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The results are interpreted as follows:

  The average throughput is 0.5725. The throughput is mostly affected by the reference pattern, which makes a difference of 0.1257 and thus explains 77% of its variation. The network type contributes 0.0595 to the throughput. Omega networks give that much higher than the average, and crossbar networks give that much lower than the average. Thus, the net difference between the two types of networks is 0.119. The choice of the network is affected by the address pattern since there is a slight interaction. Depending upon the address pattern and network combination, the throughput can go up or down by 0.0346.
  The 90% transit time is also affected mostly by the address pattern. Since qA is negative, the transit time is higher for A = –1 or the crossbar networks. This applies to both address patterns since there is no interaction between the address pattern and the network type.
  The response time also depends mostly on the address pattern. The interaction between the pattern and network type is low.

Thus, we notice that all three metrics are affected more by the address patterns than by the network type This is because the address patterns chosen are very different.

17.5 GENERAL 2k FACTORIAL DESIGNS

A 2k experimental design is used to determine the effect of k factors, each of which have two alternatives or levels. We have already discussed the special case of two factors (k = 2) in the last two sections. Now we generalize the analysis to more than two factors.

The analysis techniques developed so far for 22 designs can be easily extended to a 2k design. Given k factors at two levels each, a total of 2k experiments are required. The analysis produces 2k effects. These include k main effects, two-factor interactions, three-factor interactions, and so on. The sign table method of analyzing the results and allocating the variation is also valid. We illustrate this with an example.

Example 17.3 In designing a LISP machine, the three factors that need to be studied are: cache size, memory size, and whether one or two processors will be used. The three factors and their level assignments are shown in Table 17.7.

The 23 design and the measured performance in MIPS is shown in Table 17.8.

To analyze this, we prepare a sign table as shown in Table 17.9. As shown in the last row of this table, the effects of memory, cache, and processors are qA = 10, qB = 5, and qC = 20, respectively. The three two-factor interactions are qAB = 5, qAC = 2, and qBC = 3. The three-factor interaction qABC is 1. The portion of the variation explained by the various factors and interactions are proportional to the square of the effects. The SST can

TABLE 17.7 Factors and Levels in Example 17.3

Factor Level –1 Level 1

Memory size, A 4 Mbytes 16 Mbytes
Cache size, B 1 kbyte 2 kbytes
Number of processors, C 1 2

TABLE 17.8 Results of a 23 Experiment

4 Mbytes
16 Mbytes
Cache Size (kbytes) One Processor Two Processor One Processor Two Processor

1 14 46 22 58
2 10 50 34 86


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