Upload
sade-jordan
View
41
Download
1
Embed Size (px)
DESCRIPTION
Coding for Atomic Shared Memory Emulation. Viveck R. Cadambe (MIT) Joint with Prof. Nancy Lynch (MIT), Prof. Muriel Médard (MIT) and Dr. Peter Musial (EMC). Erasure Coding for Distributed Storage. Erasure Coding for Distributed Storage. - PowerPoint PPT Presentation
Citation preview
Coding for Atomic Shared Memory Emulation
Viveck R. Cadambe (MIT)
Joint with Prof. Nancy Lynch (MIT), Prof. Muriel Médard (MIT) and Dr. Peter Musial
(EMC)
Erasure Coding for Distributed Storage
• Locality, Repair Bandwidth, Caching and Content Distribution– [Gopalan et. al 2011, Dimakis-Godfrey-Wu-Wainwright- 10, Wu-
Dimakis 09, Niesen-Ali 12]
Erasure Coding for Distributed Storage
• Locality, Repair Bandwidth, Caching and Content Distribution– [Gopalan et. al 2011, Dimakis-Godfrey-Wu-Wainwright- 10, Wu-
Dimakis 09, Niesen-Ali 12]
• Queuing theory– [Ferner-Medard-Soljanin 12, Joshi-Liu-Soljanin 12, Shah-Lee-
Ramchandran 12]
Erasure Coding for Distributed Storage
• Locality, Repair Bandwidth, Caching and Content Distribution– [Gopalan et. al 2011, Dimakis-Godfrey-Wu-Wainwright- 10, Wu-
Dimakis 09, Niesen-Ali 12]
• Queuing theory– [Ferner-Medard-Soljanin 12, Joshi-Liu-Soljanin 12, Shah-Lee-
Ramchandran 12]
Erasure Coding for Distributed Storage
This talk: Theory of distributed computingConsiderations for storing data that changes
6
Consistency: Value changing, get the “latest” version
Failure tolerance, Low storage costs, Fast reads and writes
7
Shared Memory Emulation - History
Atomic (consistent) shared memory
• [Lamport 1986]• Cornerstone of distributed
computing and multi-processor programming
8
Shared Memory Emulation - History
Atomic (consistent) shared memory
Emulation over distributed storage
systems
• [Lamport 1986]• Cornerstone of distributed
computing and multi-processor programming
• “ABD” algorithm [Attiya-Bar-Noy-Dolev95], 2011 Dijsktra Prize,
• Amazon dynamo key-value store
[Decandia et. al. 2008]• Replication-based
9
Shared Memory Emulation - History
Atomic (consistent) shared memory
Emulation over distributed storage
systems
Costs of emulation
• [Lamport 1986]• Cornerstone of distributed
computing and multi-processor programming
• “ABD” algorithm [Attiya-Bar-Noy-Dolev95], 2011 Dijsktra Prize,
• Amazon dynamo key-value store
[Decandia et. al. 2008]• Replication-based
• Low cost coding based algorithm
• Communication and storage costs
(This talk) • [C-Lynch-Medard-Musial 2014],preprint available
10
Shared Memory Emulation - History
Atomic (consistent) shared memory
Emulation over distributed storage
systems
Costs of emulation
• [Lamport 1986]• Cornerstone of distributed
computing and multi-processor programming
• “ABD” algorithm [Attiya-Bar-Noy-Dolev95], 2011 Dijsktra Prize,
• Amazon dynamo key-value store
[Decandia et. al. 2008]• Replication-based
• Low cost coding based algorithm
• Communication and storage costs
• [C-Lynch-Medard-Musial 2014],preprint available(This talk)
11
12
Write
Readtime
13
Write
Readtime
14
Atomicity [Lamport 86]
aka linearizability. [Herlihy, Wing 90]
Write
Readtime
15
Write
Read
Atomicity [Lamport 86]
aka linearizability. [Herlihy, Wing 90]
time
16
Write
Read
Atomicity [Lamport 86]
aka linearizability. [Herlihy, Wing 90]
time
17
Write
Read
Atomicity [Lamport 86]
aka linearizability. [Herlihy, Wing 90]
time
Atomic
18
Atomic
Not atomic
Write
Read
Atomicity [Lamport 86]
aka linearizability. [Herlihy, Wing 90]
time
time
time
19
Shared Memory Emulation - History
Atomic (consistent) shared memory
Emulation over distributed storage
systems
Costs of emulation
• [Lamport 1986]• Cornerstone of distributed
computing and multi-processor programming
• “ABD” algorithm [Attiya-Bar-Noy-Dolev95], 2011 Dijsktra Prize,
• Amazon dynamo key-value store
[Decandia et. al. 2008]• Replication-based
• Low cost coding based algorithm
• Communication and storage costs
• [C-Lynch-Medard-Musial 2014],preprint available(This talk)
20
• Client server architecture, nodes can fail (no. of server failures is limited)
• Point-to-point reliable links (arbitrary delay).
