DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE Transactions on Automatic Control 11
So, given completion time T it is optimal for each component i to select a mode by the
following:
Max L ( t )
i v i
(7)
subject to
[ i i i i
i
R ( t ) + L ( t ) f ( v )] / MRA ( t ) ≤ T − t . (8)
Consequently, the programming model can be formulated in a straightforward way as in (9),
named naïve decision model. The model maximizes QoS by trading off the value of solution and
the cost of completion time.
Naïve decision model
Max
s.t.
∑
i∈A
[ R ( t ) + L ( t ) f ( v )] / MRA( t ) ≤ T − t
v
L ( t )v
i
i
i(min)
≤ v
i
i
− CCT(T )
i
≤ v
i
i(max)
i
for all i ∈ A
for all i ∈ A
(9)
The naïve decision model maximizes QoS as if all the tasks of each component are available
in its queue at current time t. That is, a network under the naïve decision model can achieve a
performance close to the optimal performance of an ideal network with maximal task availability
when L i (t)s are large. As any mixed strategy (i.e. using different modes for processing tasks)
cannot perform better in the ideal network due to the convexity of value functions, it is optimal
for each component to use a pure strategy. We will refine the model so that it can be applicable
even though L i (t)s are small in the next section.