$\Delta\tau$ for the IBM-SP2

The values of $\Delta\tau$s for the IBM-SP2 computer was calculated from equation (5.22) where $\tau_N$ is the actual wall clock timing on N processors. In tables 5.10, 5.11, 5.12 and 5.13 we show the $\Delta\tau$s corresponding to results of tables 5.6, 5.7, 5.8 and 5.9 respectively.

 

1|c|# of processors 1|c| Source Iteration 1|c| Fission Matrix 1c| Correlated Sampling

2 29.2 6.58 15.0

4 10.0 11.4 26.4

8 12.5 15.1 30.8

10 13.7 20.9 27.9

 

1|c|# of processors 1|c| Source Iteration 1|c| Fission Matrix 1c| Correlated Sampling

2 11.4 14.4 62.8

4 17.3 13.0 16.3

8 15.7 18.7 33.9

10 24.6 18.3 45.0

 

1|c|# of processors 1|c| Source Iteration 1|c| Fission Matrix 1c| Correlated Sampling

2 4.4 18.3 13.1

4 6.9 9.9 9.3

8 7.7 6.1 11.9

10 8.4 8.6 17.1

 

1|c|# of processors 1|c| Source Iteration 1|c| Fission Matrix 1c| Correlated Sampling

2 6.4 6.5 22.8

4 9.6 14.4 20.3

8 12.9 8.4 25.7

10 10.6 11.0 17.5

Even though it is difficult to predict an empirical formula that exactly determines $\Delta\tau$s, we notice that for most of the cases $\Delta\tau$ is about a constant. If $\Delta\tau$ is assumed to be a constant then $\alpha$ is proportional to ${\frac{1}{N}}$. Hence speedup models for IBM-SP2 can be predicted reasonably well with two parameters, the serial time constant a and the proportionality constant for ${\frac{1}{N}}$.