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Example 23.2 The data of Example 23.1 is presented again in Table 23.9. The rows have been sorted in order of decreasing throughputs for the word processing jobs. Notice that in column A, all -1’s are in the top half while the 1’s are in the bottom half. Thus, it is clear that A = -1 (no preemption) is good for word processing jobs and also that A = 1 is bad. In column B, the top four rows are 1’s. Thus, B = 1 (large time slice) is good for such jobs. Notice, however, that there is no corresponding pattern at the bottom of the table. Thus, no strong negative comment can be made about B = -1. Factor C has no pattern at the top. However, the bottom two values are -1. Thus, given a choice, C should be chosen at 1, that is, there should be two queues. Factor E has I in the top two rows, but the I also appears in the bottom four rows. Thus, the effect of E is no longer clear. If we have already chosen other factors at levels corresponding to the top rows, then E = 1 is a good choice. Thus, we see that the ranking method, in general, gives more information than the observation method.

23.3.3 Range Method

One way to find out the importance of a factor in a model is to find the percentage of variation explained by the factor. Another simpler informal alternative is to find the average response corresponding to each level of the factor and find the difference between the maximum and the minimum of such averages. This difference is called the range. A factor with a large range is considered important. It is assumed, though, that the observations have been transformed into a scale for which arithmetic averaging makes sense.

TABLE 23.10 Factor Averages and Range for the Paging Study

Factor Level 1 Level 2 Level 3 Range of
of Averages

Replacement algorithm 2056 2986 3781 1725
Deck arrangement 1584 2913 4326 2742
Problem program 592 2047 6185 5593
Memory size 305 2006 6512 6207

Example 23.3 Consider the data of the paging study. The averages corresponding to the three levels of each of the four factors and their ranges are listed in Table 23.10. From the range column in the table, it can be seen that memory size is the most influential factor. Problem program, deck arrangement, and replacement algorithm are next in order. This, in fact, is also the order that would have been obtained from percentage of variation explained.

EXERCISES

  23.1 Using the observation method on data of Thble 23.8, find the factor levels that maximize the throughput for interactive jobs (TI). Repeat the problem for background jobs (TB).
  23.2 Repeat Exercise 23.1 using the ranking method.

FURTHER READING FOR PART IV

The concepts of experimental design were developed for agriculture, and therefore, most of the examples in books on experimental design are from this held and not from computer science. It is therefore not surprising that this topic has been ignored in most textbooks on computer science performance analysis.

There are numerous books on design and analysis of experiments. In particular, see Mason, Gunst, and Hess (1989); Box, Hunter, and Hunter (1978); Dunn and Clark (1974); Hicks (1973); and Montgomery (1984). One of the recent developments in experimental design is the so-called Taguchi method. For details of this method see Ross (1988).

The scheduler design case study is from McHugh and Tzelnic (1981). The data for the code size comparison study of Examples 20.1 to 20.6 was adopted from that presented by Patterson and Sequin (1982). The data for Case Study 21.4 is from Hansen et al. (1982). The data as well as analysis for Case Study 23.1 is from Tsao and Margolin (1971).


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