Question

An Example CPU Burst 4 5 6 10 4 12 The Guess 10 7 6 6 Ti All quantities in ms with a = 1/2 To = 10 Tn+1 = Qtn +(1 - «) Tn Ti = (1/2)to +(1 - 1/2)TO Ti = (1/2)(4) + (1/2)(10) = 7ms
Slide 9 is given above

Answer 1

tn = The length of the nth CPU Burst

$\tau$(n+1) = Predicted value for the CPU Burst

$\tau$(0 )= 10

$\tau$(n+1) = $\alpha$ tn + (1-$\alpha$)$\tau$(n)

1. $\alpha$ = 0

   $\tau$ (n+1 ) = (0)tn + (1-0)$\tau$(n)

                = 0+ (1) $\tau$ (n)

                 $\tau$ (n+1 ) = $\tau$ (n)

(n=0)     $\tau$ 1 =$\tau$0 = 10                                                         (given $\tau$ 0 = 10)

(n=1)     $\tau$ 2 =$\tau$1 = 10

(n=2,3,4,5)            Similarly, $\tau$ 6=$\tau$5=$\tau$4=$\tau$3=$\tau$2=10

ti		t0	t1	t2	t3	t4	t5
		4	5	6	10	4	12
$\tau$i	$\tau$0	$\tau$1	$\tau$2	$\tau$3	$\tau$4	$\tau$5	$\tau$6
	10(given)	10	10	10	10	10	10

2. $\alpha$ = 1

    $\tau$ (n+1 )= (1)tn + (1-1) $\tau$ (n)

                = tn+ (0) $\tau$ (n)

               $\tau$ (n+1 )= tn

(n=0)     $\tau$ 1 = t0 = 4

(n=1)     $\tau$ 2 = t1 = 5

(n=2)     $\tau$ 3 = t2= 6

(n=3)    $\tau$4 = t3= 10

(n=4)     $\tau$ 5 = t4 = 4

(n=5)     $\tau$ 6 = t5 = 12
   

ti		t0	t1	t2	t3	t4	t5
		4	5	6	10	4	12
$\tau$i	$\tau$0	$\tau$1	$\tau$2	$\tau$3	$\tau$4	$\tau$5	$\tau$6
	10(given)	4	5	6	10	4	12

3. $\alpha$ = 0.75

   $\tau$ (n+1 ) = (0.75)tn + (1-0.75) $\tau$ (n)

                = (0.75)tn+ (0.25) $\tau$ (n)

       $\tau$ (n+1 ) = (0.75)tn+ (0.25) $\tau$ (n)

(n=0)    $\tau$1 = (0.75)t0+ (0.25)$\tau$0

                   = (0.75)(4) + (0.25)(10)                                                                (given $\tau$ 0 = 10)

                   = 3+2.5

                   = 5.5

(n=1)     $\tau$ 2 = (0.75)t1+ (0.25)$\tau$1

                   = (0.75)(5)+ (0.25)(5.5)

                   = 3.75 + 1.375

                   = 5.125

(n=2)     $\tau$ 3 = (0.75)t2+ (0.25)$\tau$2

                   = (0.75)(6)+ (0.25)(5.125)

                   = 4.5 + 1.28125

                   = 5.78125

(n=3)    $\tau$4 = (0.75)t3+ (0.25)$\tau$3

                   = (0.75)(10)+ (0.25)(5.78125)

                   = 7.5 + 1.4453125

                   = 8.9453125

(n=4)     $\tau$ 5 = (0.75)t4+ (0.25)$\tau$4

                   = (0.75)(4)+ (0.25)(8.9453125)

                   = 3 + 2.236328125

                   = 5.236328125

(n=5)     $\tau$ 6 = (0.75)t5+ (0.25)$\tau$5

                   = (0.75)(12)+ (0.25)(5.236328125)

                   = 9 + 1.309082031

                   = 10.309082031

ti		t0	t1	t2	t3	t4	t5
		4	5	6	10	4	12
$\tau$i	$\tau$0	$\tau$1	$\tau$2	$\tau$3	$\tau$4	$\tau$5	$\tau$6
	10(given)	5.5	5.125	5.78125	8.9453125	5.236328125	10.309082031

4. $\alpha$ = 0.25

   $\tau$ (n+1 ) = (0.25)tn + (1-0.25) $\tau$ (n)

                = (0.25)tn+ (0.75) $\tau$ (n)

    $\tau$ (n+1 ) = (0.25)tn+ (0.75) $\tau$ (n)

(n=0)     $\tau$ 1 = (0.25)t0+ (0.75)$\tau$0

                   = (0.25)(4) + (0.75)(10)                                                                (given $\tau$ 0 = 10)

                   = 1+7.5

                   = 8.5

(n=1)    $\tau$2 = (0.25)t1+ (0.75)$\tau$1

                   = (0.25)(5)+ (0.75)(8.5)

                   = 1.75 + 6.375

                   = 8.125

(n=2)     $\tau$ 3 = (0.25)t2+ (0.75)$\tau$2

                   = (0.25)(6)+ (0.75)(8.125)

                   = 1.5 + 6.09375

                   = 7.59375

(n=3)     $\tau$ 4 = (0.25)t3+ (0.75)$\tau$3

                   = (0.25)(10)+ (0.75)(7.59375)

                   = 2.5 + 5.6953125

                   = 8.1953125

(n=4)     $\tau$ 5 = (0.25)t4+ (0.75)$\tau$4

                   = (0.25)(4)+ (0.75)(8.1953125)

                   = 1 + 6.146484375

                   = 7.146484375

(n=5)     $\tau$ 6 = (0.25)t5+ (0.75)$\tau$5

                   = (0.25)(12)+ (0.75)(7.146484375)

                   = 3 + 5.3598632813

                   = 8.3598632813

ti		t0	t1	t2	t3	t4	t5
		4	5	6	10	4	12
$\tau$i	$\tau$0	$\tau$1	$\tau$2	$\tau$3	$\tau$4	$\tau$5	$\tau$6
	10(given)	8.5	8.125	7.59375	8.1953125	7.146484375	5.3598632813