Digital Signal Processing Reference
In-Depth Information
Resource profile properties
•
The finite set of discrete control dimension configurations can be ordered ac-
cording to minimal resource requirement.
•
The system resource requirement,
R
, is defined as the sum of the per flow
requirements:
R
=
i
=
1
R
i
.
Quality profile properties
•
The finite set of discrete control dimension configurations can be ordered with
quality.
•
The system quality,
Q
, is met when each individual user's constraint is met:
JFR
i
≤
JFR
i
,1
≤
i
≤
n
.
The finite set of discrete control dimensions can be ordered, describing a range
of possible costs, resources and quality for the system in each system state. For each
additional unit of resource allocated, we only need to consider the configuration
that satisfies the quality constraint and achieves the minimal cost for that resource
unit. For each system state (e.g., channel and application loads), a subset of points
is determined by pruning the Cost-Resource-Quality set of points to yield only the
minimum cost configurations, which will be denoted by
C
i
(R
i
,Q
i
)
.
We define a calibration function
p
i
, that is computed for every state
S
i,m
min
C
i
|
p
i
(R
i
,Q
i
)
=
(
K
i
,S
i,m
→
R
i
)
∧
(
K
i
,S
i,m
→
Q
i
)
K
i
}
and defines a mapping between the Resource, Cost and the Quality of a node in
a system state,
S
i,m
, as shown in Fig.
6.8
.
∧
(
K
i
,S
i,m
→
C
i
)
∧
(
K
i
)
∈{
{
K
i
}
is the set of configuration vectors
for node
i
. Given the points after calibration in the Cost-Resource-Quality space,
we are only interested in the ones that represent optimally the trade-off between
energy, resource and quality for our system. Although the discrete settings and non-
linear interactions in real systems do not lead to a convex trade-off, it can be well
approximated as follows.
We calculate the
convex minorant
[87] of these pruned curves along the Cost,
Resource and Quality dimensions, and consider the intersection of the results. We
call this set the optimal Cost-Resource-Quality trade-off in the remainder. The
optimal Cost-Resource-Quality trade-off is plotted in the dimensions TXOP-JFR-
Energy/frame in Fig.
6.9
(a) for the considered 802.11a WLAN design case. We
will show later that the maximum segment size of the convex minorant determines
the solution's deviation from the optimum.
2
Configurations on segments that are
small compared to the largest segment size can be pruned away without affecting
the bounds of the solution. As a result, we can typically expect less than 30 config-
urations per state. At run-time, the resource allocation scheme in the AP adapts to
2
To achieve an optimum, it is necessary to retain the set of points that are Pareto-optimal or domi-
nant in the Cost-Resource-Quality dimensions. A complex optimization problem with backtracking
has to be solved at run-time to achieve the optimum based on the Pareto-points.
