1.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 1 Principles of Reliable Distributed Systems Lecture 9: Paxos Spring 2007 Prof. Idit Keidar

2.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 2 Material Paxos Made Simple Leslie Lamport ACM SIGACT News (Distributed Computing Column) 32, 4 (Whole Number 121, December 2001) 18-25.

3.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 3 Issues in the Real World I/III Problem: Sometimes messages take longer than expected Solution 1: Use longer timeouts –Slow convergence Solution 2: Assume asynchrony –FLP Solution 3: Assume eventual synchrony or unreliable failure detectors –See last week – MR Algorithm

4.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 4 Issues in the Real World II/III Problem: Sometimes messages are lost Solution 1: Use retransmissions –In case of transient partitions, a huge backlog can build up – catching up may take forever –More congestion, long message delays for extensive periods Solution 2: Allow message loss –2 Generals Solution 3: Assume eventually reliable links –That’s what we’ll do today

5.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 5 Issues in the Real World III/III Problem: Processes may crash and later recover (aka crash-recovery model) Solution 1: Store information on stable storage (disk) and retrieve it upon recovery –What happens to messages arriving when they’re down? –See previous slide

6.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 6 MR and Unreliable Links From MR Algorithm Phase II: wait for (r,e) from n-t processes Transient message loss violates liveness What if we move to the next round in case we can’t get n-t responses for too long? –Notice the next line in MR: if any non-  value e received then val  e

7.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 7 What If MR Didn’t Wait … 11 2 n...... (1, v 1 ) 1 2 n...... est =  (2, v 2 ) no waiting no change of val 2 (1, v 1 ) decide v 1 (1,  ) will decide v 2

8.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 8 What Did We Learn? Do not get stuck in a round –Move on upon timeout –Move on upon hearing that others moved on But, a new leader before proposing a decision value must learn any possibly decided value (must check with a majority)

9.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 9 Paxos: Main Principles Use “leader election” module –If you think you’re leader, you can start a new “ballot” Paxos name for a round Always join the newest ballot you hear about –Leave old ballots in the middle if you need to Two phases: –First learn outcomes of previous ballots from a majority –Then propose a new value, and get a majority to endorse it

10.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 10 Leader Election Failure Detector  – Leader –Outputs one trusted process –From some point, all correct processes trust the same correct process Can easily implement ◊S Is the weakest for consensus [Chandra, Hadzilacos, Toueg 96]

11.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 11  Implementations Easiest: use ◊P implementation –In eventual synchrony model –Output lowest id non-suspected process  is implementable also in some situations where ◊P isn’t Optimizations possible –Choose “best connected”, strongest, etc.

12.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 12 Paxos: The Practicality Overcomes message loss without retransmitting entire message history Tolerates crash and recovery Does not rotate through dead coordinators Used in replicated file systems –Frangipani – DEC, early 90s –Nowadays Microsoft

13.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 13 The Part-Time Parliament [Lamport 88,98,01] Recent archaeological discoveries on the island of Paxos reveal that the parliament functioned despite the peripatetic propensity of its part-time legislators. The legislators maintained consistent copies of the parliamentary record, despite their frequent forays from the chamber and the forgetfulness of their messengers. The Paxon parliament’s protocol provides a new way of implementing the state-machine approach to the design of distributed systems.

14.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 14 Annotation of TOCS 98 Paper This submission was recently discovered behind a filing cabinet in the TOCS editorial office. …the author is currently doing field work in the Greek isles and cannot be reached … The author appears to be an archeologist with only a passing interest in computer science. This is unfortunate; even though the obscure ancient Paxon civilization he describes is of little interest to most computer scientists, its legislative system is an excellent model for how to implement a distributed computer system in an asynchronous environment.

15.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 15 The Setting The data (ledger) is replicated at n processes (legislators) Operations (decrees) should be invoked (recorded) at each replica (ledger) in the same order Processes (legislators) can fail (leave the parliament) At least a majority of processes (legislators) must be up (present in the parliament) in order to make progress (pass decrees) –Why majority?

