  With the current high levels of energy consumption of data centers, reducing
power consumption by even a small percentage is beneficial. We propose a
framework for thermal-aware workload distribution in a data center to reduce
cooling power consumption. The framework includes linearization of the general
optimization problem and proposing a heuristic to approximate the solution for
the resulting Integer Linear Programming (ILP) problems. We first define a
general nonlinear power optimization problem including several cooling
parameters, heat recirculation effects, and constraints on server temperatures.
We propose to study a linearized version of the problem, which is easier to
analyze. As an energy saving scenario and as a proof of concept for our
approach, we also consider the possibility that the red-line temperature for
idle servers is higher than that for busy servers. For the resulting ILP
problem, we propose a heuristic for intelligent rounding of the fractional
solution. Through numerical simulations, we compare our heuristics with two
baseline algorithms. We also evaluate the performance of the solution of the
linearized system on the original system. The results show that the proposed
approach can reduce the cooling power consumption by more than 30 percent
compared to the case of continuous utilizations and a single red-line
temperature.
