
246 Low Power Dynamic Scheduling for Computing Systems
9.1.8 Performance of the Task Scheduling Algorithm
For simplicity, the performance theorem is presented in terms of zero initial
conditions. It is assumed throughout that the problem (9.3)-(9.6) is feasible,
so that it is possible to satisfy the constraints.
Theorem 1. Suppose Q
n
[0] = 0 for all n ∈{1,...,N}, and that the problem
(9.3)-(9.6) is feasible. Then under the above task scheduling algorithm:
a) For all frames K ∈{1, 2, 3,...} we have:
3
e[K]
D[K]+I[K]
≤ power
opt
+
B
V (D[K]+I[K])
(9.25)
where B is defined in Lemma 3, power
opt
is the minimum power solution for
the problem (9.3)-(9.6),and
e[K], D[K