From elementary physics, we know that when an object is subjected to a constant acceleration a, the relationship between distance d and time t is given by d = 1/2 at2. Suppose that, during a seek, the disk in Exercise 12.2 accelerates the disk arm at a constant rate for the first half of the seek, then decelerates the disk arm at the same rate for the second half of the seek. Assume that the disk can perform a seek to an adjacent cylinder in 1 millisecond and a full-stroke seek over all 5000 cylinders in 18 milliseconds.
a. The distance of a seek is the number of cylinders that the head moves. Explain why the seek time is proportional to the square root of the seek distance.
b. Write an equation for the seek time as a function of the seek distance. This equation should be of the form t = x + y √L, where t is the time in milliseconds and L is the seek distance in cylinders.
c. Calculate the total seek time for each of the schedules in Exercise 12.2. Determine which schedule is the fastest (has the smallest total seek time).
d. The percentage speedup is the time saved divided by the original time. What is the percentage speedup of the fastest schedule over FCFS?