Energy-Aware Policies in Ubiquitous Computing Facilities - Cloud Computing with e-Science Applications - page 280

tool that allows checking whether a certain formula satisfies a condition. SMT
solvers are fast and lightweight and thus can be used in nodes with limited
resources in a distributed way. Our proposal leverages the idea developed in
Reference 36 and proposes that each node of the network, to decide whether
to execute a task or offload it to the data center, should run the SMT solver.
The SMT solver calculates which tasks of the workload satisfy the conditions
to be executed at the node and the amount of tasks that can be executed.

12.5.2 Mixed-Integer Linear Programming

Regarding IT power only, the proposed resource allocation algorithms aim
to minimize the overall energy consumption of the data center by assign-
ing tasks in a spatiotemporal way to the most appropriate processors.
Mathematically, let us denote by M a set of machines, by P a set of processors,
and by T a set of tasks that must be executed. Each processor p belongs to one
machine m , denoted as p m . Each machine m consumes an idle power of ≠ m .
Every task t has a duration and consumes a certain amount of energy over
idle depending on the target processor, σ tp and e tp , respectively. The problem
consists of finding the most appropriate allocation of tasks t in processors p
to minimize the energy consumption, as expressed in the next equation:

∑∑

max

Min k · e + πτ

tp tp m

tTpP ∈∈ , mM ∈

where k tp is a binary variable that is set to 1 if the task t is executed in pro-
cessor p . τ max is the time instant at which all the tasks have been executed.
As can be seen, the first part of the formula accounts for the dynamic energy
consumption, whereas the second part accounts for static power consump-
tion of the servers.
The optimization is subjected to the following constraints:

∑ = 1 , ∑

max

k k ·σγ +≤ τ

tp tp tp pm

m

pP ∈ tT ∈

The factor γ pm is a time offset that represents the amount of time that a pro-
cessor is occupied (executing previous tasks) when the new job set arrives.
In this way, the system can take into account the initial use of processors.

12.5.3 Genetic Algorithms

The previous MILP solution is valid for a data center room with a lim-
ited amount of computational resources and an optimization objective
that can be expressed as a linear problem. However, when scaling in the