SOLUTIONS TO THE EXERCISES - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 474

SOLUTIONS FOR CHAPTER 7

7.1 Applying Equation (7.19), we can verify that

i

C k
T k

+ B i i (2 1 /i ∀ i, 1 ≤ i ≤ n,

T i ≤

− 1) .

k =1

So we have

C 1 + B 1
T 1

9
10 < 1

=

C 1
T 1

+ C 2 + B 2
T 2

4
10 +

6
15 =0 . 8 < 0 . 83

=

C 1
T 1

+ C 2
T 2

+ C 3
T 3

4
10 +

3
15 +

4
20 =0 . 8 > 0 . 78 .

=

Being condition (7.19) only sufficient, we cannot conclude anything about fea-
sibility. By applying the response time analysis we have to verify that

∀ i, 1 ≤ i ≤ n, R i ≤ D i

where

R i
T k

C k .

i− 1

R i = C i + B i +

k =1

So we have

R 1 = C 1 + B 1 =9 < 10

R (0)
2

= C 1 + C 2 + B 2 =10

C 2 + B 2 + 10
10

4=10 < 15

R (1)
2

=

R (0)
3

= C 1 + C 2 + C 3 =11

C 3 + 11
10

4+ 11
15

3=15

R (1)
3

=

C 3 + 15
10

4+ 15
15

3=15 < 20 .

R (2)
3

=

Hence, we can conclude that the task set is schedulable by RM.