Consider a disk with N tracks numbered from 0 to (N €“ 1) and assume that requested sectors are distributed randomly and evenly over the disk. We want to calculate the average number of tracks traversed by a seek.
a. Calculate the probability of a seek of length j when the head is currently positioned over track t.
b. Calculate the probability of a seek of length K, for an arbitrary current position of the head.
c. Calculate the average number of tracks traversed by a seek, using the formula for expected value

d. Show that for large values of N, the average number of tracks traversed by a seek approaches N / 3.

Transcribed Image Text:

N-1 Elx = n(n+1) ; n(n + 1)(2n + 1) .2