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Coding for Atomic Shared Memory Emulation

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.

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Coding for Atomic Shared Memory Emulation

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  1. 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)

  2. Erasure Coding for Distributed Storage

  3. 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]

  4. 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]

  5. 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] This talk: Theory of distributed computing Considerations for storing data that changes

  6. Failure tolerance, Low storage costs, Fast reads and writes Consistency: Value changing, get the “latest” version

  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 • [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 Emulation over distributed storage systems

  9. Shared Memory Emulation - History Atomic (consistent) shared memory • [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 Emulation over distributed storage systems • Costs of emulation • Low cost coding based algorithm • Communication and storage costs • [C-Lynch-Medard-Musial 2014], • preprint available (This talk)

  10. Shared Memory Emulation - History Atomic (consistent) shared memory • [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 Emulation over distributed storage systems • Costs of emulation • Low cost coding based algorithm • Communication and storage costs • [C-Lynch-Medard-Musial 2014], • preprint available (This talk)

  11. Write time Read

  12. Write time Read

  13. Atomicity [Lamport 86] aka linearizability. [Herlihy, Wing 90] Write time Read

  14. Atomicity [Lamport 86] aka linearizability. [Herlihy, Wing 90] Write time Read

  15. Atomicity [Lamport 86] aka linearizability. [Herlihy, Wing 90] Write time Read

  16. Atomicity [Lamport 86] aka linearizability. [Herlihy, Wing 90] Atomic Write time Read

  17. Atomicity [Lamport 86] aka linearizability. [Herlihy, Wing 90] Atomic Write time Read Not atomic time time

  18. Shared Memory Emulation - History Atomic (consistent) shared memory • [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 Emulation over distributed storage systems • Costs of emulation • Low cost coding based algorithm • Communication and storage costs • [C-Lynch-Medard-Musial 2014], • preprint available (This talk)

  19. Distributed Storage Model Read Clients Write Clients Servers • 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

  20. Distributed Storage Model Read Clients Write Clients Servers • 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

  21. Distributed Storage Model Read Clients Write Clients Servers • 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

  22. Requirements and cost measure Read Clients Write Clients Servers • Design write, read and server protocolssuch that • Atomicity • Concurrent operations, no waiting. • Communication overheads: Number of bits sent over links • Storage overheads: (Worst-case) server storage costs

  23. The ABD algorithm (sketch) Read Clients Write Clients Servers Quorum set: Every majority of server snodes. Any two sets intersect at at least one nodes Algorithm works if at least one quorum set is available.

  24. The ABD algorithm (sketch) Read Clients Write Clients Servers Write: Send time-stamped value to every server; return after receiving sufficeintacks. Read: Send read query; wait for sufficient responses and return with latest value. Servers: Store latest value from server; send ack Respond to read request with value

  25. The ABD algorithm (sketch) ACK ACK ACK Read Clients Write Clients ACK ACK ACK Servers 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 ack Respond to read request with value

  26. The ABD algorithm (sketch) Read Clients Write Clients Query Query Query Query Query Query Query Servers Write: Send time-stamped value to every server; return after receiving sufficeintacks. Read: Send read query; wait for sufficient responses and return with latest value. Servers: Store latest value from server; send ack Respond to read request with value

  27. The ABD algorithm (sketch) Read Clients Write Clients Servers Write: Send time-stamped value to every server; return after receiving sufficeintacks. Read: Send read query; wait for quorum of responses; return with latest value. Servers: Store latest value from server; send ack Respond to read request with value

  28. The ABD algorithm (sketch) Read Clients Write Clients Servers Write: Send time-stamped value to every server; return after receiving sufficeintacks. Read: Send read query; wait for quorum responses; send latest value to quourm; latest value. Servers: Store latest value from server; send ack Respond to read request with value

  29. The ABD algorithm (sketch) ACK ACK Read Clients Write Clients ACK ACK ACK ACK Servers Write: Send time-stamped value to every server; return after receiving sufficeintacks. 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 ack Respond to read request with value

  30. 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.

  31. Performance Analysis Storage Communication (write) Communication (read) • f represents number of failures • a lower communication cost algorithm in [Fan-Lynch 03]

  32. Shared Memory Emulation - History Atomic (consistent) shared memory • [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 Emulation over distributed storage systems • Costs of emulation • Low cost coding based algorithm • Communication and storage costs • [C-Lynch-Medard-Musial 2014], • preprint available (This talk)

  33. 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

  34. Erasure Coded Shared Memory

  35. Erasure Coded Shared Memory Smaller packets, smaller overheads Example: (6,4) MDS code • Value recoverable from any 4 coded packets • Size of coded packet is ¼ size of value

  36. Erasure Coded Shared Memory Smaller packets, smaller overheads Example: (6,4) MDS code • 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

  37. Coded Shared Memory – Quorum set up Read Clients Write Clients Servers Quorum set: Every subset of 5 server snodes. Any two sets intersect at 4 nodes Algorithm works if at least one quorum set is available.

  38. Coded Shared Memory – Why is it challenging? Read Clients Write Clients Servers

  39. Coded Shared Memory – Why is it challenging? Query Query Query Query Read Clients Write Clients Servers Servers store multiple versions 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

  40. 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 δcodeword 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.

  41. 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 δcodeword 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.

  42. 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 δcodeword 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.

  43. 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 δcodeword 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.

  44. 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 δcodeword 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.

  45. 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 • Number of failed nodes smaller than (N-k)/2 • Number of writes concurrent with a read smaller than δ

  46. Performance comparisons Storage Communication (write) Communication (read) • N represents number of nodes, f represents number of failures • δ represents maximum number of writes concurrent with a read

  47. Proof Steps • After every operation terminates, - there is a quorum of servers with the codewordsymbol - there is a quorum of servers with the finalize label - because every pair of servers intersects in k servers, readers can decode the value

  48. Proof Steps • After every operation terminates, - there is a quorum of servers with the codewordsymbol - 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)

  49. 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

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