Tuesday, November 4, 2008

Formulating the Grid Reliability and Performance Model (II)
Exhibit 1. Block-Matrix Grid Visualization

Exhibit 2. Block-Matrix Grid Visualization

An application to grid computing aggregation relies obviously in Linear Algebra, Linear Programming, and other related topic for the most part, which ties together quite well with both Oracle statistics and metrics, and their practical interpretation.

My study of grid computing suggests that beyond Oracle aggregation, it is possible to derive further grid matrix-driven models.

The inclusion of mathematical models to approximate an actual grid scenario suggests that the usage of structure matrices, block matrices, and polynomials can lead to the closest approximation and estimation to grid realities.

For instance, a block matrix representing a grid made out of application servers farms, denoted by an A, cluster databases and RAC instances denoted by an R, standalone database servers named with a D, and other middleware, collaboration servers, and applications denoted with a M, for mix. Every element in the matrix, and individually in the block matrix represents a polynomial coefficient for each row in the matrix, and each row is subject to desirable transformation into a structure matrix model, such, Toeplitz, Haenkel, Vandermonde, or Cauchy structure, which can potentially derive significant computational advantage for large grid models.

Equivalently, the entire grid matrix model can be recoded into one single matrix notation for various computational purposes, in relation to aggregation, statistical usability, metrics interpretation, and other stochastically predictable model, such as in a Markov Chain or a Bayesian Model subject to prior and posterior probability factors. In general, the product of the probability vector Pm,1 with the transition state matrix G m,n, systematically, generates the predicted grid state, and aligns with real data. The usage of other methods such as ARIMA to balance predicted and real-life matrix-driven linear polynomial information consistently support both probabilistic and statistical models. Ultimately, modeling or expanding grid models with the purpose of forecasting or predicting grid behavior, estimating reliability, optimizing grid performance conveys further complex mathematical models that derive productivity, business continuity, and provide comprehensive support in areas such as optimal workflow, end-user satisfaction, and various other categories of grid tuning.

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