DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 13
Consequently, the programming model can be formulated with two sub-models: optimization
model as in (14) and resource allocation model as in (15). The optimization model maximizes
QoS by trading off the value of solution and the cost of completion time, and the resource
allocation model allocates resources proportional to the load indices of residing components
based on the solution of (14).
Programming model
Max
s.t.
∑
i∈A
∑
i∈K
v
L ( t )v
n
i
i(min)
[ R ( t ) + L ( t
i
≤ v
i
i
− CCT(T )
≤ v
i
) f
i(max)
i
( v )] ≤ T − t
i
for all
for all
n ∈ N
i ∈ A
(14)
w
*
i
=
*
Ri
( t)
+ Li
( t)
fi
( vi
)
ω
* n(
i)
∑[
R p ( t)
+ L p ( t)
f p ( v p )]
(15)
p∈K
n(
i)
The optimal QoS from (14) with t=0 forms a QoS upper bound QoS UB and a network can
achieve a performance close to QoS UB in the limit of large number of tasks. The programming
model is efficient in terms of complexity because the two different kinds of control actions are
completely separated. It is solvable in polynomial time as will be discussed in the next section.
4. Decentralization
The next question is how to decentralize the mathematical programming model. Centralized
control mechanisms scale badly, due to the rapid increase of computational and communicational
overheads with system size. Single point failure of the controller will often lead to failure of the
complete system leading to non-robust network. Decentralization can address these issues by