Paxos Made SimpleLeslie Lamport

Summary: Piras Maha

OutlineHistoryProblemChoosing A ValueLearningSimple Example

HistoryLeslie Lamport

Presented in 1990Almost everyone dismissed itThe first paper was a difficult read, hard to

understandTook 10 years before publication, required

almost a complete re-writeGained popularity really quickly in

distributed systemLots of decomposition and optimizations, still

being applied to date

The ProblemAssume a collection of processesEach process proposes a valueConsidered consensus algorithm( chooses a

single value is chosen)If no value is proposed then no value should

be chosenIf a value has been chosen processes should

be able to learn chosen value

The ProblemSafety requirement for consensus

Only a value proposed may be chosenOnly single value is chosenProcess never learns value has been chosen

unless it actually has beenThree roles of algorithm preformed by three

classes of agentsProposersAcceptorsLearners

The ProblemAgents can communicate with each

asynchronously (through messaging)Agents operate at arbitrary speedMay fail, may restart (information should be

remembered)Messages may take arbitrary delivery times,

can be duplicated, can be lost but not corrupted

Choosing A Value – Simple LogicA simple method: have one acceptor

A proposer sends a proposal to acceptorAcceptor chooses first value it receivesIssue: if acceptor fails, make further progress

not possible

Choosing A Value – P1What if we used multiple acceptors?

Proposer sends value to a set of acceptorsAn acceptor may accept proposed valueValue chosen if majority (or large enough set of

acceptors) chooses itIn absence of message loss or failure, want a

value chosen even if only one value proposed by proposer

P1: An acceptor must accept the first proposal that it receives

Choosing A Value – P1P1 raises an issue: several values proposed

by different proposers , where every accepted a value but no majority

Or two values were proposed and half were chosen by one set of acceptors

Failure of single acceptor could make it impossible to learn which value was chosen

Choosing A Value – P1P1 and requirement considering value is

chosen when accepted by a majority imply acceptor must be allowed to accept multiple proposals

To track the proposals, each proposal consists of proposal number and value

Different proposal would have different numbers

A value is chosen when single proposal with that value is accepted by majority of acceptors

Choosing A Value – P2Multiple proposals may be chosen but value

must be same in allP2: If a proposal with value v is chosen, then

every higher-number proposal that is chosen has value v

This guarantees that only single value will be chosen

Again, to be chosen, proposal must be accepted by at least one acceptor

P2a: If a proposal with a value v is chosen, then every higher-numbered proposal accepted by any acceptor has value v

Choosing A ValueSince communication is asynchronous, a

proposal may be chosen with an acceptor c, not received any proposal

At this point if a new proposer issues a higher-number proposal with a different value, P1 requires c to accept, thereby violating P2a

P2b: IF a proposal with value v is chosen then every higher number proposal issued by any proposer has value v

Choosing A ValueSince proposal must be issued before it is

accepted, P2b implies P2a which implies P2Prove P2

Assume proposal with number m and value v chosen

Any proposal issued with number n, n>m has value v

Using induction on n, can prove n had value v, with additional assumption: every proposal number with a number in the range m to (n-1) has value v

For proposal m to be chosen, a majority of acceptors C, where every acceptor in C has accepted it

Choosing A ValueThis m (Hypothesis ) is chosen and it implies:

Every acceptor in C has accepted a proposal with number in the range m ...(n-1) and every proposal with a number in m...(n-1) accepted by any acceptor has value v

Since any set S, with majority acceptors, contains at least one C leads to proposal number n has value v by(leading to) :

P2c: For any v and n, if a proposal with value v and number n is issued, then there is a set S consisting of a majority of acceptors such that either (a) no acceptor in S has accepted any proposal number

less than n

Choosing A Value – Issuing ProposalsOr (b) v is the value of the highest numbered proposal

among all proposals numbered less than n accepted by the acceptors in S

A proposer that wants to issue a proposal numbered n, must learn the highest numbered proposal with number less than n, if any, that has been accepted so far

To do this: a proposer chooses number n, sends request to acceptors asking for response containingPromise to not accept proposal numbered less than nProposal with highest number less than n, that has been

acceptedCalled: Prepare Request

Choosing A Value – Issuing ProposalsIf proposer receives requested responses

from majority, then issue proposal with number n and value v (where v is highest numbered proposal among responses or new number if no proposals reported)

Proposer later sends a request that proposal has been accepted

Choosing A Value - AcceptorAcceptor can receive two kinds of requests

from proposersPrepare requestAccept request

Can ignore requestsP1a: an acceptor can accept a proposal

number n if and only if it has not responded to a prepare request having a number greater than n