16.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 16 Eventually Reliable Links There is a time after which every message sent by a correct process to a correct process eventually arrives Usual failure-detector-based algorithms do not work –Homework question

17.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 17 The Paxos (  ) Atomic Broadcast Algorithm Leader based: each process has an estimate of who is the current leader To order an operation, a process sends it to its current leader The leader sequences the operation and launches a Consensus algorithm (Synod) to fix the agreement

18.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 18 The (Synod) Consensus Algorithm Solves non-terminating consensus in asynchronous system –or consensus in a partial synchrony system –or consensus using an  failure detector Overcomes transient crashes & recoveries and message loss –can be modeled as message loss

19.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 19 The Consensus Algorithm Structure Two phases Leader contacts a majority in each phase There may be multiple concurrent leaders Ballots distinguish among values proposed by different leaders –unique, locally monotonically increasing –correspond to rounds of ◊S-based algorithm [MR] –processes respond only to leader with highest ballot seen so far

20.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 20 Ballot Numbers Pairs  num, process id   n1, p1  >  n2, p2  –if n1 > n2 –or n1=n2 and p1 > p2 Leader p chooses unique, locally monotonically increasing ballot number –if latest known ballot is  n, q  –p chooses  n+1, p 

21.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 21 The Two Phases of Paxos Phase 1: prepare –If trust yourself by   believe you are the leader) Choose new unique ballot number Learn outcome of all smaller ballots from majority Phase 2: accept –Leader proposes a value with his ballot number –Leader gets majority to accept its proposal –A value accepted by a majority can be decided

22.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 22 Paxos - Variables BallotNum i, initially  0,0  Latest ballot p i took part in (phase 1) AcceptNum i, initially  0,0  Latest ballot p i accepted a value in (phase 2) AcceptVal i, initially   Latest accepted value (phase 2)

23.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 23 Paxos Phase I: Prepare - Leader Periodically, until decision is reached do: if leader (by  ) then BallotNum   BallotNum.num+1, myId  send (“prepare”, BallotNum) to all Goal: contact other processes, ask them to join this ballot, and get information about possible past decisions

24.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 24 Paxos Phase I: Prepare - Cohort Upon receive (“prepare”, bal) from i if bal  BallotNum then BallotNum  bal send (“ack”, bal, AcceptNum, AcceptVal) to i This is a higher ballot than my current, I better join it! Tell the leader about my latest accepted value

25.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 25 Paxos Phase II: Accept - Leader Upon receive (“ack”, BallotNum, b, val) from n-t if all vals =  then myVal = initial value else myVal = received val with highest b send (“accept”, BallotNum, myVal) to all /* proposal */ The value accepted in the highest ballot might have been decided, better propose this value

26.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 26 Paxos Phase II: Accept - Cohort Upon receive (“accept”, b, v) if b  BallotNum then AcceptNum  b; AcceptVal  v /* accept proposal */ send (“accept”, b, v) to all (first time only) This is not from an old ballot

27.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 27 Paxos – Deciding Upon receive (“accept”, b, v) from n-t decide v periodically send (“decide”, v) to all Upon receive (“decide”, v) decide v Why don’t we ever “return”?

28.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 28 In Failure-Free Synchronous Runs 11 2 n...... (“accept”,  1,1 ,v 1 ) 1 2 n...... 11 2 n...... (“prepare”,  1,1  ) (“ack”,  1,1 ,  0,0 ,  ) decide v 1 (“accept”,  1,1 ,v 1 ) Simple  implementation always trusts process 1

29.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 29 Correctness: Agreement Follows from Lemma 1: If a proposal (b,v) is accepted by a majority of the processes, then for every proposal (b’, v’) with b’>b, it holds that v’=v.

30.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 30 Proving Agreement Using Lemma 1 Let v be a decided value. The first process that decides v receives n-t accept messages for v with some ballot b, i.e., (b,v) is accepted by a majority. No other value is accepted with the same b. Why? Let (b 1,v 1 ) be the first proposal accepted by n-t. By Lemma 1, v 1 is the only possible decision value.

31.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 31 To Prove Lemma 1 Use Lemma 2: (invariant): If a proposal (b,v) is sent, then there is a set S consisting of a majority such that either –no p in S accepts a proposal ranked less than b (all vals =  ; or –v is the value of the highest-ranked proposal among proposals ranked less than b accepted by processes in S (myVal = received val with highest b).

