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6.6 / KEY TERMS, REVIEW QUESTIONS, AND PROBLEMS 215

b. Next, calculate the probability of a seek of length K. Hint: this involves the sum-
ming 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
N -1
E[x] = i * Pr[x = i]
a
i=0
n n(n + 1) n n(n + 1)(2n + 1)
2
Hint: Use the equalities: i = ; i = .
a 2 a 6
i=1 i=1
d. Show that for large values of N, the average number of tracks traversed by a seek
approaches N/3.
6.2 Define the following for a disk system:
t s = seek time; average time to position head over track
r = rotation speed of the disk, in revolutions per second
n = number of bits per sector
N = capacity of a track, in bits
t A = time to access a sector
Develop a formula for t A as a function of the other parameters.
6.3 Consider a magnetic disk drive with 8 surfaces, 512 tracks per surface, and 64 sectors
per track. Sector size is 1 KB.The average seek time is 8 ms, the track-to-track access
time is 1.5 ms, and the drive rotates at 3600 rpm. Successive tracks in a cylinder can be
read without head movement.
a. What is the disk capacity?
b. What is the average access time? Assume this file is stored in successive sectors
and tracks of successive cylinders, starting at sector 0, track 0, of cylinder i.
c. Estimate the time required to transfer a 5-MB file.
d. What is the burst transfer rate?
6.4 Consider a single-platter disk with the following parameters: rotation speed:
7200 rpm; number of tracks on one side of platter: 30,000; number of sectors per
track: 600; seek time: one ms for every hundred tracks traversed. Let the disk receive
a request to access a random sector on a random track and assume the disk head
starts at track 0.
a. What is the average seek time?
b. What is the average rotational latency?
c. What is the transfer time for a sector?
d. What is the total average time to satisfy a request?
6.5 A distinction is made between physical records and logical records.A logical record is
a collection of related data elements treated as a conceptual unit, independent of how
or where the information is stored. A physical record is a contiguous area of storage
space that is defined by the characteristics of the storage device and operating system.
Assume a disk system in which each physical record contains thirty 120-byte logical
records. Calculate how much disk space (in sectors, tracks, and surfaces) will be re-
quired to store 300,000 logical records if the disk is fixed-sector with 512 bytes/sector,
with 96 sectors/track, 110 tracks per surface, and 8 usable surfaces. Ignore any file
header record(s) and track indexes, and assume that records cannot span two sectors.
6.6 Consider a disk that rotates at 3600 rpm.The seek time to move the head between ad-
jacent tracks is 2 ms. There are 32 sectors per track, which are stored in linear order
from sector 0 through sector 31.The head sees the sectors in ascending order.Assume
the read/write head is positioned at the start of sector 1 on track 8. There is a main
memory buffer large enough to hold an entire track. Data is transferred between disk