Towards a BellCurve Calculus and its Application to

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

Content n Background n n n Bell-Curve calculus n n Workflow Qo. S properties Interval arithmetic Experimental environment Importance Definition Methodology Discussion

Background (1) -- workflow n What is workflow? n n n 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

Background (2) -- workflow An example of workflow: Query information n Query Ticket information Check_available 1 Ticket information Check_available 2 Booking information 1 Booking information 2 Deal_made Deal information n Ticket booking system Four services (generally sequential, partially parallel)

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

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

Background (5) – experimental environment n Agrajag n n n 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

Bell-Curve calculus (1) -importance n Why Bell-Curve n n n 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

Bell-Curve calculus (2) -importance n Evidence n Experimental evidence from DIGS: A possible approximation to probabilistic behaviour of run time, accuracy and reliability (mean time to failure) n 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. ” n May extend calculus to more complicated curves in due course

Bell-Curve calculus (3) -definition n Normal Distribution (Bell-curve)

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

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

Bell-Curve calculus (6) – basic combination functions n 12 bell-curve simple situations Seq Para_All Para_Fir Cond run time sum max min accuracy mult combine 1 varies? cond 2 reliability mult combine 2 varies? cond 3 cond 1

Bell-Curve calculus (7) – proposed work n Our proposed work: n n 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

Bell-Curve calculus (8) -- sum

Bell-Curve calculus (9) -- max

Bell-Curve calculus (10) -methodology is the 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 3 D graph ( vs. error)

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

Discussion (2) f. d. t. : An instantiation of run time f. d. t. n seq Para_All Para_Fir Cond sum max min cond 4 More combination situations? e. g. voting service

The end Any questions?