DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

assigned to machine k as S I[k] and the clusters assigned to machine k as S J[k] . If ω k a of total
managed weight ω k is available to assign in machine k (i.e. ω k -ω k a
is reserved by other
applications), the constraints of resource allocation variables for a given topology are as in (2).
Resource allocation constraints
∑
i∈S
I
[ k ]
a
w i( t ) ≤ ω k for all k ∈ K
(2)
2.4 Problem definition
As the completion time T is a function of network topology (X) and resource allocation (w),
the objective is to quantify the minimal completion time T *
represented in (3) with the
constraints of (1) and (2).
T
*
= Min T
X ,w
. (3)
3. Minimal completion time
As stated earlier, we design a method of quantifying the minimal completion time by limiting
to the cases where the number of tasks to be processed by each component is large. In this
section, we investigate the impacts of the largeness on the optimal resource allocation for a given
topology. Then, we formulate the problem by incorporating network topology and provide a
heuristic algorithm for solving the problem formulation.
3.1 Optimal resource allocation
For a given topology, we define Load Index LI i which represents component i’s total CPU
time required to process its tasks. As a component needs to process its own root tasks as well as
incoming tasks from its predecessors, its number of tasks L i is identified as in (4), where i
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