Question

Suppose we want to read k blocks that are randomly
placed/stored in a disk cylinder i. These blocks could be on the same surface or
different surfaces of cylinder i. Determine, on average, how far around the track must
we go to read these k blocks.

Answer 1

Answer:

Let the radius of track closest to disk cylinder be r1 and that of farthest track be r2.

So, the average radius will be (r1 + r2)/2.

On average, each time disk head had to wait half of the rotation to reach the correct sector where it can perform the read or write operation. (Sometime it reaches there too early so it had to wait for less than half rotation and when it reaches there late it has to wait for more than half rotation to reach the desired sector on the track.)

average distance = [ 1/2 * (2 * * (r1 + r2)/2 ) ] * k

                             = [ * (r1 + r2)/2 ] * k

So, on average it must go [*(r1+r2)/2]*k around the track to read these k blocks.

Note: Here we have not include the distance travelled by the head during reading the sector as sector length is not given ie, (number of sectors per track).