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Aside Computing The Average Seek

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  • Explain the main ideas and vocabulary in Aside Computing The Average Seek.
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  • module-04-file-systems-io

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  • Source chapter: Aside Computing The Average Seek
  • Raw source file: 174-aside-computingthe-average-seek.md

Merged source​

Aside Computing The Average Seek​

ASIDE: COMPUTINGTHE"AVERAGE" SEEK

In many books and papers, you will see average disk-seek time cited as being roughly one-third of the full seek time. Where does this come from?

Turns out it arises from a simple calculation based on average seek distance, not time. Imagine the disk as a set of tracks, from0toN. The seek distance between any two tracksxandyis thus computed as the absolute value of the difference between them:|x-y|.

To compute the average seek distance, all you need to do is to first add up all possible seek distances:

∑N ∑N

|x-y|. (37.4)

x=0y=0

Then, divide this by the number of different possible seeks: N2. To compute the sum, we'll just use the integral form:

∫ N ∫ N

|x-y|dydx. (37.5)

x=0 y=0

To compute the inner integral, let's break out the absolute value:

∫ x ∫ N

(x-y) dy+ (y-x) dy. (37.6)
y=0 y=x

∣x ∣N

Solving this leads to (xy-1y2)∣ + (1y2-xy)∣ which can be sim- 2 0 2 x plified to(x2-N x+1N2). Now we have to compute the outer integral:

2

∫ N

2 1 2

(x -N x+N) dx, (37.7)
x=0

which results in:

∣N 1 2 ∣ 3 3 N 2 N ∣ N

( x - x + x)∣ = . (37.8)

3 2 2 3 0

Remember that we still have to divide by the total number of seeks 2 N3 2 1 (N) to compute the average seek distance:( )/(N) = N. Thus the 3 3 average seek distance on a disk, over all possible seeks, is one-third the full distance. And now when you hear that an average seek is one-third of a full seek, you'll know where it came from.

9 8 10 21 20 22 33 7 32 34 11 19 23 31 35

Spindle 6 18 30 24 12 0 29 25 17 13 5 28 26 1 27 16 14 15 4 2 3

Figure 37.7:SSTF: Scheduling Requests 21 And 2