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

1. Application of Real-Time Scheduling Techniques to Agent-Based Distributed Production Systems 04.11.2002

2. 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

3. 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

4. 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.

5. Workload considerations in a traditional PCS Raw material Broaching Parts Machining Parts Galvanic Parts Assembly Product 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

6. Workload considerations in a RT- PCS Raw material Broaching Parts Machining Parts Galvanic Parts Assembly Product 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

7. 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.

8. 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

9. Comparative study of relevant RT Multiprocessor Scheduling Algorithms

10. 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!

11. System characteristics •  = {s1, s2, s3, ..., sm} / m  * and sjsj+1 for all j, 1  j< m: • m-machine uniform multiprocessor platform with speeds or production capacitiess1, 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.

12. 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 t=rj • Cj + 2Oj,m • dj = rj + • Us

13. TBS on uniform multiprocessors • Definition: (Funk et al.) • m •  sk • k=j+1 • = max ______ • Sj • measures the „degree“ by which  differs from an identical multiprocessor platform. • Speed of processors differ from each other becomes smaller.

14. TBS on uniform multiprocessors • Lemma 1. (Funk et al.) • If the following condition is satisfied • S‘m  ‘. 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.

15. TBS on uniform multiprocessors Theorem 1. If the condition of Lemma 1 is satisfied S‘m  ‘. s1 + Sm then I will meet all deadlines when scheduled using TBS algorithm executing on ‘.

16. 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 ‘ S‘m  ‘ * max{u1,Up/m}+ Up

17. Schedulability Analysis Theorem 4 ... S‘m = ‘‘* u1+ Up+ Us The aperiodic task system J has a utilization Us = S‘m - ‘‘* u1 - Up

18. 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 {(1+0.5)/3, 0.5/1} = 0.5 • By (Funk et al.)  is feasible on some 3-processor multiprocessor platform having a total computing capacity • 1,5+0,8+0,7+0,4+0,2=3,6 • and with the fastest processor having a computing capacity s1=u1=1,5 • By Theorem 4, we obtain Us=0,15 • dj=max{5,0}+(3/0.15)=35

19. Performance Evaluation

20. Performance Evaluation

21. Performance Evaluation