Mass Storage Template

  1. Suppose that a disk drive has 5,000 cylinders, numbered 0 to 4,999. The drive is currently serving a request at cylinder 2,150, and the previous request was at cylinder 1,805. The queue of pending requests, in FIFO order, is:

2,069   1,212   2,296   2,800   544      1,618   356      1,523   4,956   3,681

Starting from the current head position, what is the total distance (in cylinders) that the disk arm moves to satisfy all the pending requests for each of the following disk-scheduling algorithms?  Record your answers in the table below.

  Question 1: Total Distance Question 2 (a): Total Seek Time
a.       FCFS    
b.      SSTF    
c.       SCAN    
d.      LOOK    
e.      C-SCAN    
f.        C-LOOK    

 

  1. Elementary physics states that when an object is subjected to a constant acceleration a, the relationship between distance d and time t is given by d = ½ at2. Suppose that, during a seek, the disk in Question 1 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 5,000 cylinders in 18 milliseconds.

We can express an equation for the seek time as a function of the seek distance.  This equation should be of the form t = x + y , where t is the time in milliseconds and L is the seek distance in cylinders.  First, we solve the simultaneous  equations t = x+y  that result from (t = 1, L =1) and (t =18, L =4999) to obtain

t =0.7561+0.2439 . 

Using this equation, perform the following calculations:

  1. Calculate the total seek time for each of the schedules in Question 1.

 

(Note that you have to calculate the individual distances for each access, apply the formula to them, then add them all up to get the total seek time for each method.)  Record your answers in the table above.

 

  1. The percentage speedup is the time saved divided by the original time. What is the percentage speedup of the fastest schedule over FCFS?  To receive full credit for this question, you must show your calculations.

Answer: