Performance Modeling of Parallel Computers NOW and Grid

Abstract

The paper describes development, realization and verification of more precise analytical models for the study of the basic performance parameters of parallel computers based on connected parallel computers (Cluster, NOW, Grid). At first the paper describes very shortly the developing steps of parallel computer architecture and then he summarized the basic concepts for performance modeling of mentioned parallel computers. To illustrate theoretical evaluation concepts the paper considers in its experimental part the achieved results on concrete analyzed examples and their comparison. The suggested model considers for every node of the NOW or Grid networks one part for the own workstation's activities and another one for node's communication channel modeling of performed data communications. In case of using multiprocessor system, as modern node's communication processor, the suggested model considers for own node's activities M/D/m queuing theory system and for every node's communication channel M/D/1 system. Based on these more realistic assumptions we have been developed improved analytical models to account the real no exponential nature of the inputs to the modeling queuing systems. The achieved results of the developed models were compared with the results of the common used analytical and simulation model to estimate the magnitude of their improvement. The developed analytical models could be used under various ranges of input analytical parameters, which influence the architecture of NOW or Grid computer networks and which are interested from the sight of practical using. These consequences are in relation to the developed analytical models and their verifications through simulation model.

Unified Analytical Models of Parallel and Distributed Computing

“…We have already introduced many notations for the quantities of interest for random variables and stochastic processes. For the analysis of parallel computers including their communication network communication networks we have been developed in [9] following analytical models • standard analytical model on the basis of Jackson's theorem. In this case we suppose decomposition to the independent computing nodes on the basis of the M/M/m systems with infinite buffer.…”

“…Queuing theory systems are classified according to various characteristics, which are often summarized using Kendall`s notation [7,9]. The basic parameters of queuing theory systems are as following…”

“…In [9] we have presented open multi nodes module NOW consisting of U computation nodes including theirs communication network. Model of i-th computing node illustrates The intern input flow to i-th node is defined as the input from all other connected computing nodes.…”

“…Principally analytical methods (AM) belong to the preferred method in comparison to the simulation method, because of their potential ability of more general analysis and also of ability to analyze massive parallel computers. This article goes further in developing AM based on queuing theory results in relation to our published paper in [9]. The extensions are in extending derived AM to whole range of parallel computers and also to sum up public acceptance of our published paper.…”

“…In [9] we have characterized developing periods of parallel computers and their basic classification from the point of programmer as potential developers of parallel algorithms. In relation to it and also to other performed classifications [1,8] we have divided them as following…”