eﬃcient(mrc(construc0on( with(shards( - usenix · 2019. 12. 18. · mrc(algorithm(research(1965...

Efficient MRC Construc0on with SHARDS

Carl Waldspurger Nohhyun Park Alexander Garthwaite Irfan Ahmad

USENIX Conference on File and Storage Technologies February 17, 2015

CloudPhysics, Inc.

Mo0va0on

•  Cache performance highly non-‐linear •  Benefit varies widely by workload •  Opportunity: dynamic cache management

– Efficient sizing, allocaSon, and scheduling –  Improve performance, isolaSon, QoS

•  Problem: online modeling expensive – Too resource-‐intensive to be broadly pracScal – Exacerbated by increasing cache sizes

CloudPhysics, Inc. USENIX FAST '15 2

Modeling Cache Performance

•  Miss RaSo Curve (MRC) –  Performance as f (size) – Working set knees –  Inform allocaSon policy

•  Reuse distance –  Unique intervening blocks between use and reuse

–  LRU, stack algorithms ��

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MRC Algorithm Research

1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 1965

separate simulation per cache size

Bennett & Kruskal balanced tree

O(N), O(N log N)

Olken tree of unique refs

O(M), O(N log M)

SHARDS spatial hashing

Counter Stacks probabilistic counters

O(1), O(N)

O(log M), O(N log M)

PARDA parallelism

UMON-DSS hw set sampling

RapidMRC on-off periods

Kessler, Hill & Wood set, time sampling

Bryan & Conte cluster sampling

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Mattson Stack Algorithm single pass

O(M), O(NM)

Space, Time Complexity N = total refs, M = unique refs

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Key Idea

•  Track only a small subset of blocks –  Filter input to exisSng algorithm –  Run full algorithm, using only sampled blocks –  Cheap/accurate enough for pracScal online MRCs?

•  SHARDS approximaSon algorithm –  Randomized spaSal sampling – Uses hashing to capture all reuses of same block – High performance in Sny constant footprint –  Surprisingly accurate MRCs


Spa0ally Hashed Sampling

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Li

hash(Li) mod P

Ti

randomize

process

skip

no

yes

sample?

< T

CloudPhysics, Inc.

subset inclusion property maintained as R is lowered T

adjustable threshold

0 P

sampled unsampled sampling rate R = T / P

Basic SHARDS

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Each sample staSsScally represents 1 /R blocks Scale up reuse distances by same factor

CloudPhysics, Inc.

randomize sample?

Li

hash(Li) mod P

Ti < T yes

compute distance

Standard Reuse Distance

Algorithm

scale up

÷ R

skip

no

SHARDS in Constant Space

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randomize scale up sample? compute distance

Li

hash(Li) mod P

Ti < T yes Standard

Reuse Distance Algorithm

÷ R

sample set

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evict samples to bound set size

lower threshold T = Tmax reduces rate R = T / P

T 0 P

Tmax

Example SHARDS MRCs

•  Block I/O trace t04 –  ProducSon VM disk –  69.5M refs, 5.2M unique

•  Sample size smax –  Vary from 128 to 32K –  smax ≥ 2K very accurate

•  Small constant footprint •  SHARDSadj adjustment

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Exact MRC32K8K2K512128

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Dynamic Rate Adapta0on

•  Adjust sampling rate –  Start with R = 0.1 –  Lower R as M increases –  Shape depends on trace

•  Rescale histogram counts –  Discount evicted samples –  Correct relaSve weighSng –  Scale by Rnew / Rold

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CloudPhysics, Inc.

Experimental Evalua0on

•  Data collecSon –  SaaS caching analyScs –  Remotely stream VMware vscsiStats

•  124 trace files –  106 week-‐long traces CloudPhysics customers

–  12 MSR and 6 FIU traces SNIA IOTTA

•  LRU, 16 KB block size


Exact MRCs vs. SHARDS

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msr_mds (1.10%) msr_proj (0.06%) msr_src1 (0.06%) t01 (0.05%)

t06 (0.33%) t08 (0.04%) t14 (0.38%) t15 (0.10%)

t18 (0.08%) t19 (0.06%) t30 (0.06%) t32 (0.98%)

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0 100 200 0 200 400 0 100 200 300 0 9 18Cache Size (GB)

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atio

smax = 8K exact MRC

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Error Analysis

•  Mean Absolute Error (MAE) –  | exact – approx | –  Average over all cache sizes

•  Full set of 124 traces •  Error ∝ 1 / √smax

•  MAE for smax = 8K –  0.0027 median –  0.0171 worst-‐case

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256 512 1K 2K 4K 8K 16K 32KSample Size (smax)

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Memory Footprint

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Baseline (unsampled) SHARDS R = 0.010 SHARDS R = 0.001 SHARDS Smax = 8K

•  Full set of 124 traces •  SequenSal PARDA •  Basic SHARDS

– Modified PARDA – Memory ≈ R × baseline for larger traces

•  Fixed-‐size SHARDS –  New space-‐efficient code –  Constant 1 MB footprint


Processing Time

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Baseline (unsampled) SHARDS R = 0.010 SHARDS R = 0.001 SHARDS Smax = 8K

•  Full set of 124 traces •  SequenSal PARDA •  Basic SHARDS

– Modified PARDA –  R=0.001 speedup 41–1029×

•  Fixed-‐size SHARDS –  New space-‐efficient code –  Overhead for evicSons –  Smax= 8K speedup 6–204×


Counter Stacks Comparison Algorithm Memory

(MB) Throughput (Mrefs/sec)

Error (MAE)

Counter Stacks 80.0 2.3 0.0025 SHARDS Smax=32K 2.0 16.9 0.0026 SHARDS Smax=8K 1.3 17.6 0.0061

•  QuanStaSve –  Same merged MSR “master” trace –  Counter Stacks roughly 7× slower, 40–62× bigger

•  QualitaSve –  Counter Stacks checkpoints support splicing/merging –  SHARDS maintains block ids, generalizes to non-‐LRU


Generalizing to Non-‐LRU Policies

•  Many sophisScated replacement policies – ARC, LIRS, CAR, CLOCK-‐Pro, … – AdapSve, frequency and recency – No known single-‐pass MRC methods!

•  SoluSon: efficient scaled-‐down simulaSon – Filter using spaSally hashed sampling – Scale down simulated cache size by sampling rate – Run full simulaSon at each cache size

•  Surprisingly accurate results USENIX FAST '15 17 CloudPhysics, Inc.

Scaled-‐Down Simula0on Examples

ARC — MSR-‐Web Trace CLOCK-‐Pro — Trace t04

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CloudPhysics, Inc.

Conclusions

•  New SHARDS algorithm – Approximate MRC in O(1) space, O(N) Sme – Excellent accuracy in 1 MB footprint

•  PracScal online MRCs – Even for memory-‐constrained drivers, firmware – So lightweight, can run mulSple instances

•  Scaled-‐down simulaSon of non-‐LRU policies


Ques0ons?

•  {carl,nohhyun,alex,irfan}@cloudphysics.com •  Visit our poster •  BoF 9-‐10pm tonight in Bayshore West

CloudPhysics, Inc. USENIX FAST '15 20

•  PotenSal academic and industry collaboraSon •  ApplicaSon areas include capacity planning, dynamic parSSoning, tuning, policies, …

•  We’re also hiring!

eﬃcient(mrc(construc0on( with(shards( - usenix · 2019. 12. 18. · mrc(algorithm(research(1965...

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