Performance analysis calculations, for models of any complexity, require a distributed computation effort that can easily occupy a large compute cluster for many days. Producing a simple steady-state measure involves an enormous dominant eigenvector calculation, with even modest performance models having upwards of 10 12 variables. Computations such as passage-time analysis are an order of magnitude more difficult, producing many hundreds of repeated linear system calculations. As models describe greater concurrency, so the state space of the model increases and with it the magnitude of any performance analysis problem that may be being attempted. The PageRank algorithm is used by Google to measure the relative importance of web pages. It does this by formulating and solving a similarly enormous dominant eigenvector problem, with one variable for every page on the web. As with performance problems, as the number of web pages grows, so the size of the underlying system calculation grows also. With the number of web pages currently estimated to exceed one trillion, the PageRank problem requires many thousands of computers running concurrently over many different clusters. Both problems share the same underlying mathematical type and also the same requiremen
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