One can uncover the pattern size with the following code. The code accesses the raw device to avoid file system optimizations. The key to all of the Shear algorithms is to use random requests to avoid triggering any of the prefetch or caching mechanisms within the RAID or within individual disks. The basic idea of this code sequence is to access N random blocks at a fixed interval p within the RAID array and to measure the completion time of each interval.

If you run this code on a RAID array and plot the measured time for the N requests as a function of p, then you will see that the time is highest when all N

Figure 6.26 Results from running the pattern size algorithm of Shear on a mock storage system.
Requests fall on the same disk; thus, the value of p with the highest time corresponds to the pattern size of the RAID.
a. Figure 6.26 shows the results of running the pattern size algorithm on an unknown RAID system.
€¢ What is the pattern size of this storage system?
€¢ What do the measured times of 0.4, 0.8, and 1.6 seconds correspond to in this storage system?
€¢ If this is a RAID 0 array, then how many disks are present?
€¢ If this is a RAID 0 array, then what is the chunk size?
b. Draw the graph that would result from running this Shear code on a storage system with the following characteristics:
€¢ Number of requests: N = 1000
€¢ Time for a random read on disk: 5 ms
€¢ RAID level: RAID 0
€¢ Number of disks: 4
€¢ Chunk size: 8 KB

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for (p = BLOCKS IZE; p <= testsize, p += BLOCKSIZE) { for (i = 0; i < N; i++) { request[i]- random()*p randomO*p; begin time gettime(); issues all request [N] to raw device in parallel; wait for all request[N] to complete; interval time gettime() begin time; printf("PatternSize: %d Time: %d\n", p, interval time); 1.5 1.0 0.5 0.0 32 64 96 128 160 192 224 256 Pattern slze assumed (KB)