Refined quorum systems
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Refined Quorum Systems. Rachid Guerraoui and Marko Vukoli ć. Ecole Polytechnique Federale de Lausanne School of Computer and Communication Sciences EPFL / IC. " Plan for the worst, hope for the best.«  English proverb. Distributed algorithms. Hope for: Few (no) failures Synchrony

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Refined Quorum Systems

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Refined quorum systems

Refined Quorum Systems

Rachid Guerraoui and Marko Vukolić

Ecole Polytechnique Federale de Lausanne

School of Computer and Communication Sciences

EPFL / IC


Refined quorum systems

" Plan for the worst, hope for the best.« 

English proverb

PODC ’07: Refined Quorum SystemsSlide 2


Distributed algorithms

Distributed algorithms

Hope for:

  • Few (no) failures

  • Synchrony

  • No Contention

Plan for:

  • Many failures

  • Asynchrony

  • Contention

Optimistic algorithms

optimize w.r.t complexity

(e.g., latency)

Resilient algorithms

PODC ’07: Refined Quorum SystemsSlide 3


Contribution

Contribution

An abstraction to devise

resilient & optimistic algorithms

Refined Quorum Systems

(RQS)

PODC ’07: Refined Quorum SystemsSlide 4


The paper

The paper

  • RQS definition

  • Optimal algorithms built around RQS

    • Atomic storage (register abstraction)

    • Consensus (state machine replication)

PODC ’07: Refined Quorum SystemsSlide 5


This talk

This talk

  • Why RQS?

  • What is RQS?

  • How to use RQS?

PODC ’07: Refined Quorum SystemsSlide 6


A simple example

A simple example

  • Single writer crash-tolerant atomic storage

  • Implemented over 5 servers

  • Any majority is a quorum (2 servers may crash)

WRITE (v1)

W

S

E

R

V

E

R

S

1

2

3

4

5

R1

R2

READ -> v1

READ

PODC ’07: Refined Quorum SystemsSlide 7


A simple example1

A simple example

What if we want to expedite only best-case operations

that access all (5) servers?

WRITE (v1)

W

S

E

R

V

E

R

S

1

2

3

4

5

R1

R2

READ -> v1

READ

PODC ’07: Refined Quorum SystemsSlide 8


A simple example2

A simple example

Do we really need to access all servers?

Is it sufficient to access only 4?

WRITE (v1)

W

S

E

R

V

E

R

S

1

2

3

4

5

R1

R2

READ -> v1

READ

PODC ’07: Refined Quorum SystemsSlide 9


What is really going on

What is really going on?

  • Traditional quorum intersections are too small for building optimistic, yet resilient, atomic storage

W Quorum

R1 Quorum

3

4

2

5

1

R2 Quorum

PODC ’07: Refined Quorum SystemsSlide 10


What is really going on1

What is really going on?

  • Intuitively, if all servers are accessed operations can be expedited

W Quorum

R1 Quorum

3

4

2

5

1

R2 Quorum

PODC ’07: Refined Quorum SystemsSlide 11


What is really going on2

What is really going on?

  • In a set of 5 servers, an intersection of any 2 subsets of 4 servers, intersects with a subset of 3 servers

R1 Quorum

W Quorum

3

4

2

5

1

R2 Quorum

PODC ’07: Refined Quorum SystemsSlide 12


Question

Question

  • What mathematical abstraction captures these "larger" intersections in the general context of

    • Byzantine failures (w/o authentication)?

    • Non-threshold quorums/failures?

    • Graceful degradation?

Answer:

Refined Quorum Systems

PODC ’07: Refined Quorum SystemsSlide 13


Refined quorum systems1

Refined Quorum Systems

  • Consider object O implemented over a set of processes S

  • RQS: 3 classes of refined quorums (subsets of S)

    Class 3  Class 2  Class 1

  • Let l1 be the best possible latency for O: no failures, synchrony and no-contention

    • Let l2,l3 be the next best possible latencies

Class j quorum

correct

Synchrony

no contention

=

+

+

=

Latency lj is achieved!

PODC ’07: Refined Quorum SystemsSlide 14


Back to the example

Back to the example

  • Any quorum that contains at least 4 servers is class 1

  • Other quorums (simple majorities) are class 2

W quorum

(Class 1)

R1 quorum

(Class 1)

3

4

2

5

  • l1 – 1 round trip

  • l2 – 2 round trips

1

R2 quorum

(Class 2)

PODC ’07: Refined Quorum SystemsSlide 15


Refined quorum systems definition

Refined Quorum Systems(definition)

Consider a set S, let RQS be any set of quorums (subsets of S)

Consider an adversary structure BforS:

Bis a set of subsets of S such that: B’B: B’’ B’  B’’B

RQS is a refined quorum system, if:

 QC1, QC2: QC1  QC2  QC3 = RQS, such that:

(elements ofQCiare called class i quorums)

P1)  Q3, Q3’ QC3: Q3  Q3’  B

P2)  Q1, Q1’ QC1,  Q3QC3 ,  B1, B2B:

Q1  Q1’  Q3  B1  B2

P3)  Q2QC2,  Q3QC3 ,  B1, B2B:

 Q2  Q3  B1  B2

  Q1QC1: Q1  Q2  Q3  B

PODC ’07: Refined Quorum SystemsSlide 16


Application 1 storage

Application 1: Storage

  • Single writer atomic storage (register)

  • Clients

    • Crash faulty (non-Byzantine)

  • Servers

    • RQS formed around servers

    • Do not communicate among themselves

    • Send messages only in response to clients

  • Safety

    • Byzantine server failures: adversary B

    • Any number of crash failures!

  • Liveness

    • As long as there is (any) quorum of correct servers

PODC ’07: Refined Quorum SystemsSlide 17


Application 1 storage1

Application 1: Storage

Client

(reader or writer)

2nd round-trip

3rd round-trip

Class 2

quorum

S

E

R

V

E

R

S

Class 3 quorum

Class 1 quorum

li = i round-trips (i=1..3)

Synchrony + no contention

PODC ’07: Refined Quorum SystemsSlide 18


Application 2 consensus

Application 2: Consensus

  • Consensus (Lamport’s SMR framework)

  • Proposers, learners

    • Any number may be Byzantine

  • Acceptors

    • RQS formed around acceptors

    • may communicate among each other

  • Safety

    • Byzantine acceptor failures: adversary B

  • Liveness

    • As long as there is (any) quorum of correct acceptors

    • Eventual synchrony (FLP)

PODC ’07: Refined Quorum SystemsSlide 19


Application 2 consensus1

Application 2: Consensus

propose(v)

proposer

Class 1 quorum

Class 2 quorum

Class 3 quorum

A

C

C

E

P

T

O

R

S

learners

learn v

learn v

learn v

li = i+1 message delays (i=1..3)

Synchrony + no contention

PODC ’07: Refined Quorum SystemsSlide 20


Some open questions

(Some) Open questions

  • Authentication and weaker semantics

  • Number of RQS given a set S and adversary

  • Opaque RQS

PODC ’07: Refined Quorum SystemsSlide 21


Summary

Summary

An abstraction to devise

resilient & optimistic algorithms

Refined Quorum Systems

(RQS)

PODC ’07: Refined Quorum SystemsSlide 22


Refined quorum systems

Thank you

PODC ’07: Refined Quorum SystemsSlide 23


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