On the Latency-Accuracy Tradeoff in Approximate MapReduce Jobs
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1 On the Latency-Accuracy Tradeoff in Approximate apreduce Jobs Juan F. Pérez Universidad del Rosario, Colombia Robert Birke and Lydia Chen IB Research Zurich, Switzerland IEEE INFOCO ay, 2017 J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
2 Introduction Outline 1 Introduction 2 System Operation 3 The odel 4 Experimental assessment 5 Wrap-up J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
3 Introduction What? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
4 Introduction apreduce Jobs Large data sets Exploit large number of parallel resources Open source implementations (Hadoop) Well studied for batch jobs Online job execution Deadlines: constraints on response time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
5 Introduction apreduce Jobs Large data sets Exploit large number of parallel resources Online job execution Deadlines: constraints on response time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
6 Introduction Online apreduce Jobs Deadlines: constraints on response time Process all data exact answer Approximate Computing Process some data approximate answer Save computing time and resources Comply with deadlines J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
7 Introduction Why? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
8 Introduction Latency-Accuracy Tradeoff Drop more data Reduce latency Reduce accuracy Drop less data Increase latency Increase accuracy Solve the Latency-Accuracy Tradeoff J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
9 Introduction Goal? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
10 Introduction Solve Latency-Accuracy Tradeoff Given a Latency objective Determine Achievable Accuracy Given an Accuracy objective Determine Achievable Latency Additional considerations: Jobs arrive in a random fashion Queueing times waiting for jobs in front to be processed How to drop data for approximate computations? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
11 Introduction Solve Latency-Accuracy Tradeoff Given a Latency objective Determine Achievable Accuracy Given an Accuracy objective Determine Achievable Latency Additional considerations: Jobs arrive in a random fashion Queueing times waiting for jobs in front to be processed How to drop data for approximate computations? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
12 Introduction How? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
13 Introduction Our Approach to the Latency-Accuracy Tradeoff Stochastic models to predict Job Latency Capture Online apreduce operation Capture Approximate Computing Data Drop options J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
14 Introduction Our Approach to the Latency-Accuracy Tradeoff Stochastic models to predict Job Latency Capture Online apreduce operation Capture Approximate Computing Data Drop options J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
15 System Operation Outline 1 Introduction 2 System Operation 3 The odel 4 Experimental assessment 5 Wrap-up J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
16 System Operation Basic Operation J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
17 System Operation Basic Operation C computing slots R Jobs Queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
18 System Operation Basic Operation C computing slots R Jobs Queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
19 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
20 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
21 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
22 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
23 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
24 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
25 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
26 System Operation Basic Operation C computing slots R Jobs Queue Reduce task queue R R R J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
27 System Operation Basic Operation C computing slots R Jobs Queue Reduce task queue R R R J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
28 System Operation Basic Operation C computing slots R Jobs Queue Reduce task queue R R R J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
29 System Operation Basic Operation C computing slots R Jobs Queue Reduce task queue R R R J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
30 System Operation Basic Operation C computing slots R Jobs Queue ap task queue J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
31 System Operation Approximate Computing J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
32 System Operation Data Drop R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
33 System Operation Early Dropping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
34 System Operation Data Drop: Task drop - Early R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
35 System Operation Data Drop: Task drop - Early R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
36 System Operation Data Drop: Task drop - Early R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
37 System Operation Straggler Dropping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
38 System Operation Data Drop: Task drop - Straggler R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
39 System Operation Data Drop: Task drop - Straggler R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
40 System Operation Data Drop: Task drop - Straggler R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
41 System Operation Input Sampling J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
42 System Operation Data Drop: Input Sampling R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
43 System Operation Data Drop: Input Sampling R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
44 System Operation Data Drop: Input Sampling R R time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
45 System Operation Error J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
46 System Operation t Nm 1,1 α/2 N m (( 1 θ m 1 ) ( ) ) 1 su s 2 i, η m J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
47 The odel Outline 1 Introduction 2 System Operation 3 The odel 4 Experimental assessment 5 Wrap-up J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
48 The odel Basic Operation - ain parameters C computing slots N m : number of map tasks N r : number of reduce tasks 1/µ m : mean map task execution time 1/µ r : mean reduce task execution time J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
49 The odel Basic Operation - Job Service Time Job Service Time: Phase-type distribution Phase: number of tasks to complete J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
50 The odel Basic Operation - Job Service Time C m C m C m N m +N r N m -1+N r N m -2+N r J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
51 The odel Basic Operation - Job Service Time C m (C-1) m (C-2) m C+N r C-1+N r C-2+N m J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
52 The odel Basic Operation - Job Service Time m C m C m 1+N r N r N r -1 J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