With this, a complete algorithm for choosing value

Choosing A Value – Algorithm OptimizationConsider acceptor receives a prepare request

with number n, but already responded to prepare request with number greater than nTherefore promised not to accept any proposal

numbered nWhich means no reason to respond to this

request or respond to a request for a for a proposal that was already accepted

Choosing A ValueNow, acceptor only needs to remember the

highest –number proposal that was accepted and the number of highest-numbered prepare request which was responded to

Since P2c kept invariant regardless of failures, acceptor must remember this information if failure or restart

Note: proposer can abandon proposal and forget all about it, as long as it doesn’t issue another proposal with same number

Choosing A Value - AlgorithmPhase 1

Proposer sends prepare request with number n to majority of acceptors with proposal number n

If an acceptor receives a prepare request with number n (this n is greater than any prepare request which it has already responded up until now), then it responds to the request with a promise not to accept any more proposals numbered less than n and with the highest-numbered proposal (if any) that it has accepted

Choosing A Value - AlgorithmPhase 2

If proposer receives response to its prepare request (for example numbered n) from majority of acceptors Proposer sends accept request to all acceptors with

proposal number n (with value v), where v is the value of the highest-numbered proposal from the responses OR is any value, if no responses were heard

If acceptor receives request for proposal number n, it will accept this proposal unless it already responded to a prepare with a number greater than n

Choosing A ValueMultiple proposals can be made

Follows algorithm each timeProposer can abandon in the middle of

protocolCorrectness should be maintained

Sequence with no errors

Learning A Chosen ValueTo learn a value is chosen, learner must first

know the proposal has been accepted by majority

Obvious solution to let each acceptor respond to all learners (sending proposal)

Good: allows all learners find out about chosen value quickly

Bad: requires each acceptor to respond to each learner (large number of responses, number of learners x number of acceptors)

Learning A Chosen ValueAnother option: have one distinguished

learnerHave this learner communicate to all other

learners (which value chosen)Bad: less reliable, if distinguished learner

failsRequires extra round for all learners to

discover chosen valueGood: requires less responses( number of

acceptors + number of learners)

Learning A Chosen ValueNext approach would be to have a set of

distinguished learnersAcceptors send acceptances to the set of

distinguished learnersLarger the set, more reliable but adds

complexity/greater communication

ProgressConsider: proposer p, completes phase 1, proposal

number n1Another proposer q, then completes phase 1 for

proposal number n2, n2>n1Proposer p’s accept request for n1 are ignored

since acceptors promised not to accept proposal number< n2

Then p, begins and completes phase 1 for n3, n3>n2

Therefore q’s phase 2 accept requests ignored, ...

ProgressUse distinguished proposer, only one to try

issuing proposalsIf distinguished proposer communicates with

majority of acceptors, using proposal number greater than any already used, then it can succeed issuing an accepted proposal

Abandon proposal then trying again if it learns of new request with higher proposal number, this distinguished proposer will eventually choose high enough proposal number

ProgressIf enough of proposers, acceptors and

communication network is working properly, electing single distinguished proposer can lead to liveness

Reliable algorithm for electing distinguished proposer may require randomness or real-time (based on research results)

The ImplementationPaxos algorithm assumes network of processesIn its heart, considered consensus algorithm, with

agents playing proposer, acceptor, learnerLeader is chosen, plays distinguished proposer and

learnerPaxos consensus algorithm requests and responses

sent as ordinary messagesStable storage (alive during failure) contains

information acceptor must rememberAcceptor records in stable storage before sending

response

State Machine ImplementationUse collection of servers, each one

implementing state machine independentlyDeterministicGuarantee execution osfsame sequence of state

machine commands

Another LookTo put it simple terms: Paxos is used to have

consistency (ordering of semantics) on a platform with multiple machinesWhy is this important?

If ordering is jumbled, the meaning is lost Unreliable Could cause safety issues

Another Look - ExampleJane has $0 in her accountJoe sends $100 to JaneWhen Jane is notified she received $100, she

sends $50 cheque to CRACRA cashs the cheque and spends it on

something useless

Without consistent ordering, each machine might view these in different order

Author QAWhat would you like to convey to current and

future researchers and practitioners? Don’t pay attention to pedantic old farts like me telling you what to do.

What are the most important lessons you’ve learned in your career?

My career has been idiosyncratic. Any meaningful lessons I could draw from it would, at best, apply to people starting their careers 30 years ago.

Ref: http://research.microsoft.com/en-us/um/people/lamport/pubs/ds-interview.pdf

Referenceshttp://ayende.com/blog/4496/paxos-enlightme

nthttp://www.inf.usi.ch/faculty/pedone/MScThes

is/marco.pdfhttp://the-paper-trail.org/blog/?p=173Paxos Made Simple by Leslie Lamport (2001)