Application of Real-Time Scheduling Techniques to Agent-Based Distributed Production Systems

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Application of Real-Time Scheduling Techniques
to Agent-Based Distributed Production Systems

• 04.11.2002

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Goals

• Novel application area of RT Systems
• Put the RT scheduling theory into Production
  Control System practical applications
• Allow predictable aperiodic scheduling in the
  presence of periodic tasks in a production stage
  and shift of a PCS

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Overview

• Main focuses
• Taxonomy of multiprocessor platforms
• Parallel uniform platforms Why?
• Comparative study of relevant RT Multiprocessor
  Scheduling Algorithms
• Resource augmentation technique
• System characteristics
• TBS on uniform multiprocessors
• Schedulability analysis
• Example
• Performance evaluation

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Main focuses

• structure and present a methodology of a
  manufacturing system under RT-Contraints
• thorougly examine and compare the literature of
  real-time scheduling theory and its application
  to Production Control Systems
• Present a firm real-time scheduling technique of
  a distributed production control system
• to develop predictable computational methods for
  studying the aperiodic scheduling problem in uni-
  and multiprocessor manufacturing systems under
  real-time constraints.

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Workload considerations in a traditional PCS
Raw material
Product
Parts
Parts
Parts
Assembly
Galvanic
Machining
Broaching
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Pre-planned production of parts realized by
traditional production planning and control
systems
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Workload considerations in a RT- PCS
Raw material
Product
Parts
Parts
Parts
Assembly
Galvanic
Machining
Broaching
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Parallel uniform machines
Periodic and aperiodic production of parts in a
production system underlying real-time constraints
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Taxonomy of multiprocessor platforms

• Parallel identical machines Same task
  production time for all machines
• Parallel uniform machines Machines differ in
  their production time, but production time does
  not depend from the type of the task
• Parallel unrelated machines The production time
  of the machine depends from the type of the task.

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Parallel uniform platforms Why?

• give production system designers the possibility
  to use machines with different production speeds
• Need for machines with lower production capacity
  to execute non-real-time or aperiodic tasks
• Need for upgrade of some machines

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Comparative study of relevant RT Multiprocessor
Scheduling Algorithms
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Resource Augmentation technique

• Philipps et al. (1997)
• Preemptive identical multiprocessor
  setting.
• Several on-line algorithms that prove poor
  performance from
• an absolute worst-case perspective, are
  optimal when allowed
• moderately more resources.
• Funk et al. (2001)
• extended this method to be applied upon
  uniform parallel
• machines.
• However, their results apply only to
  periodic tasks!

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System characteristics

• ? s1, s2, s3, ..., sm / m ? ? and sj? sj1
  for all j, 1 ? jlt m
• m-machine uniform multiprocessor platform with
  speeds or production capacities s1, s2, s3, ...,
  smrespectively.
• ? ?i,j / i,j ? ? A set of periodic tasks
  with hard deadlines
• J Ji,j / i,j ? ? A set of hard aperiodic
  tasks ordered by increasing deadlines
• Each job is characterized by arrival time ri ,
  production time ci, deadline di, period pi.
• ui ci / pi is the utilization of a task. The
  tasks in ? and J are indexed according to a
  decreasing utilization
• Job preemption is permitted. O Oj,m / i ? ?
  changeover time caused by the arrival of part
  from type j at the machine m.
• Job parallelism is forbidden.

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TBS on uniform multiprocessors

• Advantages on uniprocessor platforms
• good performance
• low memory capacity
• low implementation complexity
  better maintainability
• low computational complexity
  less changeover time
• overheads
• Rules
• 1. No machine is idled while there is an active
  job awaiting
• execution
• 2. When fewer than m jobs are active, they are
  executed upon
• the fastest machines while the slowest are
  idled
• 3. Higher priority jobs are executed on faster
  processors
• 4. When the jth aperiodic request arrives at
  time trj
• Cj 2Oj,m
• dj rj
• Us

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TBS on uniform multiprocessors

• Definition (Funk et al.)
• m
• ? sk
• kj1
• ?? max ______
• Sj
• measures the degree by which ? differs from an
  identical multiprocessor platform.
• Speed of processors differ from each other
  ?? becomes smaller.

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TBS on uniform multiprocessors

• Lemma 1. (Funk et al.)
• If the following condition is satisfied
• Sm ? ??. s1 Sm
• then for any set of jobs I and at any
  time-instant t ?0
• W(A, ?,I,t) ? W(A, ?,I,t)
• Condition expresses the additional production
  capacity needed by ? in terms of the parameter
  ?? and the speed of the fastest processor in ?
• the smaller the value of ??, the more ?
  deviates from being an identical multiprocessor,
  the smaller the amount of this excessing
  processing power needed.

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TBS on uniform multiprocessors
Theorem 1. If the condition of Lemma 1 is
satisfied Sm ? ??. s1 Sm then I will
meet all deadlines when scheduled using TBS
algorithm executing on ?.
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Schedulability Analysis
Theorem 2 Given a set of n periodic tasks with
machine utilization Up and a TBS with machine
utilization Us, the whole set is feasibly
scheduled upon a multiprocessor platform if and
only if Up Us ? Sm where Up Up1 Up2
... Upm Theorem 3 (Funk et al) A periodic
task system ? will meet all deadlines when
scheduled on ? Sm ? ?? maxu1,Up/m Up
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Schedulability Analysis
Theorem 4 ... Sm ?? u1 Up Us The
aperiodic task system J has a utilization Us
Sm - ?? u1 - Up
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Example

• Consider a task system ? comprised of five
  periodic tasks (ci,pi)
• ? (15,10) , (4,5) , (14,20) , (6,15) , (2,10)
  
• and an aperiodic task (ri,ci)
• J (5,3)
• to be TBS scheduled upon the uniform
  multiprocessor platform
• ? 3,1,0.5. Will all deadlines be met?
• By definition ?? max (10.5)/3, 0.5/1 0.5
• By (Funk et al.) ? is feasible on some
  3-processor multiprocessor platform having a
  total computing capacity
• 1,50,80,70,40,23,6
• and with the fastest processor having a computing
  capacity s1u11,5
• By Theorem 4, we obtain Us0,15
• djmax5,0(3/0.15)35

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Performance Evaluation
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Performance Evaluation
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Performance Evaluation