32.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 32 To Prove Lemma 2 A process can accept a proposal numbered b if and only if it has not responded to a prepare request having a number greater than b. The “ack” response to “prepare” is a promise not to accept lower-ballot proposals in the future.

33.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 33 Termination Assume no loss for a moment. Once there is one correct leader – –It eventually chooses the highest ballot number –No other process becomes a leader with a higher ballot –All correct processes “ack” its prepare message and “accept” its accept message and decide

34.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 34 What About Message Loss? Does not block in case of a lost message –Phase 1 can start with new rank even if previous attempts never ended Conditional liveness: If n-t correct processes including the leader can communicate with each other then they eventually decide Holds with eventually reliable links

35.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 35 Optimization Allow process 1 (only!) to skip Phase 1 –Initiate BallotNum to  1,1  –Propose its own initial value 2 steps in failure-free synchronous runs 2 steps for repeated invocations with the same leader –Common case

36.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 36 Atomic Broadcast by Running A Sequence of Consensus Instances

37.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 37 The Setting Data is replicated at n servers Operations are initiated by clients Operations need to be performed at all correct servers in the same order –state-machine replication

38.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 38 Client-Server Interaction (Benign Version) Leader-based: each process (client/server) has an estimate of who is the current leader A client sends a request to its current leader The leader launches the Paxos consensus algorithm to agree upon the order of the request The leader sends the response to the client

39.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 39 Failure-Free Message Flow S1 S2 Sn...... C S1 S2 Sn...... S1 S2 Sn...... (“accept”)(“prepare”)(“ack”) C Phase 1Phase 2 request response

40.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 40 Observation In Phase 1, no consensus values are sent: –Leader chooses largest unique ballot number –Gets a majority to “vote” for this ballot number –Learns the outcome of all smaller ballots from this majority In Phase 2, leader proposes either its own initial value or latest value it learned in Phase 1

41.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 41 Message Flow: Take 2 S1 S2 Sn...... C S1 S2 Sn...... S1 S2 Sn...... (“accept”) (“prepare”)(“ack”) C Phase 1 Phase 2 request response S1

42.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 42 Optimization Run Phase 1 only when the leader changes –Phase 1 is called “view change” or “recovery mode” –Phase 2 is the “normal mode” Each message includes BallotNum (from the last Phase 1) and ReqNum –e.g., ReqNum = 7 when we’re trying to agree what the 7 th operation to invoke on the state machine should be Respond only to messages with the “right” BallotNum

43.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 43 Paxos Atomic Broadcast: Normal Mode Upon receive (“request”, v) from client if (I am not the leader) then forward to leader else /* propose v as request number n */ ReqNum  ReqNum +1; send (“accept”, BallotNum, ReqNum, v) to all Upon receive (“accept”, b, n, v) with b = BallotNum /* accept proposal for request number n */ AcceptNum[n]  b; AcceptVal[n]  v send (“accept”, b, n, v) to all (first time only)

44.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 44 Recovery Mode The new leader must learn the outcome of all the pending requests that have smaller BallotNums –The “ack” messages include AcceptNums and AcceptVals of all pending requests For all pending requests, the leader sends “accept” messages What if there are holes? –e.g., leader learns of request number 13 and not of 12 –fill in the gaps with dummy “do nothing” requests

45.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 45 Leslie Lamport’s Reflections Inspired by my success at popularizing the consensus problem by describing it with Byzantine generals, I decided to cast the algorithm in terms of a parliament on an ancient Greek island. To carry the image further, I gave a few lectures in the persona of an Indiana-Jones-style archaeologist. My attempt at inserting some humor into the subject was a dismal failure.

46.  Idit Keidar, Principles of Reliable Distributed Systems, Technion EE, Spring 2007 46 The History of the Paper by Lamport I submitted the paper to TOCS in 1990. All three referees said that the paper was mildly interesting, though not very important, but that all the Paxos stuff had to be removed. I was quite annoyed at how humorless everyone working in the field seemed to be, so I did nothing with the paper. A number of years later, a couple of people at SRC needed algorithms for distributed systems they were building, and Paxos provided just what they needed. I gave them the paper to read and they had no problem with it. So, I thought that maybe the time had come to try publishing it again.