256 Low Power Dynamic Scheduling for Computing Systems
flow control variables γ
n
[k] in (9.46) make “bang-bang” decisions that admit
all newly arriving tasks of class n on frame k if Q
n
[k] ≤ Vw
n
, and admit none
otherwise. This property makes the algorithm naturally adaptive to situations
when the arrival rates change, as shown in the simulations of Section 9.2.4.
Note that if ˆe(0,m,I) < ˆe(c, m, I) for all c ∈{1,...,N}, m ∈M, I ∈
[0,I
max
], so that the energy associated with processing no task is less than
the energy of processing any class c = 0, then the minimization in (9.47) will
never select a class c such that Q
c
[k] = 0. That is, the algorithm naturally
will never select a class for which no task is available.
9.2.3.2 Deterministic Queue Bounds ...