• Nodes do not know if other nodes fail
• An operation should not have to wait for others to complete
Distributed Storage Model
Servers
Write Clients Read Clients
21
• Client server architecture, nodes can fail (no. of server failures is limited)
• Point-to-point reliable links (arbitrary delay)
• Nodes do not know if other nodes fail
• An operation should not have to wait for others to complete
Distributed Storage Model
Servers
Write Clients Read Clients
22
• Client server architecture, nodes can fail (no. of server failures is limited)
• Point-to-point reliable links (arbitrary delay).
• Nodes do not know if other nodes fail
• An operation should not have to wait for others to complete
Distributed Storage Model
Servers
Write Clients Read Clients
23
Write Clients Read Clients
Servers
Requirements and cost measure
Design write, read and server protocols such that
• Atomicity
• Concurrent operations, no waiting.
Communication overheads: Number of bits sent over links Storage overheads: (Worst-case) server storage costs
24
The ABD algorithm (sketch)
Servers
Write Clients Read Clients
Quorum set: Every majority of server snodes. Any two sets intersect at at least one nodesAlgorithm works if at least one quorum set is available.
25
The ABD algorithm (sketch)
Write:Send time-stamped value to every server; return after receiving sufficeint acks.
Read: Send read query; wait for sufficient responses and return with latest value.
Servers:Store latest value from server; send ackRespond to read request with value
Servers
Write Clients Read Clients
26
The ABD algorithm (sketch)
Write:Send time-stamped value to every server; return after receiving acks from quorum.
Read:: Send read query; wait for sufficient responses and return with latest value.
Servers:Store latest value; send ackRespond to read request with value
Servers
ACK
ACK
ACK
ACK
ACK
ACK
Write Clients Read Clients
27
The ABD algorithm (sketch)QueryQueryQueryQueryQueryQuery
QueryWrite Clients Read Clients
Write:Send time-stamped value to every server; return after receiving sufficeint acks.
Read: Send read query; wait for sufficient responses and return with latest value.
Servers:Store latest value from server; send ackRespond to read request with value
Servers
28
The ABD algorithm (sketch)
Servers
Write:Send time-stamped value to every server; return after receiving sufficeint acks.
Read: Send read query; wait for quorum of responses; return with latest value.
Servers:Store latest value from server; send ackRespond to read request with value
Write Clients Read Clients
29
The ABD algorithm (sketch)
Servers
Write:Send time-stamped value to every server; return after receiving sufficeint acks.
Read: Send read query; wait for quorum responses; send latest value to quourm; latest value.
Servers:Store latest value from server; send ackRespond to read request with value
Write Clients Read Clients
30
The ABD algorithm (sketch)
Servers
Write:Send time-stamped value to every server; return after receiving sufficeint acks.
