calculating average access time of a magnetic disk

Question

A magnetic disk has 2000 cylinders, 8 tracks per cylinder, 64 sectors per track, and 2KB per sectors. The rotation time is 25msec, maximum seek time is 600 msec, and switching between adjacent cylinders take 300 msec. Assume the disk has a file of 4MB stored consecutively. Find the average access time (in msec) to read file. i have the the solution i was wondering if there is a easier way to do this with formulas or something

T his is the solution provided by my tutor
https://i.stack.imgur.com/KAZ37.png

Answer 1

Storing data consecutively is called “contiguous.” This means that a complete track (64 sectors of 2KB per sector) may read into a buffer in one rotation of the disk drive (25 ms). Now, without moving the read heads, other tracks may be read in successive rotations (25 msec each).

File systems write files in sector groups (called “clusters”) with directory information to specify the next cluster. Since this file is contiguous, we save seek time. It is only needed when the disk read heads must move to start reading and to the adjacent cylinder.

The file size is:
     4 MB

    (4 MB)*((1024 KB)/(1 MB)

    (4 MB)*((1024 KB)/(1 MB)*((1 sector)/(2KB))*((1 track)/(64 sectors))*((1 cylinder)/(8 tracks))

      4 cylinders                   [note: other units cancel]

Let’s assume that the file begins at the first track on the cylinder and at the first sector on the track. The total time is:

        Maximum seek time:                                 600 msec

                  Read 4 cylinders:

                       Read first cylinder                   8*25 msec

                    Switch to adjacent cylinder           300 msec

                       Read second cylinder              8*25 msec

                     Switch to adjacent cylinder          300 msec

                        Read third cylinder                8*25 msec

                     Switch to adjacent cylinder          300 msec

                        Read fourth cylinder              8*25 msec

                                                          -------------------------

                                                                    2300 msec

Other storage possibilities do not start at the first track on a cylinder or the first sector on a track. We used the maximum seek time, but the average could be something between 300 msec and 600 msec. The maximum number of cylinders partially used is 5 (the file is contiguous), so one additional switch to adjacent cylinder could occur. To compute the “average access time,” these values should be considered.

Note: We also assumed that the software was ready to read the next track immediately (without skipping a rotation – this is very costly in time!).

Answer 2

i will try to answer this question to the best of my ability and since you have the answer you will be able to determine if my approach is right 

 

step 1 - determine how many cylinders will be used to save the 4MB file

 

number of cylinders = 4,000,000 / (2000 x 64 x 8) = 3.9 

this means that 4 cylinders will be used to store the file

 

step 2 - calculate the time

 

access time to read the file = number of cylinders (rotation time + seek time + switch time)

time = 4 (25+600+300) = 3700 msec