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Stochastic DAG Scheduling Using Monte Carlo Approach for Heterogeneous Computing Systems

This presentation delves into a Monte Carlo sampling method for optimizing static schedules in heterogeneous environments with variable task execution times. By addressing deviations in performance observed in grid computing, we aim to minimize makespan—the total execution time of a directed acyclic graph (DAG) comprised of individual tasks. The methodology involves generating a stochastic model of task execution times and using existing deterministic scheduling algorithms, like HEFT, to derive efficient resource mappings. The results demonstrate that Monte Carlo-based techniques can lead to better performance in workflow scheduling while minimizing the overhead associated with task scheduling changes.

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Stochastic DAG Scheduling Using Monte Carlo Approach for Heterogeneous Computing Systems

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  1. Stochastic DAG Scheduling using Monte Carlo Approach Heterogeneous Computing Workshop (at IPDPS) 2012 Extended version: Elsevier JPDC (accepted July 2013, in Press) Wei Zheng Department of Computer Science, Xiamen University, Xiamen, China RizosSakellariou SchoolofComputerScience,TheUniversityofManchester,UK

  2. Previous Presentation (9/06/13) • Research Area: Scheduling workflows under heterogeneous environment with variable performance.

  3. This Presentation

  4. Introduction • General DAG Scheduling assumption: • Estimated Execution time for each task is known in advance. • Several techniques of estimation: e.g. average over several runs • Similarly, estimated data transfer time is known in advance. • A study* has shown, there might be significant deviations in observed performance in Grids. • To address this deviations, Two approaches are prevalent • Just-In-Time (high overhead) • RunTime (static schedule + runtime changes) (hypothesis**: might waste resources and increase makespan if static schedule is not very good) • * A. Lastovetsky, J. Twamley, Towards a realistic performance model for networks of heterogeneous computers, in:M.Ng,A.Doncescu,L.Yang,T.Leng (Eds.), High Performance Computational Science and Engineering, in: IFIP InternationalFederationforInformationProcessing,vol.172,Springer,Boston, 2005,pp.39–57. • ** R.Sakellariou,H.Zhao,A low-cost rescheduling policy for efficient mapping of workflows on grid systems, Sci. Program. 12(4) (2004) 253–262

  5. Problem Addressed • Generating a better (minimize makespan) “Static” schedule based on the stochastic model of the variations in the performance (execution time) of individual tasks in the graph.

  6. Background and Related Work • Heterogeneous Earliest Finish Time heuristic (discussed in the previous presentation) • List based scheduling. • Prioritize tasks based on the “bLevel” (essentially, tasks on the critical path get higher priority) • Once task is chosen, map it to “best” available resource. bLevel(i) = wi + max j∈Succ(i){wi→j +bLevel(j)}

  7. Problem Description • G = (N, E) -> DAG with one entry, one exit node. • R -> set of heterogeneous resources • Eti,p-> Random variable for execution time • Assumption: Network bandwidth is constant. • M -> Makespan = finish time of exit node. Goal: Find schedule Ω to minimize makespan (assign N to R, no overlap, no preemption, no migration)

  8. Methodology • Assumption: Analytical methods that solve the probabilistic optimization problem are too expensive. • Use Monte Carlo Sampling (MCS) method. • Define a space comprising possible input values • IG ={ETi,p :i∈N,p∈R}. • Take an independent sample randomly from the space • PG =fsmp(IG) ={ti,p :i∈N,p∈R} • Perform deterministic computation using the sample input (store the result) • ΩG =Static_SchedulingHEFT(G,PG) • Repeat 2 and 3 till some exit condition (no. of repetitions) • Aggregate the stored results of the individual computations into the final result.

  9. MCS Based Scheduling • Complexity: • Depends on the deterministic scheduling algorithm • For HEFT it is O(v + e * r) = O(e*r) • First loop: O(e*r*m) • Second loop: O(e * n * k) • Total = O(e*r*m + e*n*k)

  10. Example

  11. Example 10,000 iterations - production phase (Gaussian Distribution) 200 iterations - selection phase 20% reduction in makespan Absolute increase in algorithm time: 1.2s

  12. Evaluation • Graphs

  13. Threshold Calculation

  14. Convergence (no. of repetitions)

  15. Convergence

  16. Makespan performance evaluation • Static HEFT (baseline) with Mean ET values • Autopsy – Static HEFT With known ET values • MCS - Static • ReStatic • ReMCS • Graph Generation (random generator of given type) • Task Execution Time for different runs • Select “Mean” for each task. • Use a probability distribution to select actual execution time. The variation is bounded by Quality of Estimation (QoE) (0<QoE<1)

  17. Makespan performance evaluation

  18. Summary • It is possible to obtain a good full-ahead static schedule that performs well under prediction inaccuracy, without too much overhead. • MCS, which has a more robust procedure for selecting an initial schedule, generally results in better performance when rescheduling is applied

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