Characterizing Task-Machine Affinity in Heterogeneous Computing Environments

Abstract

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.

Energy-aware fast scheduling heuristics in heterogeneous computing systems

“…For each task the information on its processing time and the voltage rate of the processor to execute one unit of time is sufficient to measure the energy consumption for that task. In this context, we additionally promote the heterogeneity capability of the computing system to efficiently use the energy of the system [3][4][5]. The main idea is to match each task with the best resource to execute it, that is, the resource that optimizes the completion time of the task and executes it fastest with minimum energy.…”

Controlling and Assessing Correlations of Cost Matrices in Heterogeneous Scheduling

“…Additionally, few instances have high task correlation and are thus underrepresented. Two matrices extracted from the SPEC benchmarks on five different machines are provided in [1]. There are 12 tasks in CINT2006Rate and 17 tasks in CFP2006Rate.…”

“…The TMA (Task-Machine Affinity) quantifies the specialization of a platform [1,2], i.e., whether some machines are particularly efficient for some specific tasks. This measure proceeds in three steps: first, it normalizes the cost matrix to make the measure independent from the matrix heterogeneity; second, it performs the singular value decomposition of the matrix; last, it computes the inverse of the ratio between the first singular value and the mean of all the other singular values.…”

“…This measure proceeds in three steps: first, it normalizes the cost matrix to make the measure independent from the matrix heterogeneity; second, it performs the singular value decomposition of the matrix; last, it computes the inverse of the ratio between the first singular value and the mean of all the other singular values. The normalization happens on the columns in [2] and on both the rows and columns in [1]. If there is no affinity between the tasks and the machines (as with uniform machines), the TMA is close to zero.…”

“…The TMA is a measure based on the singular values of the normalized inverse cost matrix. We consider the variant in which the normalization is done alternatively on both the rows and columns [1]. The cost matrix is first inverted before being normalized with an iterative procedure.…”