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The average seek time and rotational delay in a disk system are 6ms and 3ms, respectively.  The rate of data transfer to or from the disk is 30 Mbytes/sec and all disk accesses are for 8Kbytes of data. Disk DMA controller, the processor and the main memory are all attached to a single bus. The bus data width is 32bits and a bus transfer to or from the main memory takes 10nano seconds.

a) what is the maximum number of disk units that can be simultaneously transferring data to or from the main memory?

b) what percentage of main memory cycles are stolen by a disk unit, on average over a long period of time during which a sequence of independent 8K-byte transfers takes place?

Solution:

a) The rate of transfer to or from any one disk is 30 megabytes per second.
Maximum memory transfer rate is 4/(10 × 10−9
) = 400 × 106 bytes/s, which is
400 megabytes per second. Therefore, 13 disks can be simultaneously flowing
data to/from the main memory.

(b) 8K/30M = 0.27 ms is needed to transfer 8K bytes to/from the disk. Seek and
rotational delays are 6 ms and 3 ms, respectively. Therefore, 8K/4 = 2K words
are transferred in 9.27 ms. But in 9.27 ms there are (9.27 × 10−3
)/(0.01 ×
10−6
) = 927 × 103 memory (word) cycles available. Therefore, over a long
period of time, any one disk steals only (2/927) × 100 = 0.2% of available
memory cycles.
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