23-1©2008 Raj JainCSE567MWashington University in St. LouisGeneral Full Factorial General Full Factorial Designs With Designs With kkFactorsFactorsRaj Jain Washington University in Saint LouisSaint Louis, MO [email protected] slides are available on-line at:http://www.cse.wustl.edu/~jain/cse567-08/23-2©2008 Raj JainCSE567MWashington University in St. LouisOverviewOverview! Model! Analysis of a General Design! Informal Methods" Observation Method" Ranking Method" Range Method23-3©2008 Raj JainCSE567MWashington University in St. LouisGeneral Full Factorial Designs With k FactorsGeneral Full Factorial Designs With k Factors! Model: k factors ⇒ 2k-1 effectsk main effectstwo factor interactions,three factor interactions,and so on. Example: 3 factors A, B, C:23-4©2008 Raj JainCSE567MWashington University in St. LouisModel ParametersModel Parameters! Analysis: Similar to that with two factors ! The sums of squares, degrees of freedom, and F-test also extend as expected. }23-5©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: Paging ProcessCase Study 23.1: Paging Process! Total 81 experiments.23-6©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1 (Cont)Case Study 23.1 (Cont)! Total Number of Page Swaps! ymax/ymin= 23134/32 = 723 ⇒ log transformation23-7©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1 (Cont)Case Study 23.1 (Cont)! Transformed Data For the Paging Study23-8©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1 (Cont)Case Study 23.1 (Cont)! Effects:! Also" Six two-factor interactions," Four three-factor interactions, and" One four-factor interaction.23-9©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: ANOVA TableCase Study 23.1: ANOVA Table23-10©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: Simplified modelCase Study 23.1: Simplified model! Most interactions except DM are small.Where,23-11©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: Simplified Model (Cont)Case Study 23.1: Simplified Model (Cont)! Interactions Between Deck Arrangement and Memory Pages23-12©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: Error ComputationCase Study 23.1: Error Computation!23-13©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: Visual TestCase Study 23.1: Visual Test! Almost a straight line.! Outlier was verified.23-14©2008 Raj JainCSE567MWashington University in St. LouisCase Study 23.1: Final ModelCase Study 23.1: Final ModelStandard Error= Stdv of sample mean= Stdv of Error23-15©2008 Raj JainCSE567MWashington University in St. LouisObservation MethodObservation Method! To find the best combination.! Example: Scheduler Design! Three Classes of Jobs:" Word processing" Interactive data processing" Background data processing! Five Factors 25-1design23-16©2008 Raj JainCSE567MWashington University in St. LouisExample 23.1: Measured ThroughputsExample 23.1: Measured Throughputs23-17©2008 Raj JainCSE567MWashington University in St. LouisExample 23.1: ConclusionsExample 23.1: ConclusionsTo get high throughput for word processing jobs,:1. There should not be any preemption (A=-1)2. The time slice should be large (B=1)3. The fairness should be on (E=1)4. The settings for queue assignment and re-queueing do not matter.23-18©2008 Raj JainCSE567MWashington University in St. LouisRanking MethodRanking Method! Sort the experiments.23-19©2008 Raj JainCSE567MWashington University in St. LouisExample 23.2: ConclusionsExample 23.2: Conclusions1. A=-1 (no preemption) is good for word processing jobs and also that A=1 is bad.2. B=1 (large time slice) is good for such jobs. No strong negative comment can be made about B=-1.3. Given a choice C should be chosen at 1, that is, there should be two queues. 4. The effect of E is not clear. 5. If top rows chosen, then E=1 is a good choice.23-20©2008 Raj JainCSE567MWashington University in St. LouisRange MethodRange Method! Range = Maximum-Minimum! Factors with large range are important. ! Memory size is the most influential factor.! Problem program, deck arrangement, and replacement algorithm are next in order.23-21©2008 Raj JainCSE567MWashington University in St. LouisSummarySummary! A general k factor design can have k main effects, two factor interactions, three factor interactions, and so on.! Information Methods:" Observation: Find the highest or lowest response" Ranking: Sort all responses" Range: Largest - smallest average response23-22©2008 Raj JainCSE567MWashington University in St. LouisExercise 23.1Exercise 23.1Using the observation method on data of Table 23.8, find the factor levels that maximize the throughput for interactive jobs (TI). Repeat the problem for background jobs (TB).23-23©2008 Raj JainCSE567MWashington University in St. LouisExercise 23.2 Exercise 23.2 Repeat Exercise 23.1 using ranking method.23-24©2008 Raj JainCSE567MWashington University in St. LouisHomework 23Homework 23! Analyze the following results using observation and ranking
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