13.2

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1. FCFS

   The seek order is: 86, 1470, 913, 1774, 948, 1509, 1022, 1750, 130.

   The total number of cylinders seeked over is: 7081.

2. SSTF

   The seek order is: 130, 86, 913, 948, 1022, 1470, 1509, 1750, 1774.

   The total number of cylinders seeked over is: 1745.

3. SCAN

   The seek order is: 913, 948, 1022, 1470, 1509, 1750, 1774, 4999, 130, 86.

   The total number of cylinders seeked over is: 9769.

4. LOOK

   The seek order is: 913, 948, 1022, 1470, 1509, 1750, 1774, 130, 86.

   The total number of cylinders seeked over is: 3319.

5. C-SCAN

   The seek order is: 913, 948, 1022, 1470, 1509, 1750, 1774, 4999, 0, 86, 130.

   The total number of cylinders seeked over is: 9985.

13.3

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1. The seek time is proportional to the square root of the seek distance because if then .

2. Using the equation , we can calculate c and d from our two data points (1cyl, 1ms) and (4999cyl, 18ms). Given two unknowns and and data points we can solve for those unknowns. It turns out that c = .76 and d = .24.

   However, we still haven not said what these coefficients really represent in terms of the acceleration, a, of the disk head, the actually seek time and the overhead of doing a seek . The total seek time we will call .

   First off, . Also half the seek time is given by the formula from above with d as half the cylinder distance. This is because it accelerates half way there and then decelerates the rest of the way. So, .

   Plugging this in with our formula for we get:
   

   This means that and . We could not solve for a if we wanted.

   Note that is close to 1. If we had made the simple approximation that the (1cyl, 1ms) data point was purely overhead and that the (4999cyl, 18ms) data point was 1ms overhead and 17ms seek time, we would not have been far off.
   
   

3. Plugging the formula in for each seek in the schedule we get the following seek times:
   1. FCFS: 64ms.
   2. SSTF: 31ms.
   3. SCAN: 61ms.
   4. LOOK: 40ms.
   5. C-SCAN: 64ms.

   The fastest schedule was SSTF. Calculating the percentage speedup when compared to FCFS, we get: