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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