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A mathematical model for empowerment of Beowulf clusters for exascale computing

High-performance computing (HPC) clusters are currently faced with two major challenges - namely, the dynamic nature of new generation of applications and the heterogeneity of platforms - if they are going to be useful for exascale computing. Processes running these applications may well demand unpredictable requirements and changes to system configuration and capabilities at runtime, thereby requiring fast system response without sacrificing the transparency and integrity of the reconfigured empowered system that is running on a heterogeneous platform. While a challenge in and of itself, platform heterogeneity is both useful and instrumental in the handling of unpredictable requests. The realization of such a dynamically reconfigurable and heterogeneous HPC cluster system for exascale computing requires a model to guide running processes to determine if they need empowerment of the current cluster, and if yes, by how much. To show the feasibility of empowerment of traditional HPC clusters for exascale computing, we have selected Beowulf as a noble candidate cluster and present a mathematical model for the empowerment of Beowulf clusters for exascale computing (EBEC). We have developed the model in line with Beowulf's cluster approach and by using vector space algebra. In contrast to traditional hardware-oriented approaches to improvise the performance of clusters, we use a software approach to the development of the proposed model by emphasizing processes, which act as the creators of the cluster and thus should decide on system (re)configuration, as the principal building blocks of the system. We have also adopted a new approach to heterogeneity by considering heterogeneity at different levels including hardware, system software, application software, and system functionality. In addition to support for heterogeneity and dynamic reconfiguration, the proposed model includes support for scalability that is crucial to exascale computing too.