Experiments on Models of Computations and Systems

Abstract

This paper reports results of experiments on models of computational sequences and models of computer systems. The validity of these models is a step in the evolution of methods for prediction of complex computer system performance. A graph model representing computational sequences was implemented and mapped onto a model of computer systems using programmable assignment and sequencing strategies. An approximate procedure for a priori estimation of path length (computation time) through an assigned graph was checked against more conventional simulation. The graph model was also perturbed to probe sensitivity of estimates of operation times, cycle factors, and branching probabilities. Problems arising in numerical weather prediction, X-ray analysis, nuclear modeling, and graph computations were transformed into acyclic directed graphs and have undergone computer analysis. Effectiveness of parallel processing, convergence properties of the successive approximation assignment and sequencing procedure, sensitivity to input parameter variation, the cost in computer time of the graph analysis, and comparison with more conventional SIMSCRIPT simulation are presented. The reduction in time required to obtain an estimate of path length compared to conventional simulation is found to range from a little less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> to more than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> . Computational tests indicate that additional factors may be gained without severe loss in validity of the approximation.