Read: Send read query; wait for acks from quorum responses; send latest value to servers; return latest value after receiving acks from quorum.Servers:Store latest value from server; send ackRespond to read request with value
Write Clients Read Clients
ACK
ACK ACK
ACK
ACK
ACK
The ABD algorithm (summary)
• The ABD algorithm ensures atomic operations.
• Operations terminate is ensured as long as a majority of nodes do not fail.
• Implication: A networked distributed storage system can be used as shared memory.
• Replication to ensure failure tolerance.
ABD
Storage
Communication(read)
Communication(write)
Performance Analysis
• f represents number of failures• a lower communication cost algorithm in [Fan-Lynch 03]
33
Shared Memory Emulation - History
Atomic (consistent) shared memory
Emulation over distributed storage
systems
Costs of emulation
• [Lamport 1986]• Cornerstone of distributed
computing and multi-processor programming
• “ABD” algorithm [Attiya-Bar-Noy-Dolev95], 2011 Dijsktra Prize,
• Amazon dynamo key-value store
[Decandia et. al. 2008]• Replication-based
• Low cost coding based algorithm
• Communication and storage costs
(This talk)• [C-Lynch-Medard-Musial 2014],
preprint available
Shared Memory Emulation – Erasure Coding
• [Hendricks-Ganger-Reiter 07, Dutta-Guerraoui-Levy 08, Dobre-et.al 13, Androulaki et. al 14]
• New algorithm, a formal analysis of costs
• Outperforms previous algorithms in certain aspects• Previous algorithms incur infinite worst-case storage costs• Previous algorithms incur large communication costs
35
Erasure Coded Shared Memory
36
Erasure Coded Shared Memory
Example:(6,4) MDS code
• Value recoverable from any 4 coded packets
• Size of coded packet is ¼ size of value
Smaller packets,smaller overheads
37
• Value recoverable from any 4 coded packets
• Size of coded packet is ¼ size of value
• New constraint, need 4 packets with same time-stamp
Erasure Coded Shared Memory
Smaller packets,smaller overheads
Example:(6,4) MDS code
38
Quorum set: Every subset of 5 server snodes. Any two sets intersect at 4 nodesAlgorithm works if at least one quorum set is available.
Coded Shared Memory – Quorum set up
Servers
Write Clients Read Clients
39
Coded Shared Memory – Why is it challenging?
Servers
Write Clients Read Clients
40
Coded Shared Memory – Why is it challenging?
Servers
QueryQuery
Query
Query
Challenges: reveal elements to readers only when enough elements are propagated discard old versions safely
Solutions: Write in multiple phases Store all the write-versions concurrent with a read
Servers store multiple versions
Write Clients Read Clients
Coded Shared Memory – Protocol overview
Write:Send time-stamped value to every server; send finalize message after getting acks from quorum; return after receiving acks from quorum.
Read: Send read query; wait for time-stamps from a quorum;Send request with latest time-stamp to servers; decode and return value after receiving acks from quorum.
Servers:Store the coded symbol; keep latest δ codeword symbols and delete older ones; send ack. Set finalize flag for tag on receiving finalize message.Respond to read query with latest finalized tag.Finalize the requested tag; respond to read request with codeword symbol.
Coded Shared Memory – Protocol overview
Write:Send time-stamped value to every server; send finalize message after getting acks from quorum; return after receiving acks from quorum.
Read: Send read query; wait for time-stamps from a quorum;Send request with latest time-stamp to servers; decode and return value after receiving acks from quorum.
Servers:Store the coded symbol; keep latest δ codeword symbols and delete older ones; send ack. Set finalize flag for time-stamp on receiving finalize message. Send ack.Respond to read query with latest finalized tag.Finalize the requested tag; respond to read request with codeword symbol.
Coded Shared Memory – Protocol overview
Write:Send time-stamped value to every server; send finalize message after getting acks from quorum; return after receiving acks from quorum.
Read: Send read query; wait for time-stamps from a quorum;Send request with latest time-stamp to servers; decode and return value after receiving acks from quorum.
