Batch Scheduling for Identical Multi-Tasks Jobs on Heterogeneous Platforms

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1 atch Scheduling for Identical Multi-Tasks Jobs on Heterogeneous Platforms Jean-Marc Nicod Sékou iakité, Laurent Philippe - 16/05/2008 Laboratoire d Informatique de l Université de Franche-omté - esançon 2nd Scheduling in ussois workshop

2 Presentation Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

3 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

4 Scheduling Problem efinitions Execution Platform: non oriented graph, G = (P, L) : P: processors p i, i [1, m] L: communication links l j, j [1, c] Jobs: Gs without fork (intrees), J = (T, ): T : tasks t k, k [1, n] : tasks dependencies d l, l [1, d] N instances of the same job. 2nd Scheduling in ussois workshop - 19/05/ / 45

5 Scheduling Problem haracteristics: Each task of a job must be performed by a specific function, F is the set of the functions needed to process a job, Each execution resource provides a subset of F, The execution resources are unrelated. Problem: Schedule a batch of N jobs J Objective function: max R m intrees, batch of identical jobs max 2nd Scheduling in ussois workshop - 19/05/ / 45

6 Scheduling Problem Problem illustration N instances of the same job: 1 platform for execution: Figure: Job Type p 1 p 2 p 3 p Table: Execution times 2nd Scheduling in ussois workshop - 19/05/ / 45

7 Scheduling Problem Use ases Grid: Image processing: filters, 2 or 3 reconstructions, Servers provides an application set. Micro-Factories: omposed of cells: assembly, treatments,... Less geographical constraints, Products are micro-metric easily buffered 2nd Scheduling in ussois workshop - 19/05/ / 45

8 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

9 Possible solutions lassical (Off-line): schedule a G on an heterogeneous platform, max optimization NP-Hard, batch of jobs: no use of identical jobs. Steady state technics (Off-line): flow optimization: maximize the throughput optimal solution on heterogeneous platforms, use the identical job characteristic, does not take starting/ending into account. On-line: batch waiting queue, schedule ready tasks, no use of identical job characteristic, 2nd Scheduling in ussois workshop - 19/05/ / 45

10 Used algorithms On-line scheduling: simple, assign tasks on the fly, respect dependencies, used as reference. Genetic Meta-heuristic GTS[aoud05]: improves list scheduling, good results on G schedule, needs to be adapted to batches: period, performances of a standard heuristic on batches of jobs? Steady State[eaumont04]: optimal for batches of infinite size, performances on finite size batches? 2nd Scheduling in ussois workshop - 19/05/ / 45

11 Steady State Overview efinition and resolution of a linear program: define the constraints of the problem, flow: solutions are time ratios per resources. ompute a cyclic schedule: construct allocations with respect of the ratios, 1 port model: communication intervals. Execution: starting, cyclic schedule, ending. 2nd Scheduling in ussois workshop - 19/05/ / 45

12 Steady State linear system MXIMIZE ρ = p i=1 cons(p i, t f ), UNER THE ONSTRINTS (1)p i, t k T, α(p i, t k ) = cons(p i, t k ) c i,k (2)p i, t k T, 0 α(p i, t k ) 1 (3)p i, t k T α(p i, t k ) 1 2nd Scheduling in ussois workshop - 19/05/ / 45

13 Steady State Solution t 0 t 1 t 2 t 3 Type p 1 p 2 p 3 p Figure: Job Table: ost: c p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 Table: omsumption: cons, objective ρ = 2/25 2nd Scheduling in ussois workshop - 19/05/ / 45

14 Steady State Solution P1:0 0:1 1:1 4:1 Tbegin:0:0 8 :1:1 4 P2:1 1:1 2:1 3:1 8 8 :2:1 8 2 :3:1 P3:2 1:1 2:1 3:1 8 Tend:4:0 Figure: Platform Figure: Job 2nd Scheduling in ussois workshop - 19/05/ / 45

15 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

16 Experiences Metric efficiency = makespan o /makespan r efficiency = N/(ρ makespan r ) makespan o : lower bound makespan o : N/ρ, reference time makespan r : makespan resulting from experience, Simulation results (SimGrid), ommunications neglected. 2nd Scheduling in ussois workshop - 19/05/ / 45

