The average seek time and rotational delay in a disk system are 6 ms and 3 ms, r

Question

The average seek time and rotational delay in a disk system are 6 ms and 3 ms,
respectively. The rate of data transfer to or from the disk is 30 Mbytes/sec, and all disk
accesses are for 8 Kbytes of data, stored in contiguous sectors. Data blocks are stored at
random locations on the disk. The disk controller has an 8-Kbyte buffer. The disk controller,
the processor, and the main memory are all attached to a single bus. The bus data width is
32 bits, and a single bus transfer to or from the main memory takes 10 nanoseconds.
(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 accesses are used by one disk unit, on average, over a
long period of time during which a sequence of independent 8-Kbyte transfers takes place?

Explanation / Answer

. (a) The rate of transfer to or from any one disk is 30 megabytes per second.

Maximum memory transfer rate is 4/(10 × 109 ) = 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 × 103 )/(0.01 × 106 ) = 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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