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Divisible Load Scheduling

Divisible Load Scheduling. A Tutorial. Thomas Robertazzi University at Stony Brook. What is a Divisible Load?. A computational & networkable load that is arbitrarily partitionable (divisible) amongst processors and links. There are no precedence relations. Simple Application Example.

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Divisible Load Scheduling

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  1. Divisible Load Scheduling A Tutorial Thomas Robertazzi University at Stony Brook

  2. What is a Divisible Load? • A computational & networkable load that is arbitrarily partitionable (divisible) amongst processors and links. • There are no precedence relations.

  3. Simple Application Example • Problem: Sum 1000 trillion numbers • Approach: Partition the numbers among 100 processors • But how?

  4. Simple Application Example • To optimize solution time (maximize speedup) one needs to take into account heterogeneous link and processor speeds, computation and communication intensities, interconnection topology and scheduling policy. • Divisible Load Scheduling Theory Can Do This!

  5. Applications (Generic) • Grid Computing/Meta-computing • Data Intensive Computing • Sensor Processing • Image Processing • Scientific/Engineering Computing • Financial Computing

  6. Applications (Specific) • Pattern Searching • Database Computation • Matrix-Vector Computation • E&M Field Calculation (CAD) • Edge Detection

  7. DLT Modeling Advantages • Linear and Deterministic Modeling • Tractable Recursive/Linear Equation Solution • Schematic Language • Equivalent Elements • Many Applications

  8. Interconnection Topologies • Linear Daisy Chain • Bus • Single Level and Multilevel Trees • Mesh • Hypercube

  9. Directions: Scalability 1 1 3 1 2 1 Simultaneous Distribution (Scalable) Sequential Distribution (Saturation) Cheng & Robertazzi Hung & Robertazzi

  10. An Example • Model Specifications: • A star network( single level tree network), and multi-level tree. • Computation and transmission time is a linear function of the size of load. • Level to Level: Store and Forward Switching • Same Level: Concurrent Load Distribution.

  11. Children without Front End: • After receiving the assigned data, each child proceeds to process the data.

  12. Timing Diagram (single level tree) : • Children without Front End

  13. m+1 unknows vs. m+1 Eqs. • Recursive equations: • Normalization equation:

  14. Distribution Solution:

  15. The load distribution solution is similar to the solution of the state-dependent M/M/1 queuing system.

  16. Similarities to Queueing Theory • Linear model and tractable solutions • Schematic Language • Equivalent Elelements • Infinite Size Networks

  17. Speedup Analysis

  18. Speedup Analysis (continued)

  19. Tree Network • (Children without Front Ends)

  20. Collapsing single level trees

  21. Bandwidth of Fat Tree • Definition: The bandwidth of level j in a fat tree can be defined as pj-1z.

  22. Directions: Sequencing and Installments • Daisy Chain Surprise • Efficiency Rule Ghose, Mani & Bharadwaj

  23. Directions: Sequencing and Installments • Multi-installment for Sequential Distribution 6 4 5 3 1 2 Ghose, Mani & Bharadwaj

  24. Directions: Sequencing and Installments Diminishing returns in using multi-installment distribution. Ghose, Mani & Bharadwaj

  25. Directions: Sequencing and Installments Drozdowski

  26. Directions: Time Varying Modeling Sohn & Robertazzi Can be solved with integral calculus.

  27. Directions: Monetary Cost Optimization • Min CTotal = S ancnwnTcp N n=1 Bus Processors Optimal Sequential Distribution if: cn-1wn-1 less thancnwn for all n Sohn, Luryi & Robertazzi

  28. Directions: Monetary Cost Optimization • 2 US Patents: Patent 5,889,989 (1999): Processor Cost Patent 6,370,560 (2001): Processor and Link Cost Enabling technology for an open e-commerce market in leased proprietary computing. Sohn, Charcranoon, Luryi & Robertazzi

  29. Directions: Database Modeling Expected time to find multiple records in flat file database Ko & Robertazzi

  30. Directions: Realism Finite Buffers (Bharadwaj) Job Granularity (Bharadwaj) Queueing Model Integration

  31. Directions: Experimental Work Database Join (Drozdowski)

  32. Directions: Future Research • Operating Systems: Incorporate divisible load scheduling into (distributed) operating systems • Measurement Process Modeling: Integrate measurement process modeling into divisible scheduling

  33. Directions: Future Research • Pipelining (Dutot) Concept: Distribute load to further processors first for speedup improvement Improvement reported for daisy chains

  34. Directions: Future Research • System Parameter Estimation (Ghose): Concept: Send small “probing” loads across links and to processors to estimate available effort Challenge: Rapid change in link & processor state

  35. DLT has a Good Future • Many Applications including wireless sensor networks • Tractable (Modeling & Computation) • Rich Theoretical Basis

  36. Thank you! Questions???

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