17 Figure: Job j 0 Type p 1 p 2 p 3 p 4 p 5 p Table: Grid G 0 Efficiency Steady state GTS On line atch size Figure: Execution of batches j 0 on G 0 Global results: Steady state tends toward optimal, GTS good for small batches, then collapses, on-line is constant. 2nd Scheduling in ussois workshop - 19/05/ / 45

18 Type p 1 p 2 p 3 p 4 p 5 p Figure: Job j 1 Table: Grid G 0 Efficiency Steady state GTS On line atch size Sames tasks as j 0, GTS collapses earlier (250 instances vs. 300). Figure: Execution of batches j 1 on G 0 2nd Scheduling in ussois workshop - 19/05/ / 45

19 Figure: Job j 2 Type p 1 p 2 p 3 p 4 p 5 p Table: Grid G 0 Efficiency Steady state GTS On line atch size Steady state uses p 6 (: 1000), Figure: Execution of batches j 2 on G 0 2nd Scheduling in ussois workshop - 19/05/ / 45

20 Type p 1 p 2 p Figure: Job j 2 Table: Grid G 1 Efficiency Steady state GTS On line atch size The efficiency of GTS decreases starting at 200 instances. Figure: Execution of batches j 2 on G 1 2nd Scheduling in ussois workshop - 19/05/ / 45

21 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

22 Experiences Synthesis Small batches: 50 Medium batches: 100 Large batches: 500 On-line Steady GTS On-line Steady GTS On-line Steady GTS Table: Mean efficiency Synthesis: GTS: up to 200, Steady state: from 500. Time consumption for 1000 instances: steady state: 0.08s, on-line: 35.04s, GTS: s, 2nd Scheduling in ussois workshop - 19/05/ / 45

23 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

24 Steady state for small batches Means of action im: improve (decrease) the global makespan for small batches, The steady state phase is optimal. Schedule starting/ending phases on the heterogeneous platform: NP-Hard find a good schedule, reduce the work in initialization/ending phases. What can be done on starting/ending phases? Keeping steady state optimal: re-organise affectations to reduce the period size, resolve dependencies inside the period. eterioration of steady state: reduce the number of instances per periods 2nd Scheduling in ussois workshop - 19/05/ / 45

25 Steady state schedule Type p 1 p 2 p 3 p Figure: Job j 3 Table: Grid G 2 Period 1 Period 2 Period N... 2nd Scheduling in ussois workshop - 19/05/ / 45

26 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

27 Steady state for small batches Example t 0 t 1 t 2 t 3 Type p 1 p 2 p 3 p Figure: Job Table: ost p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 Period = 200. Table: onsumption 2nd Scheduling in ussois workshop - 19/05/ / 45

28 Steady state for small batches lgorithm p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 Table: onsumptions: cons p 1 p 2 p 3 p 4 t t t t Table: Integer consuptions: consint 2nd Scheduling in ussois workshop - 19/05/ / 45

29 Steady state for small batches Initial steady state schedule S P: period, P : LM of the matrix denominators, ρ: throughput, ρ = a/b, reduced fraction. Let P min be the minimum possible period P 0 = b, P min = α P 0, α [1, P/b] Find P min, that respect the constraints: For lines L j : P i L i cons(i, j) = ρ, For columns i : P j j cons(i, j) w ij < 1 2nd Scheduling in ussois workshop - 19/05/ / 45

30 Steady state for small batches Example t 0 t 1 t 2 t 3 Type p 1 p 2 p 3 p Figure: Job Table: ost p 1 p 2 p 3 p 4 t0 7/ /200 t1 3/100 1/ t2-1/20 3/100 - t /100 1/100 p 1 p 2 p 3 p 4 t0 1/ /25 t1 1/50 3/ t2-1/25 1/25 - t /50 1/50 Table: onsumption Table: Modified consumption 2nd Scheduling in ussois workshop - 19/05/ / 45