Servers:Store the coded symbol; keep latest δ codeword symbols and delete older ones; send ack. Set finalize flag for tag on receiving finalize message.Respond to read query with latest finalized tag.Finalize the requested tag; respond to read request with codeword symbol.
Coded Shared Memory – Protocol overview
Write:Send time-stamped value to every server; send finalize message after getting acks from quorum; return after receiving acks from quorum.
Read: Send read query; wait for time-stamps from a quorum;Send request with latest time-stamp to servers; decode and return value after receiving acks/symbols from quorum.
Servers:Store the coded symbol; keep latest δ codeword symbols and delete older ones; send ack. Set finalize flag for tag on receiving finalize message.Respond to read query with latest finalized tag.Finalize the requested time-stamp; respond to read request with codeword symbol if it exists, else send ack.
Coded Shared Memory – Protocol overview
Write:Send time-stamped value to every server; send finalize message after getting acks from quorum; return after receiving acks from quorum.
Read: Send read query; wait for time-stamps from a quorum;Send request with latest time-stamp to servers; decode and return value after receiving acks/symbols from quorum.
Servers:Store the coded symbol; keep latest δ codeword symbols and delete older ones; send ack. Set finalize flag for time-stamp on receiving finalize message.Respond to read query with latest finalized tag.Finalize the requested time-stamp; respond to read request with codeword symbol if it exists, else send ack.
Coded Shared Memory – Protocol overview
• Use (N,k) MDS code, where N is the number of servers
• Ensures atomic operations
• Operations terminate is ensured as long as o Number of failed nodes smaller than (N-k)/2o Number of writes concurrent with a read
smaller than δ
Performance comparisons
ABD Our Algorithm
Storage
Communication(read)
Communication(write)
• N represents number of nodes, f represents number of failures• δ represents maximum number of writes concurrent with a read
48
Proof Steps
• After every operation terminates, - there is a quorum of servers with the codeword symbol - there is a quorum of servers with the finalize label - because every pair of servers intersects in k servers,
readers can decode the value
49
Proof Steps
• After every operation terminates, - there is a quorum of servers with the codeword symbol - there is a quorum of servers with the finalize label - because every pair of servers intersects in k servers,
readers can decode the value
• When a codeword symbol is deleted at a server– Every operation that wants that time-stamp has terminated– (Or the concurrency bound is violated)
50
Main Insights
• Significant savings on network traffic overheads
- Reflects the classical gain of erasure coding over replication
• (New Insight) Storage overheads depend on client activity• Storage overhead proportional to the no. of writes concurrent
with a read• Better than classical techniques for moderate client activity
51
Future Work – Many open questions
Refinements of our algorithm- (Ongoing) More robustness to client node failures
Information theoretic bounds on costs- New coding schemes
Finer network models- Erasure channels, different topologies, wireless channels
Finer source models- Correlations across versions
Dynamic networks
52
Future Work – Many open questions
Refinements of our algorithm- (Ongoing) More robustness to client node failures
Information theoretic bounds on costs- New coding schemes
Finer network models- Erasure channels, different topologies, wireless channels
Finer source models- Correlations across versions
Dynamic networks
53
Storage costs
ABD
Our algorithm
Number of writes concurrent with a read
Storage Overhead
What is the fundamental cost
curve?
54
Future Work – Many open questions
Refinements of our algorithm- (Ongoing) More robustness to client node failures
Information theoretic bounds on costs- New coding schemes
Finer network models, finer source models- Erasure channels, different topologies, wireless channels- Correlations across versions
Dynamic networks
55
Future Work – Many open questions
Refinements of our algorithm- (Ongoing) More robustness to client node failures
Information theoretic bounds on costs- New coding schemes
Finer network models, finer source models- Erasure channels, different topologies, wireless channels- Correlations across versions
Dynamic networks
- Interesting replication based algorithm in [Gilbert-Lynch-Shvartsman 03]
- Study of costs in terms of network dynamics