Cost model for disk I⧸O

The time it takes to move data to/from a disk involves

1. Seek time
   • The time it takes to move the read/write heads to the appropriate track
     • Depends on seek distance
     • Values range from 0ms to max seek time
2. Rotational latency
   • The time it takes for the desired sectors spin to the read/write heads
     • Depends on rotational speed of disk
     • Value range from 0ms to time for single rotation
3. Transfer time
   • The time it takes until the desired sectors spin under the read/write heads
     • Depends on the rotational speed of the disk
     • Amount of data accessed
       Request service time = Seek time + Rotational latency + Transfer time

How many bytes are in a track?

• Bytes per track = Disk capacity / num tracks = $2^{32}/2^{20}=2^{12}$

How many bytes per sector?

• Bytes per sector = bytes per track / number of sectors = $2^{12}/2^8=2^4$

What is the maximum rotational latency?

• Max latency = 60 / RPM = 60 / 10000 = 6ms

What is the average seek time?

• Average seek = max seek / 3 = 30 / 3 = 10ms

What is the average rotational latency assuming a uniform distribution?

• Average latency = Max latency / 2 = 6 / 2 = 3ms

What is the cost to transfer 1 sector?

• Sector latency = Max latency / num sectors per track = 6 / $2^8$ = 0.0234 ms per sector

What is the expected cost to read 10 consecutive sectors

• Average seek + average rotational latency + Transfer time = 10 + 3 + 10 * 0.0234= 13.234ms