31 Steady state for small batches lgorithm im: maximize of the onsint matrix that respect the constraints, Optimisation problem with integers. onstraints programming with finite domains (swi-prolog) Exponential complexity but the problem is small lgorithm 1: reduceperiod(cons: Matrix, cost: Matrix ) : Matrix cd periodlength/throughputenominator; while cd > 1 do newons : Matrix; if newons reorganize(cons, cost, cd) then return newons; else cd cd 1; end end return cons; 2nd Scheduling in ussois workshop - 19/05/ / 45

32 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

33 Steady state for small batches Metric efficiency = makespan o /makespan r efficiency = atch size/(rate makespan r ) Steady state rate is optimal time reference: N/ρ, lower bound for optimal makespan (makespan o ), makespan r : makespan of the algorithm. 2nd Scheduling in ussois workshop - 19/05/ / 45

34 Figure: Job j 3 Type p 1 p 2 p 3 p Table: Grid G 3 Efficiency Normal period Reduced period atch size Period: 16/200 4/50 (/4), Figure: Execution of batches j 3 on G 2 2nd Scheduling in ussois workshop - 19/05/ / 45

35 Figure: Job j 3 Type p 1 p 2 p 3 p Table: Grid G 4 Efficiency Normal period Reduced periode atch size 96/1200 4/50 (/24), Figure: Execution of batches j 3 on G 3 2nd Scheduling in ussois workshop - 19/05/ / 45

36 Type p 1 p 2 p 3 p Figure: Job j 4 Table: Grid G 3 Efficiency Normal period Reduced period atch size 48/1320 4/110 (/12), starting: 194 instances, never in steady state. Figure: Execution of batches j 4 on G 2 2nd Scheduling in ussois workshop - 19/05/ / 45

37 Type p 1 p 2 p 3 p Figure: Job j 4 Table: Grid G 4 Efficiency Normal period Reduced period atch size 12/330 4/110 (/3), starting: 38 instances, 2 full periods for a batch of 150 jobs, 10 Figure: Execution of batches j 4 on G 3 Max efficiency difference: 1%. 2nd Scheduling in ussois workshop - 19/05/ / 45

38 Outline Problem definition lgorithms evaluation Presentation Experiences Synthesis Steady state for small batches Means of action Reduce period size Experiences onclusion and futur works 2nd Scheduling in ussois workshop - 19/05/ / 45

39 onclusion and futur works onclusion: omparison of algorithms performances, Minimal period while keeping steady state, Large gain for small batches, Not always possible. Futur works: Keeping an optimal steady state: omparison of dependencies resolutions. eterioration of steady state: Reduce the number of instances per periods. 2nd Scheduling in ussois workshop - 19/05/ / 45

40 The end Thanks for your attention.

41 Steady state for small batches Reminder Initialization prepares all the dependencies needed before entering in steady state: For each task or communication in the period: execute all the preceding tasks/communications in the graph Ending: finish all the remaining tasks/communications, ommon work with Loris Marchal (LIP) Reduce the number of tasks computed in the starting and ending phases. 2nd Scheduling in ussois workshop - 19/05/ / 45

42 ependencies resolution Period 1 Period 2 Period N Figure: Job j 3 Type p 1 p 2 p 3 p Table: Grid G 5 Figure: Execution of batches j 3 on G 5 2nd Scheduling in ussois workshop - 19/05/ / 45

43 ependencies resolution Initial Schedule: Period 1 Period 2 Period N... Schedule with less dependencies: Period 1 Period 2 Period N... 2nd Scheduling in ussois workshop - 19/05/ / 45

44 ependencies resolution P1:0 0:1 1:1 4:1 Tbegin:0:0 8 :1:1 4 P2:1 1:1 2:1 3:1 8 8 :2:1 8 2 :3:1 P3:2 1:1 2:1 3:1 8 Tend:4:0 Figure: Platform Figure: Job 2nd Scheduling in ussois workshop - 19/05/ / 45

45 ependencies resolution 8 1 suppressed dependency = 1 subgraph less, alance starting and ending, How to optimize dependencies resolution? How to mesure the gain? The more... the less re there better dependencies? Max number of dependencies: two-partition Reoganize the periodic schedule: heuristics Find a good scheduling algorithm for starting and ending phases. Link number of jobs <=> period size 2nd Scheduling in ussois workshop - 19/05/ / 45

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