Towards a Bell-Curve Calculus For e-ScienceLin Yang Supervised by Alan Bundy, Dave Berry and Conrad Hughes

ContentBackgroundBell-Curve Calculus (BCC)ImportanceDefinitionMethodologyResult and AnalysisEvaluationFuture Work and Conclusion

BackgroundWhy QoS PropertiesPrediction, description and evaluationLikelihood of each data valueAimsDefine a suitable calculus for runtimeApply it to e-Science workflows

BCC (1) Importance Why Bell Curve

An average case analysis: likely or unlikely

Easy to store, calculate and propagate

Deal with complex workflows efficiently

BCC (2) Importance

Bell Curve = Normal Distribution

Commonly occurs in the real world

EvidenceExperimental evidenceCentral Limit Theorem

BCC (3) DefinitionBell Curve

BCC (4) Definition QoS Property: RuntimeFour ways of combining Grid ServicesSequentialParallel_AllParallel_FirstConditionalFour fundamental combination functions: sum, max, min & cond

BCC (5) Definition Four CombinationsSequential(sum)Parallel_All(max)Parallel_First(min)Conditional(cond)

BCC (6) Methodology Two input bell curves and One output bell curve The combination method =

Parameters Calculatione.g. and

BCC (7) Methodology Two main tasksTo find a satisfactory formulafor each combination methodTo evaluate accuracy and efficiencyAgrajagDeveloped by Conrad HughesDefine classic distribution functions, operations and numeric approximation of function combinations

BCC (8) Result & Analysis Max

BCC (9) Result & Analysis Max

BCC (10) Result & Analysis Refine Perfect parametersDefined in AgrajagApproximate the perfect valuesFix one parameterUse linear function to approach the perfect values in terms of the other parameter as the asymptoteDerive the linear parameters

BCC (11) Result & Analysis Refine

Use exponential compensationGet exponential parametersFind the regular pattern of the linear and exponential parameters in terms of the first parameterCombine and describe the perfect values in terms of the two BCC parameters

BCC (12) Result & Analysis Max Ref

BCC (13) Result & Analysis Max Ref

BCC (14) Result & Analysis Max Ref

BCC (15) Result & Analysis Max -- Ref

BCC (16) EvaluationTwo Methods

Comparison with AgrajagAccuracyEfficiency

Apply to use casesBrain atlasExtended workflows

BCC (17) Evaluation

BCC (18) Evaluation Accuracy

BCC (19) Evaluation Efficiency

BCC (20) Evaluation Extended Use Case

BCC (21) Evaluation Extended Use Case

Future Work (1)Embed In FrameworksMore EvaluationMore complex workflowsReal dataMore Calculie.g. log-normal distributionMore QoS Propertiese.g. accuracy and reliability

Future Work (2)Extended Twelve Fundamental Combination Functions

The End

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