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. First, calculate the probability of a seek of length j when the head is currently positioned over track t. Hint: This is a matter of determining the total number of combinations, recognizing that all track positions for the destination of the seek are equally likely. b. Next, calculate the probability of a seek of length K. Hint: This involves the summing over all possible combinations of movements of K tracks. c. Calculate the average number of tracks traversed by a seek, using the formula for expected value E[x] = a N-1 i=0 i * Pr[x = i] Hint: Use the equalities: a n i=1 i = n(n + 1) 2 ; a n i=1 i2 = n(n + 1)(2n + 1)
Answers
Answer:
Calculate the average number of tracks traversed by a seek, using the formula for expected value
Hint: Use the equalities: .
d. Show that for large values of N, the average number of tracks traversed by a seek approaches N/3.
Explanation:
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Answer:
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. First, calculate the probability of a seek of length j when the head is currently positioned over track t. Hint: This is a matter of determining the total number of combinations, recognizing that all track positions for the destination of the seek are equally likely.
b. Next, calculate the probability of a seek of length K. Hint: This involves the summing over all possible combinations of movements of K tracks.
c. Calculate the average number of tracks traversed by a seek, using the formula for expected value
Hint: Use the equalities: .
d. Show that for large values of N, the average number of tracks traversed by a seek approaches N/3.