53 The odel Basic Operation - Job Service Time C m (C-1) m (C-2) m C C-1 C-2 J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
54 The odel Basic Operation - Job Service Time 2 m m 2 1 J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
55 The odel odeling Approximate Computation J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
56 The odel Introducing Early Task Dropping Execute fraction θ m map tasks only Drop fraction 1 θ m map tasks Effective number of map tasks: N m = N m θ m Replace N m by N m J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
57 The odel Introducing Input Sampling Process fraction η m of each map task data only Ignore fraction 1 η m of each map task data Effective mean map task execution time: 1 µ m = ηm µ m Replace µ m by µ m J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
58 The odel Early Dropping + Input Sampling Transition Rates: Cµ m, N r + C < n N r + N m, (n N r )µ f (n) = m, N r < n N r + C, Cµ r, C < n N r, nµ r, 0 < n C. J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
59 The odel Straggler Dropping Start with N m + N r tasks Decrease one by one until N m (N m 1) + N r are left Jump down to N r Effective number of map tasks executed: N m J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
60 The odel Straggler Dropping + Input Sampling Transition Rates: min{n N r, C}µ m, N r + N m N m + 1 n f (n) = N r + N m, min{n, C}µ r, N r N r + 1 n N r. J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
61 The odel Analysis J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
62 The odel Analysis FCFS scheduling Job service time: phase-type (PH) - (α, G) Job arrival process: arkovian arrival process (AP) AP/PH/1 queue Sengupta s paper: age-based analysis (X (t), A(t), S(t)): age of job in service, arrival process phase, service phase J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
63 The odel Analysis Solve a matrix-integral equation T = I d G + 0 ( ) exp(t x) exp(d 0 x)d 1 G dx, Obtain waiting time distribution (β w, B w ) Known service-time distribution (α, G) Obtain response time distribution (β r, B r ): [ ] Bw ( B β r = [φβ w (1 φ)α], B r = w 1)α, 0 G J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
64 The odel Overlapping Execution J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
65 The odel FCFS Scheduling - Non-overlapping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
66 The odel Overlapping scheduling Allow jobs to start ap phase as soon as slots become available. At most 2 jobs in service: one in ap phase, one in Reduce phase. J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
67 The odel Overlapping Scheduling No longer a AP/PH/1 queue Service times depend on system state High load: high chance back-to-back jobs Low load: similar to non-overlapping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
68 The odel Overlapping Scheduling Generalize Sengupta s analysis (X (t), A(t), (t), R(t), Y (t)) (t): number of remaining map tasks of oldest job R(t): number of remaining reduce tasks of oldest job Y (t): number of remaining map tasks of youngest job J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
69 The odel Overlapping Scheduling Three phases: one job, map phase R one job, reduce phase R/ two jobs, oldest in reduce phase, youngest in map phase J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
70 The odel Overlapping Scheduling (Steady-state) Service time distribution: PH(β s, B s ) B s = Q R/,R/ Q R/, Q R/,R 0 Q, Q,R, (1) 0 0 B R,R [ ] β s = β R/ s β s β R s. (2) J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
71 Experimental assessment Outline 1 Introduction 2 System Operation 3 The odel 4 Experimental assessment 5 Wrap-up J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
72 Experimental assessment FCFS - Early Dropping Util=20% Util=50% Util=80% RT θ m Error J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
73 Experimental assessment FCFS - Early vs Straggler Dropping Util=20% Util=50% Util=80% Util=20% Util=50% Util=80% RT Error RT θ m θ m 0 (a) Early dropping (b) Straggler dropping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
74 Experimental assessment FCFS - Early vs Straggler Dropping vs Input Sampling Util=20% Util=20% Util=20% 80 Util=50% Util=80% Util=50% Util=80% Util=50% Util=80% RT Error RT Error RT θ m θ m η m (a) Early dropping (b) Straggler dropping (c) Input sampling J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
75 Experimental assessment FCFS - Early vs Straggler Dropping vs Input Sampling Observation 1 Best echanisms are: 1 Straggler dropping 2 Input sampling 3 Early dropping Observation 2 An x% data/task dropping removes 1 x% longest tasks (straggler dropping) 2 x% all tasks, including longest (input sampling) 3 x% tasks (early dropping) J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
76 Experimental assessment Varying number of tasks No. Tasks: 50 No. Tasks: 150 No. Tasks: No. Tasks: 50 No. Tasks: 150 No. Tasks: RT RT η m θ m (a) Input sampling (b) Straggler dropping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
77 Experimental assessment FCFS vs. Overlapping (Early dropping) RT Util=20% Util=50% Util=80% Error RT Util=20% Util=50% Util=80% θ m θ m 0 (a) FCFS (b) Overlapping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
78 Experimental assessment FCFS vs. Overlapping (Straggler dropping) Util=20% Util=50% Util=80% Util=20% Util=50% Util=80% RT Error RT θ m θ m 0 (a) FCFS (b) Overlapping J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
79 Experimental assessment FCFS vs. Overlapping (No approximation) Exclusive Overlap RT λ J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
80 Wrap-up Outline 1 Introduction 2 System Operation 3 The odel 4 Experimental assessment 5 Wrap-up J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
81 Wrap-up Wrap-up odel captures Straggler Dropping > Input Sampling > Early Dropping Overlapping > FCFS Scheduling Latency - Accuracy Tradeoff Given a: Latency Budget: what accuracy can be expected/offered? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
82 Wrap-up Wrap-up odel captures Straggler Dropping > Input Sampling > Early Dropping Overlapping > FCFS Scheduling Latency - Accuracy Tradeoff Given a: Latency Budget: what accuracy can be expected/offered? Accuracy Budget: what latency can be expected/offered? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
83 Wrap-up Wrap-up odel captures Straggler Dropping > Input Sampling > Early Dropping Overlapping > FCFS Scheduling Latency - Accuracy Tradeoff Given a: Latency Budget: what accuracy can be expected/offered? Accuracy Budget: what latency can be expected/offered? J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
84 Wrap-up Wrap-up odel captures Straggler Dropping > Input Sampling > Early Dropping Overlapping > FCFS Scheduling Latency - Accuracy Tradeoff Given a: Latency Budget: what accuracy can be expected/offered? Accuracy Budget: what latency can be expected/offered? Thank you! J. F. Pérez, R. Birke, L. Chen Latency vs. Accuracy Approx. apreduce IEEE INFOCO / 78
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