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

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

• Lin Yang
• Supervised by Alan Bundy, Dave Berry, Sophie
  Huczynska and Conrad Hughes

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Content

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

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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

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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
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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

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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

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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

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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

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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

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Bell-Curve calculus (3) -- definition

• Normal Distribution (Bell-curve)

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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

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Bell-Curve calculus (5) combination methods

• Sequential
• Parallel_All
• Parallel_First
• Conditional

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Bell-Curve calculus (6) basic combination
functions

• 12 bell-curve simple situations

Seq Para_All Para_Fir Cond
run time sum max min cond1
accuracy mult combine1 varies? cond2
reliability mult combine2 varies? cond3
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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

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Bell-Curve calculus (8) -- sum
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Bell-Curve calculus (9) -- max
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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 3D graph ( vs. vs. error)

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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
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Discussion (2)

• f.d.t. An instantiation of run time
• More combination situations?
• e.g. voting

seq Para_All Para_Fir Cond
f.d.t. sum max min cond4
voting service
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The end

• Any questions?