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The Model

channel. node. The Model. Node properties: No shared memory No global clock. Channel properties: FIFO loss free non-duplicating. C1:transfer $50. C1:empty. C1:empty. $500. $450. $450. $200. $200. $250. C2:empty. C2:empty. C2:empty. The Problem.

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The Model

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  1. channel node The Model Node properties: • No shared memory • No global clock • Channel properties: • FIFO • loss free • non-duplicating

  2. C1:transfer $50 C1:empty C1:empty $500 $450 $450 $200 $200 $250 C2:empty C2:empty C2:empty The Problem

  3. Distributed Snapshot (Global State Recording) Problems: • recording a “consistent” state of the global computation • checkpointing for fault tolerance (rollback, recovery) • testing and debugging • monitoring and auditing • detecting stable properties in a distributed system via snapshots. A property is “stable” if, once it holds in a state, it holds in all subsequent states. • termination • deadlock • garbage collection

  4. Definitions Local State and Actions: local state: LSi message send: send(mij ) message receive: rec(mij ) time: time(x) send(mij )  LSi iff time(send(mij )) < time(LSi ) rec(mij )  LSj iff time(rec(mij )) < time(LSj ) Predicates: transit(LSi , LSj ) = {mij | send(mij )  LSi !( rec(mij )  LSj ) ) } inconsistent(LSi , LSj ) = {mij | !(send(mij )  LSi )  rec(mij )  LSj ) } Consistent Global State:  i,  j : 1 <= i, j <= n :: inconsistent( LSi , LSj ) = 

  5. Global­State­Detection Algorithm Marker­Sending Rule for a Process p: For each channel c, incident on, and directed away from p: p sends one marker along c after p records its state and before p sends further messages along c. Marker­Receiving Rule for a Process q: if (q has not recorded its state) then begin q records its state; q records the state of c as the empty sequence; end else q records the state of c as the sequence of message received along c after q's state was recorded and before q received the marker along c. Detecting a Stable Property begin record a global snapshot, S*; test for the stable property in S*; end;

  6. empty M M M S3 S0 S2 S1 q q q q p p p p empty empty M’ D state A state A state A state B state D state D state C state C empty recorded state q p D state A state D p records its state (A) and sends marker M on channel before receiving the marker, q changes its state and sends message D. q receives the marker and records its state (D) and the incoming channel as empty; q send marker M' on its outgoing channel. on receiving the marker, p records the channel as having D

  7. c1 500 500 p q c2 c4 c3 r = Marker M 500 Snapshot/State Recording Example

  8. M 10 c1 470 490 p q c2 20 c4 c3 10 r 500 Snapshot/State Recording Example (Step 1)

  9. c1 480 490 p q c2 M c4 20 M c3 10 25 r 475 Snapshot/State Recording Example (Step 2)

  10. 20 c1 480 470 p q c2 M c4 20 c3 25 r M 485 Snapshot/State Recording Example (Step 3)

  11. c1 500 490 p q c2 c4 c3 25 r M 485 Snapshot/State Recording Example (Step 4)

  12. Snapshot/State Recording Example (Step 5) c1 500 515 p q c2 c4 c3 r 485

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