MATHEMATICAL MODELS PRODUCTIVITY OF CLUSTER SYSTEM BASED ON RASPBERRY PI 3B+

Abstract

Context. High-performance computing systems are needed to solve many scientific problems and to work with complex applied problems. Previously, real parallel data processing was supported only by supercomputers, which are very limited and difficult to access. Currently, one way to solve this problem is to build small, cheap clusters based on single-board computers Raspberry Pi.
 Objective. The goal of the work is the creation of a complex criterion for the efficiency of the cluster system, which could properly characterize the operation of such a system and find the dependences of the performance of the cluster system based on Raspberry Pi 3B+ on the number of boards in it with different cooling systems.
 Method. It is offered to apply in the analysis of small cluster computer systems the complex criterion of efficiency of work of cluster system which will consider the general productivity of cluster computer system, productivity of one computing element in cluster computer system, electricity consumption by cluster system, electricity consumption per one computing element, the cost of calculating 1 Gflops cluster computer system, the total cost of the cluster computer system.
 Results. The developed complex criterion of cluster system efficiency was used to create an experimental cluster system based on single-board computers Raspberry Pi 3B+. Mathematical models of the dependence of the performance of a small cluster system based on single-board computers Raspberry Pi 3B+ depending on the number of boards in it with different cooling systems have also been developed.
 Conclusions. The conducted experiments confirmed the expediency of using the developed complex criterion of efficiency of the cluster system and allow to recommend it for use in practice when creating small cluster systems. Prospects for further research are to determine the weights of the constituent elements of the complex criterion of efficiency of the cluster system, as well as in the experimental study of the proposed weights.