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Model Validation

In order to validate our formulas for comparing speedup on different architectures, we have used empirical performance data from section 7.1 and developed performance comparisons for complex variate LU factorization on the SP1 and SP2. We have extended the number of processors beyond the number actually utilized to collect the empirical data from the SPP architectures. Our implementations on the SP1 and SP2 used the Message Passing Interface (MPI), because it is being developed as a communications standard for multi-processors with strong emphasis on optimizing message-passing performance. The IBM SP2 has a 30 second latency and 30 megabyte-per-second bandwidth in present configurations [16]. In figure gif, we present actual and predicted speedup values for the complex LU factorization algorithm with the EPRI6K power systems network for

  1. empirical speedup data from the CM-5 implementation using buffered communications,
  2. empirical speedup data from the SP1 implementation using MPI,
  3. empirical speedup data from the SP2 implementation using MPI,
  4. predicted speedup for the SP1 ( processor speedup),
  5. predicted speedup for the SP2 ( processor speedup),
In this figure, we plot predicted values for both the SP1 and the SP2, where the single processor performance of the SP1 is 6.6 times the single processor performance of the Thinking Machines CM-5 and the SP2 is 50% faster than the SP1. When comparing the actual data to the predicted data, it may be possible that this simplistic technique has some difficulties in vertical displacement. While the slope of the curve splines for the predicted data and the curve splines for the empirical data are similar for the SP2, the predicted curve appears to underestimate the speedup by a nearly constant amount. These predictions have been made using a very simple model, and should only be interpreted as in indication of possible future performance. Better estimates are possible by carefully simulating the algorithms using models with more variables and greater detail.

 
Figure: Performance Validation for Parallel Complex LU Factorization  



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David P. Koester
Sun Oct 22 17:27:14 EDT 1995