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Unified Deterministic Model of Parallel and Distributed Computers

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Analytical models (standard, corrected) to the problematic of unified analytical modelling of parallel and distributed computers based on queuing theory [15]has been already published. This paper extends the published results describing non Markov (deterministic) analytical mode. This analytical model considers one M/D/m queuing theory system for every computing node to model its computing activities and another M/D/1 queuing theory system for each node’s communication channel. To illustrate the accuracy of the developed deterministic model, this paper presents, in its experimental part, the results and their comparison with the previous developed analytical models including the results of simulation model to estimate the measure of improvement. All achieved verified results allow to derive mixed analytical models using theoretically all possible combinations of M/M/m or M/D/m queuing theory systems for computing activities and M/M/1 or M/D/1 queuing theory systems for modelling communication channels. The developed non Markov analytical model that has been tested in this paper, using various input parameters, which could influence performance of actually dominant parallel systems (multiprocessor/multicore SMP, NOW, Grid and meta computer), could be interesting from the point of practical use.
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Parallel Computer; Queuing Theory; Grid; Multiprocessor/ Multicore SMP; Network of Workstation (NOW); Modelling; Optimisation; Queuing Theory System; Probability Data Structures; System of Linear Equations (SLE)

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