Level 3 Good For? When some error detection is needed High transfer rate and low number of outstanding requests. 0 Level 3 Parity Cost Use Copyright c UMaine School of Computing and Information S 33 / 34
66 Level 4, 5, 6, and beyond 0 Other s Same as Level 3, but uses independent access array: disks in array operate independently Uses larger strips strip-level parity Increases IO request rates at the expense of transfer capacity. Write penalty: have to read old data strip, old parity, then write them. Parity disk can become bottleneck. Level 5 distributes the parity bits across the disks instead of having them all on one disk, to solve a potential problem with parity disk bottlenecks for Level 4. Level 6: two parity blocks per stripe Others: some proprietary, some combinations of others (e.g., 0+1) Copyright c UMaine School of Computing and Information S 34 / 34
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