
236 Low Power Dynamic Scheduling for Computing Systems
written as follows:
Minimize:
e
D + I
(9.3)
Subject to:
1
n
D + I
≥ λ
n
∀n ∈{1,...,N} (9.4)
(c[k],m[k]) ∈{1,...,N}×M ∀k ∈{0, 1, 2,...} (9.5)
0 ≤ I[k] ≤ I
max
∀k ∈{0, 1, 2,...} (9.6)
where the objective (9.3) is average power, the constraint (9.4) ensures the
processing rate of each class n is at least λ
n
, and constraints (9.5)-(9.6) ensure
that c[k] ∈{1,...,N}, m[k] ∈M,and0≤ I[k] ≤ I
max
for each frame k.
9.1.3 Relation to Frame Average Expectations
The problem (9.3)-(9.6) is defined by frame averages. This subsection shows
that frame averages are related to frame average expectations, and hence
can be related