Verifying and Validating Recursive Performance Models of Parallel Computer System Using Z-Transform

Recursive models have been used in the past to model the variation of number of processes in all the queuing systems of heterogeneous parallel computer system. The main reasons for the use of recursive models when modeling the variation of number of processes in all the queuing systems of a heterogeneous parallel computer system is the inability of the analytic technique to determine the exact convergence of some mathematical series. The quality of this novel technique of modeling the performance of parallel computer system needs to be assessed. The assessment of the quality of recursive approach to performance modeling can be done by verifying and validating the model, which will help to assure us of the accuracy and correctness of the model. However, an alternative to the use of the recursive models when modeling variation of a performance metric is the statistical technique of the Z-Transform. The Z-Transform was developed as a result of the inability of the analytical technique to determine the exact convergence of some mathematical series. This paper uses the Z-transform to validate or assess the quality of the recursive approach to modeling variation of a performance metric of parallel computer system. KeywordsRecursive models; performance modeling; Z-Transform; parallel computer; distributed memory; parallel computer system; queuing network; variations; model verification; model validation.