Determination of Serial Fraction for BBN

Using the observed times in table 5.1 for the three cases W=0.01,0.10 and 1.0, a simple linear fit yielded the following values for the constants a and b in equation (5.11):

$$a = 3.34\;\;\; sec,$$ (116)

$$b = 0.00589\;\;\; sec/history.$$ (117)

To show the validity of the linear model in equation (5.11), table 5.2 compares the predicted values of $\tau_1$ using equation (5.11) and the observed values from table 5.1. For the cases W=10.0 and 100.0, the serial execution times were too large to attempt, and were estimated using the linear model. Also tabulated are the predicted values of the serial fraction for each workload W. Speedup in table 5.1 for these cases use the prediction for $\tau_1$ from table 5.2.