Adjustable flat layouts for Two- Failure Tolerant Storage Systems - - PowerPoint PPT Presentation

Adjustable flat layouts for Two- Failure Tolerant Storage Systems

Thomas Schwarz, SJ Marquette University

Motivation

• Storage device batches fail at different rates
• Example: Backblaze:
• 1163 Seagate Barracuda 7200.14 disks
• failed at a rate of 43% per year in 2014,
• Storage devices (sometimes) fail at different rates
• Bathtub curve seen in about 50% of all HD at Netapp
• SSD unrecoverable read error rate increases at the end
• f their lifetime

Motivation

• Large storage systems
• Currently consists of disks or SSDs organized in racks
• Individual devices are replaced
• Erasure coding for files, not devices
• My proposal
• Organize a large number of devices in a storage pod
• Level of failure tolerance in pod varies according to

prediction of device vulnerability

• Use a flat layout to increase failure tolerance

Adjustable Raid 6 Example

• Group k devices into a reliability stripe
• User data devices
• Add two parity devices to each reliability stripe
• If device failure rate appears to be high:
• Rededicate a user data device as a parity
• Overall:
• Trade capacity for additional failure tolerance when

needed

Adjustable RAID 6 Example

P0,1 P0,2 D1,7 P1,1 D0,0 D0,1 D0,2 D0,3 D0,4 D0,5 D0,6 D0,7 D1,0 D1,1 D1,2 D1,3 D1,4 D1,5 D1,6 P1,2 D2,0 D2,1 D2,2 D2,3 D2,4 D2,5 D2,6 D3,0 D3,1 D3,2 D3,3 D3,4 D3,6 P3,2 D2,7 D3,7 P3,1 P2,2 P2,1 D3,5 D4,0 D4,1 D4,2 D4,3 D4,4 D4,5 D4,6 D5,0 D5,1 D5,2 D5,3 D5,4 D5,6 P5,2 D4,7 D5,7 P5,1 P4,2 P4,1 D5,5 D6,0 D6,1 D6,2 D6,3 D6,4 D6,6 P6,2 D6,7 P6,1 D6,5 D7,0 D7.1 D7,2 D7,3 D7,4 D7,6 P7,2 D7,7 P7,1 D7,5 D8,6 D9,5 D10,4 D11,3 D12,2 D13,1 D14,0 D8,5 D9,4 D10,3 D11,2 D12,1 D13,0 P14,2 D8,4 D9,3 D10,2 D11,1 D12,0 P13,2 P14,1 D8,3 D9,2 D10,1 D11,0 P12,2 P13,1 D14,7 D8,2 D9,1 D10,0 P11,2 P12,1 D13,7 D14,6 D8,7 D9,6 D10,5 D11,4 D12,3 D13,2 D14,1 P8,1 D9,7 D10,6 D11,5 D12,4 D13,3 D14,2 P8,2 P9,1 D10,7 D11,6 D12,5 D13,4 D14,3 D8,1 P9,2 P10,1 D11,7 D12,6 D13,5 D14,4 D8,2 D9,0 P10,2 P11,1 D12,7 D13,6 D14,5 D15,0 P15,2 P15,1 D15,7 D15,6 D15,1 D15,2 D15,3 D15,4 D15,5

Adjustable RAID 6

Adjustable RAID 6 Example

Alternative to RAID Stripes

• Use a flat layout:
• Each user data device is in two or three reliability

stripes with one additional parity

• Does not use Galois field arithmetic
• Reconstruction can be done using two or three

alternatives

• Can avoid a single hot spot

Results

• Adjustable RAID 6
• Easy to find configurations
• Adjustable flat layouts
• Higher reliability
• No need for Galois field arithmetic
• Accelerators need extended instruction set
• Flexibility in reconstruction of lost data

Layout Definition

• Flat layouts:
• Each user data device is part of two reliability stripes
• Two reliability stripes have one or none data device in

common

• Each reliability stripe contains k user data devices
• Therefore:
• Each data device corresponds to an edge of an undirected

graph

• Each parity device corresponds to a reliability stripe that

corresponds to a vertex

Layout Definition

• Use graph view:
• Edges are

user data devices

• Vertices are

parity data devices

D1 D2 D3 A D4 D5 D6 B D7 D8 D9 C D E F A B C D E F D1 D2 D3 D4

D5 D6 D7 D8 D9

Layout and corresponding graph

Layout Definition

• Densest layouts correspond to a complete graph

A E C D F B 4 8 11 13 14 3 10 1 2 5 6 7 9 12

A: 0, 1, 2, 3, 4 B: 4, 5, 6, 7, 8 C: 8, 3, 9, 10, 11 D: 11, 7, 12, 13 E: 13, 10, 6, 1, 14 F: 14, 12, 9, 5, 0

Flat Layout with 6 stripes and 14 user data devices

Layout Definition

• If we want to create additional reliability stripes, we can

use a graph factorization

• Each user data device

is in three reliability stripes

• Any two stripes

intersect in one or none user data devices

• This factorization

invented by Lawless 1974

Layout Definition

• Can add additional parity devices to an ensemble in case
• f need
• How about switching some user data devices to parity?
• Cannot be done instantaneously because those data

devices need to emptied

• But it can be done

Layout Definition

• Punctured Layouts: Remove the middle edge from each

factor

1 2 3 4 5 6 7

6 3 7 8 9 1 2 4 5

Layout Definition

• Available only for certain parity - data device numbers

Reliability Evaluation

• We compare with an

adjustable RAID Level 6 configuration

• Robustness: Probability

that f device failures have let to data loss

+

• #
• Comparison Degree 10

+

• #
• Comparison Degree 5

Reliability Evaluation

• Calculation of five and six year survival probabilities:
• Degree 5
• Degree 10

Results

• Adjustable RAID 6
• Easy to find configurations
• Adjustable flat layouts
• Higher reliability
• No need for Galois field arithmetic
• Accelerators need extended instruction set
• Flexibility in reconstruction of lost data