PAXOS:

Consensus in aDistributed System

Philipp Fath

Supervisor: Dr. Diego MilanoLeslie Lamport *1941

Introduction: Consensus at PAXOS Island

non-Byzantine faults

Roles and Behaviors

Example situations

Outlook

Sources

Agenda

| Slide 2Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Agenda

| Slide 3Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: Consensus at PAXOS Island

non-Byzantine faults

Roles and Behaviors

Example situations

Outlook

Sources

| Slide 4Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: What is consensus?

Origin Latin: consentire = feel together

Definition (Merriam-Webster Britannica) general agreement: unanimity the judgment arrived at by most of those concerned group solidarity in sentiment and belief

In a Distributed System Consistent agreement on a value Different processes must not give contradictory answers

| Slide 5Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: PAXOS IslandAncient parliament of the Greek Island of Paxos*

Parliament’s primary task:determine the law (sequence of decrees passed)

Instead of having a secretary recording the law,every legislator records passed decrees in his personal ledger

Problems: > Legislator work on part-time> Communication only by (part-time) messenger possibleHowever: Legislators and Messengers are deeply honest

Requirements: Consistent, not contradicting ledgers

*) Note: The ancient parliament never really existet at Paxos, Leslie Lamport invented it totallyto popularize his consensus-algorithm named PAXOS.

Agenda

| Slide 6Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: Consensus at PAXOS Island

non-Byzantine faults

Roles and Behaviors

Example situations

Outlook

Sources

| Slide 7Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

non-Byzantine faults

Agents• operate at arbitrary speed• may fail by stopping• may restart

Messages• arbitrary deliver time• can be duplicated• can be lost

Fail-stop or Crasha process works correct until a certain moment then it crashes

Omission or partial discontinuationSome messages might be lost but all of them are correct

TimingExecution of actions and sending of messages may be early or late

Not assumed in PAXOS: Byzantine errors and inconsistencyIncorrect working processes sending corrupted messages

Agenda

| Slide 8Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: Consensus at PAXOS Island

non-Byzantine faults

Roles and Behaviors

Example situations

Outlook

Sources

| Slide 9Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Consensus-making model: Roles

proposer learneracceptor

acceptorsproposers learners

Proposes a value vand assigns a unique

proposal number N to it

Accepts the proposal if ithas not promised to accept a

Proposal with higher number N

Learns chosenProposal N with value v

Quorum must accept proposal to be chosen

| Slide 10Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Consens-making model: RolesCLIENT

leader

leader

proposers acceptors learners

fault-tolerant memory

| Slide 11Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Roles and behaviors: Basic PAXOS Phase 1a: Prepare

• a Proposer selects a proposal number N• and sends a prepare-request with number N to a majority of acceptors

Phase 1b: Promise• acceptors answer with a promise not to accept any more proposals

with a number less than N• and answer with the highest-numbered proposal (if any) accepted

Phase 2a: Accept!• if the proposer received a answer of a majority of acceptors,

it sends an accept-request N with value v to them• v is the value of the highest-numbered proposal among the answers,

or may be any value if no values were reported

Phase 2b: Accepted• acceptors accept proposal if they haven’t given a new promise in meantime

Agenda

| Slide 12Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: Consensus at PAXOS Island

non-Byzantine faults

Roles and Behaviors

Example situations

Outlook

Sources

| Slide 13Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Situation 1: Basic PAXOS [no faults]

| Slide 14Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Situation 2: Failure of Acceptor

| Slide 15Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Situation 3: Failure of redundand Learner

| Slide 16Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Situation 4: Failure of Proposer

| Slide 17Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Situation 5: Failure Duelling Proposers

Agenda

| Slide 18Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Introduction: Consensus at PAXOS Island

non-Byzantine faults

Roles and Behaviors

Example situations

Outlook

Sources

| Slide 19Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Outlook: PAXOS is a family of algorithms Multi-PAXOS

Several instances of PAXOS produce a continuous stream of agreedvalues but use the same leader.

Cheap-PAXOSAuxiliary Processors only take part during unstable periods.

Fast-PAXOSDirect Accept!-Message from client: saving one message delay

Generalized PAXOSAim is not to agree on a single value, but on an increasing set of values.

Thank you !

Questions ?

Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25 | Slide 20

| Slide 21Workshop DIS: PAXOS / Consensus in a Distributed System Philipp Fath 2010/10/25

Sources

http://www.merriam-webster.com/dictionary/consensus , 2010http://research.microsoft.com/en-us/um/people/lamport/pubs/pubs.html#lamport-paxos , 2010Highlights aus der Informatik, Ingo Wegener, Springer 1996The part-time parliament, Leslie Lamport, ACM Transactions on Computer Systems 1998Paxos Made Simple, Leslie Lamport, 2001Generalized Consensus and Paxos, Leslie Lamport, Microsoft Research 2004

Content

Imageshttp://www.nancy-universite.fr/fileadmin/public/dhc2007/Phototheque/images/4068.jpg , 2010https://belenus.unirioja.es/~mimarano/Lamport.jpg , 2010http://www.steckdosenversand.de/pics_site/netzwerk_ausschnitt_1.jpg , 2010http://en.wikipedia.org/wiki/Paxos_algorithm , 2010