FIXED-PRIORITY SERVERS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 134

C C C

s s s

DS

C C

1 1

τ

1

T

C C

1

2 2

τ

2

T

2

C

n

τ

n

0 CT + T

s s n

Figure 5.10 Worst-case task relations for a Deferrable Server.

Defining

⎧
⎨

R s = T 1 /T s
R i = T i +1 /T i
K = 2 (3 T s /T 1 +1)

⎩

and noting that

T n
T 1

R 1 R 2 ...R n− 1 = ,

the utilization factor may be written as

n− 1

K
R 1 R 2 ...R n− 1 −

U = U s + R i + n.

i =1

Following the approach used for RM, we minimize U over R i , i =1 ,...,n − 1.

Hence,

∂U
∂R i

K
R i ( n− 1

j = i R j ) .
Thus, defining P = R 1 R 2 ...R n− 1 , U is minimum when
⎧
⎨

=1 −

R 1 P = K
R 2 P = K
...
R n− 1 P = K ;

⎩

that is, when all R i have the same value:

R 1 = R 2 = ... = R n− 1 = K 1 /n .