Abstract-We consider a heterogeneous computing environment that consists of a collection of machines and task types. The machines vary in capabilities and different task types are better suited to specific machine architectures. We describe some of the difficulties with the current measures that are used to characterize heterogeneous computing environments and propose two new measures. These measures relate to the aggregate machine performance (relative to the given task types) and the degree of affinity that specific task types have to different machines. The latter measure of taskmachine affinity is quantified using singular value decomposition. One motivation for using these new measures is to be able to represent a wider range of heterogeneous environments than is possible with previous techniques. An important application of studying the heterogeneity of heterogeneous systems is predicting the performance of different computing hardware for a given task type mix.

Abstract-Many of today's data centers experience physical limitations on the power needed to run the data center. The first problem that we study is maximizing the performance (quantified by the reward collected for completing tasks by their individual deadlines) of a data center that is subject to total power consumption (of compute nodes and CRAC units) and thermal constraints. The second problem that we study is how to minimize the power consumption in a data center while guaranteeing that the overall performance does not drop below a specified threshold. For both problems, we develop novel optimization techniques for assigning the performance states of cores at the data center level to optimize the operation of the data center. The resource allocation (assignment) techniques in this paper are thermal aware as they consider effects of performance state assignments on temperature and power consumption by the CRAC units. Our simulation studies show that in some cases our assignment technique achieves about 17% average improvement in the reward collected, and about 9% reduction in power consumption compared to an assignment technique that only considers putting a core in the performance state with the highest performance or turning the core off.

Abstract-Manycomputing environments are heterogeneous, i.e., they consist of a number of different machines that vary in their computational capabilities. These machines are used to execute task types that vary in their computational requirements. Characterizing heterogeneous computing environments and quantifying their heterogeneity is important for many applications. In previous research, we have proposed preliminary measures for machine performance homogeneity and task-machine affinity. In this paper, we build on our previous work by introducing a complementary measure called the task difficulty homogeneity. Furthermore, we refine our measure of task-machine affinity to be independent of the task type difficulty measure and the machine performance homogeneity measure. We also give examples of how the measures can be used to characterize heterogeneous computing environments that are based on real world task types and machines extracted from the SPEC benchmark data.

We study heterogeneous computing (HC) systems that consist of a set of different machines that have varying capabilities. These machines are used to execute a set of heterogeneous tasks that vary in their computational complexity. Finding the optimal mapping of tasks to machines in an HC system has been shown to be, in general, an NP-complete problem. Therefore, heuristics have been used to find nearoptimal mappings. The performance of allocation heuristics can be affected significantly by factors such as task and machine heterogeneities. In this paper, we identify different statistical measures used to quantify the heterogeneity of HC systems, and show the correlation between the performance of the heuristics and these measures through simple mapping examples and synthetic data analysis. In addition, we illustrate how regression trees can be used to predict the most appropriate heuristic for an HC system based on its heterogeneity.

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