Finally, one can determine the layout of chunks to disks with the following code. The basic idea is to select N random patterns, and to exhaustively read together all pairwise combinations of the chunks within the pattern.

After running this code, you can report the measured time as a function of a and b. The simplest way to graph this is to create a two-dimensional table with a and b as the parameters, and the time scaled to a shaded value; we use darker shadings for faster times and lighter shadings for slower times. Thus, a light shading indicates that the two offsets of a and b within the pattern fall on the same disk.
Figure 6.28 shows the results of running the layout algorithm on a storage system that is known to have a pattern size of 384 KB and a chunk size of 32 KB.
a. How many chunks are in a pattern?
b. Which chunks of each pattern appear to be allocated on the same disks?

Figure 6.28 Results from running the layout algorithm of Shear on a mock storage system.

Figure 6.29 A storage system with 4 disks, a chunk size of four 4 KB blocks, and using a RAID 5 Left-Asymmetric layout. Two repetitions of the pattern are shown.
c. How many disks appear to be in this storage system?
d. Draw the likely layout of blocks across the disks.

for (a = 0; a numchunks ; a += chunksize) { for (b -a; b < numchunks; b chunksize) f for i 0; i < N iH) requestALi] random ()*patternsize a; requestB[i] - random()*patternsize b; gettime): begin time issue all requestA[N] and requestB[N] to raw device in parallel; wait for all requestA[N] and requestB[N] to complete; interval time - gettime() printf("A- %d B: %d Time: interval time); begin time; %d " , a, b, 10 4 10 Chunk 00 01 02 03 04 05 06 07 08 09 10 11 PP PP 12 13 14 15 16 17 18 19 P P P P 20 21 22 23 24 25 26 27 P PP P 28 29 30 3132 33 34 35 PPPP 3 40 41 42 43 44 45 46 47 48|49150151152|53 | 54 | 55|56 | 57| 58 | 59 | P P | PI P 60 61 62 63 64 65 66 67PP PP68 69 70 71 72 73 74 75 PPP P 76 77 78 79 80 81 82 83 PP PP 84 85 86 87 88 89 90 91 92 93 94 96 37 38 39 Party: RAID 5 Len-Asymmetric, stripe= 16, pattern= 48