Architecture of Computing Systems (Lecture Notes in Computer ...

Autonomic Workload Management for Multi-core Processor Systems 55
Fig. 3. Generation of the initial rule set
R(O T )
1.0
0.0
-1.0
O T−1 2
O T
O T−1
1.0
Fig. 4. Reward function
objective function, which evaluates all available monitor signals to determine how
well the system is currently functioning. First, a delta value is calculated for each
monitor signal to indicate how close that signal is to its optimal value (low values are
desirable):
δ frequency ∝ frequency
(2)
workload
utilization
( 100 − utilization)
δ ∝ %
(3)
δ ∝ workload − workload
(4)
local
average
The function used for each of these values is determined by the designer, and expresses
the designer’s optimization goal. For this paper, we would like each CPU to
have as low a frequency as possible, which keeps the power consumption of the system
low (voltage is automatically scaled in relation to the frequency). Likewise, we
want the CPU utilization to be as high as possible, so that no processing cycles are
wasted in an idle loop. Finally, the workload of all CPUs should be similar to avoid
temperature hot spots and to ensure similar aging across all components. Depending
on the available monitor signals and the designer’s optimization goals, other delta
functions may be chosen.
Combining the individual delta functions is accomplished by a simple weighting
scheme, which yields the system’s objective function:
f objective = w1
⋅δ
frequency + w2
⋅δ
utilization
+ w3
⋅δ
workload (5)
The weights can be chosen according to which optimization goal is most important;
for this paper each delta function is weighted equally.
Although the objective function provides a value indicating how well the system
is performing at some instant in time, in order to determine the worth of a certain
rule we need to calculate a reward R that compares the objective value sampled
before and after the rule was applied. As shown in Figure 4, if the previous objective
value OT-1 is larger than the new objective value OT, indicating that the system
has gotten closer to its optimal state, a positive reward is chosen based on the magnitude
of the change. Otherwise, a negative reward is returned. This reward is then
used to update the fitness of the applied rule, which allows the LCT to make use of
past experience when determining which rule should be applied during similar
situations in the future.