Question

Consider a single-platter disk with the following parameters: rotation speed: 7200
rpm; number of tracks on one side of platter: 30,000; number of sectors per track:
600; seek time: one ms for every hundred tracks traversed. Let the disk receive a
request to access a random sector on a random track and assume the disk head starts
at track 0.
a. What is the average seek time?
b. What is the average rotational latency?
c. What is the transfer time for a sector?
d. What is the total average time to satisfy a request?

Answer 1

a.

The seek time for every 100 tracks traversed = 1 ms

Number of tracks traversed in going from the track 1 to track 30,000 = 29,999

Seek time for 29,999 tracks traversed is

$\frac{29999}{100}=299.99\,ms$

Average seek time is generally taken to be half of time taken to traverse from the first track to the last track

So, average seek time is,

$\frac{299.99}{2}=149.99\,ms$

b.

Time to complete 7200 rotations = 1 min = 60 sec

Time to complete 1 rotation is

$\frac{60}{7200}=0.00833\,sec\,=8.33\,ms$

Average rotational latency is half of the time to complete 1 rotation

$\frac{8.33}{2}=4.165\,ms$

c.

In a full rotation an entire track can be transferred. Also it is given that there are 600 sectors per track

Time to transfer an entire track is the same as time to complete a single rotation

$\frac{60}{7200}=0.00833\,sec\,=8.33\,ms$

Time to transfer 600 sectors = 8.33 ms

Time to transfer 1 sector is

$\frac{8.33}{600}=0.01388\,ms=13.88\,\mu s$

d.

Total average time to satisfy a request = Average seek time + Average rotational latency + Transfer time of a sector

We have already calculated those values in the previous questions

Total average time to satisfy a request = 149.99 ms + 4.165 ms +0.01388 ms = 154.168 ms