1 / 36

Divisible Load Scheduling: A Tutorial for Efficient Processing

This tutorial by Thomas Robertazzi from University at Stony Brook explains the concept of Divisible Load Scheduling, a computational method for dividing tasks among processors and links for optimal efficiency. The tutorial covers theory, applications, advantages, modeling, interconnection topologies, speedup analysis, and directions for future research. Learn about this technique and its applications in various fields, from grid computing to image processing.

blamont
Download Presentation

Divisible Load Scheduling: A Tutorial for Efficient Processing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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???

More Related