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EGEE-III INFSO-RI Enabling Grids for E-sciencE EGEE and gLite are registered trademarks Modeling Grid Job Time Properties Lovro Ilijašić Lorenza Saitta University of Eastern Piedmont, Italy

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Modeling Grid Job Time Properties 2 Grid Observatory The Grid Observatory cluster of EGEE – the scientific view Data collection, analysis of behaviour and usage 20 months of data, more than 28 million jobs Development of models Grid is more than just a sum of its parts

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Emergent Behaviour Properties that are apparent only on higher levels of organization and are not present on the lower ones Emergent Behaviour is observable on all levels of reality Modeling Grid Job Time Properties 3

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Power Law Pareto distribution Zipfs law rule Self similarity Modeling Grid Job Time Properties 4

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Degree Distributions In- and out-degree distributions: How users connect (use) CEs Weighted degrees: Distribution of number of jobs Modeling Grid Job Time Properties 5

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Job Lifecycle Analysis Modeling Grid Job Time Properties 6

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Distributions of Job Lengths Modeling Grid Job Time Properties 7

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Distributions in log-log scale Modeling Grid Job Time Properties 8

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Power-law vs. Log-normal Power-law: preferential attachment Power-law: optimization of the average amount of information per unit transmission cost Power-law: monkeys typing randomly Probabilities of letters not equal: power-law or log- normal? Modeling Grid Job Time Properties 9

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Log-normal vs. Power-law Log-normal: multiplicative processes At each step, the event (X t ) may grow or shrink, according to a random variable F t : X t = F t X t-1 Multiplicative models can also generate Pareto distribution if there is not a minimum size of event. Otherwise it is log-normal Intermixing of generations, where t is random variable, leads to power law. Modeling Grid Job Time Properties 10

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Log-normal Fitted Distributions Modeling Grid Job Time Properties 11

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Alternatives Double Pareto distribution Double Pareto log-normal distribution More distribution parameters that allow better fitting Modeling Grid Job Time Properties 12

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EGEE-III INFSO-RI Enabling Grids for E-sciencE EGEE and gLite are registered trademarks Modeling Grid Job Time Properties Lovro Ilijašić Lorenza Saitta University of Eastern Piedmont, Italy

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Modeling Grid Job Time Properties 14

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Complex Networks Complex Networks – Complex systems represented as graphs Gathered experiences from Physics, Chemistry, Biology, Computer Science, Sociology, Economics… Representing Grid as a Complex Network 20 months of log data, more than 28 million jobs Edges representing jobs go from Users to CEs Modeling Grid Job Time Properties 15

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Number of jobs for each user Modeling Grid Job Time Properties 16

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Modeling Grid Job Time Properties 17

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Enabling Grids for E-sciencE EGEE-III INFSO-RI Modeling Grid Job Time Properties 18

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