Towards a Bell-Curve Calculus and its Application to e-Science

1. Towards a Bell-Curve Calculus and its Application to e-Science Lin Yang Supervised by Alan Bundy, Dave Berry, Sophie Huczynska and Conrad Hughes

2. Content • Background • Workflow • QoS properties • Interval arithmetic • Experimental environment • Bell-Curve calculus • Importance • Definition • Methodology • Discussion

3. Background (1) -- workflow • What is workflow? • Web services • The orchestration of web services • An automation of a web process • Pass documents, information or data from one web service to another for action • Grid service = web service implementing Grid functionality

4. Background (2) -- workflow An example of workflow: Query information • Ticket booking system • Four services (generally sequential, partially parallel) Query Ticket information Ticket information Check_available1 Check_available2 Booking information1 Booking information2 Deal_made Deal information

5. Background (3) – quality of service properties • Why QoS properties? • Describe/evaluate the quality of a Grid/web service • Which QoS properties? • Run time, reliability and accuracy

6. Background (4) – interval arithmetic • Error bound: an interval that represents the possible values of the result e.g. 42  [41, 43] • Propagation: extension of numerical analysis e.g. unary and monotonically increasing: f*([x, y]) = [f(x), f(y)] • A worse-case analysis: the biggest accumulated error

7. Background (5) – experimental environment • Agrajag • Developed by Conrad Hughes for Dependability Infrastructure for Grid Services (DIGS) project • Define classic distribution functions, operations and numeric approximation of function combinations • http://sourceforge.net/projects/digs

8. Bell-Curve calculus (1) -- importance • Why Bell-Curve • An average case analysis: likely or unlikely • Bell-Curve = Normal Distribution • Easy to store and propagate • To deal with complex workflows efficiently • Commonly occurs in the real world

9. Bell-Curve calculus (2) -- importance • Evidence • Experimental evidence from DIGS: A possible approximation to probabilistic behaviour of run time, accuracy and reliability (mean time to failure) • Central Limit Theorem “The distribution of an average tends to be Normal, even when the distribution from which the average is computed is decidedly non-Normal.” • May extend calculus to more complicated curves in due course

10. Bell-Curve calculus (3) -- definition • Normal Distribution (Bell-curve)

11. Bell-Curve calculus (4) -- definition • Three QoS properties: • Run time, accuracy and reliability • Four ways of combining Grid services: • Sequential • Parallel_All • Parallel_First • Conditional • So 12 fundamental combinations

12. combination FCFS detection fail succeed succeed Bell-Curve calculus (5) – combination methods • Sequential • Parallel_All • Parallel_First • Conditional

13. Bell-Curve calculus (6) – basic combination functions • 12 bell-curve simple situations

14. Bell-Curve calculus (7) – proposed work • Our proposed work: • For each 12 functions, find function for and in terms of , , and • Induce the 24 functions • By experiment using Agrajag • Find other suitable calculi to describe the combination functions

15. Bell-Curve calculus (8) -- sum

16. Bell-Curve calculus (9) -- max

17. Bell-Curve calculus (10) -- methodology • isthe bell-curve approximation of the combination curve • experimental tasks: • find functions to calculate and • e.g. for sequential/run time: • , • experiment with functions for and • determine ranges of acceptable error • plot 3D graph ( vs. vs. error)

18. Discussion (1) • A better representation of probabilistic behaviour of QoS properties? e.g. log-normal calculus • More QoS properties? e.g. failure detection time run run service down failure detection system suspect confirm time failure detection time

19. Discussion (2) f.d.t.: An instantiation of run time • More combination situations? e.g. voting voting service

20. The end Any questions?