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Unique Analytical Model of Parallel Computers

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Any parallel computer consists of coupled computing nodes. The number of computing nodes determines the parameter p. Single computing nodes are actually used as high performance sequential computers and parallel computers based on the same multiprocessor/multicore processors or cores (SMP). The paper is devoted to the modelling of dominant parallel computers based on at least one used communication network of coupled computing nodes. The paper at first characterises very shortly the basic developing steps of the parallel computer architectures and then the basic methods of the network modelling based on parallel computers. The suggested and developed analytical models are presented in the experimental part of the article. All the suggested and developed analytical models consider for every independent parallel computer module (NOW, Grid)one queuing theory system to model their own computing node’s computation activities and another one for each computing node’s communication channel within the considered parallel computer module. When using modern multiprocessor/multicore SMP system, the developed standard analytical model considers, for its own computation, the computing node’s activities M/M/m queuing theory system and M/M/1 queuing theory system for every used computing node’s communication channel. Based on the analysed results by the experimental 7- computing nodes of the communication network with the standard analytical model the present paper suggests the improved analytical model to correct the not real exponential nature of the data inputs to modelled M/M/1 queuing theory systems. The achieved results of both the developed analytical models have been compared with the developed simulation model results to estimate the magnitude of the improvement. All the developed models (analytical, simulation) have been tested under various values of the modelled input parameters which represent the influences of modelled network architecture modules of NOW and Grid and which should be interested in practical projecting and in evaluating the dominated modular parallel computers.
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Parallel Computer; Computing Node; Network of Workstation (NOW); Grid; Meta computer; Modelling; Optimisation; Queuing Theory; Queuing Theory System; Jackson Theorem; System of Linear Equations (SLE)

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