The document provides an overview of the basic Paxos protocol, detailing the roles of proposers, acceptors, and learners, and the two-phase process of preparing and accepting proposals. It discusses the normal operation of Paxos, addressing conflicts and illustrating how the protocol ensures consensus. Additionally, it introduces Flexible Paxos, highlighting its quorum intersection requirements and implications for different quorum types.

1. Flexible Paxos
Quorum Intersection Revisited

2. Part I - Basic Paxos

3. Basic Paxos
● Three Roles:
○ Proposer: a process who wishes to have a particular value chosen
○ Acceptor: a process which agrees and persists decided values or the learner
○ Learner: a process wishing to learn the decided value
● Two Phase Process:
○ Prepare / Promise
○ Accept / Commit

4. Prepare / Promise
● A proposer selects a unique proposal number p and sends prepare(p) to the acceptors
● Each acceptor receives prepare(p)
○ If p is the highest proposal number promised, then p is written to persistent
storage and the acceptor replies with promise(p’,v’)
○ (p’,v’) is the last accepted proposal (if present) where p’ is the proposal number
and v’ is the corresponding proposed value
● Once the proposer receives promise from the majority of acceptors, it proceeds to
phase two. Otherwise, it may try again with higher proposal number

5. Accept / Commit
● Proposer selects a value v
○ If any proposal was returned in phase 1 then it must choose the value associated
with the highest proposal number.
○ If no proposals were returned, then the proposer can choose its own value for v
● The proposer then sends propose(p,v) to the acceptors
● Each acceptor receives a propose(p,v)
○ If p is equal to or greater than the highest promised proposal number, then the
promised proposal number and accepted proposal is written to persistent
storage and the acceptor replies with accept(p)
● Once the proposer receives accept(p) from the majority of acceptors, it learns that the
value v is decided

6. Basic Paxos - Normal
OperationP: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P:
C:
X: 1
P:
C:
X: 2
P:
C:
X: 3
Acceptor Acceptor
Proposer, Acceptor

7. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P:
C:
P:
C:
P: 10
C:
X: 3
Acceptor Acceptor
Proposer, Acceptor
Prepare(10) Prepare(10)
Basic Paxos - Normal
Operation

8. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C:
P: 10
C:
P:
C:
X: 3
Acceptor Acceptor
Proposer, Acceptor
Promise( _, _ ) Promise( _, _ )
Basic Paxos - Normal
Operation

9. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
3 3
3
P: 10
C: (10 ,3)
P: 10
C: (10, 3)
P: 10
C: (10, 3)
X: 3
Acceptor Acceptor
Proposer, Acceptor
Commit(10, 3) Commit(10, 3)
Basic Paxos - Normal
Operation

10. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C:
P: 10
C:
P: 10
C: (10, 3)
X: 3
Acceptor Acceptor
Proposer, Acceptor
Commit(10, 3) Commit(10, 3)
Basic Paxos - Normal
Operation

11. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C:
X: 1
P: 10
C:
P:
C:
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 1

12. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C:
X: 1
P: 10
C:
P:
C:
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 1
Papare(9 )
Papare( 9 )

13. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C:
X: 1
P: 10
C:
P:
C:
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 1
Reject
Reject

14. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C:
X: 1
P: 10
C:
P: 10
C:
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 2
Papare(11 )
Papare( 11 )

15. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 11
C:
X: 1
P: 11
C:
P: 11
C:
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 2
Promise( _, _ )
Promise( _, _ )

16. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 11
C:
X: 1
P: 11
C:
P: 11
C:
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 2
Commit(11, 1)
Commit(11, 1)

17. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
1 1
1
P: 11
C: (11, 1)
X: 1
P: 11
C: (11, 1)
P: 11
C: (11, 1)
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 2

18. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
1 1
1
P: 11
C: (11, 1)
X: 1
P: 11
C: (11, 1)
P: 11
C: (11, 1)
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 3
Prepare(12) Prepare(12)

19. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
1 1
1
P: 12
C: (11, 1)
X: 1
P: 12
C: (11, 1)
P: 11
C: (11, 1)
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 3
Promise(11, 1) Promise(11, 1)

20. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
1 1
1
P: 12
C: (11, 1)
X: 1
P: 12
C: (11, 1)
P: 11
C: (11, 1)
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 3
Commit(12, 1) Commit(12, 1)

21. P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
1 1
1
P: 12
C: (12, 1)
X: 1
P: 12
C: (12, 1)
P: 11
C: (12, 1)
X: 3
Proposer, Acceptor Acceptor
Proposer, Acceptor
Basic Paxos - Conflict 3

22. Insight
● Phase 1 is not specific to the request so can be done before the request arrives and
can be reused
○ i.e., elect a leader, and then let it to propose all following proposals

23. Part II - Flexible Paxos

24. ● It is only necessary for phase 1 quorums (Q1) and phase 2 quorums (Q2) to intersect
○ no need to require that Q1’s intersect with each other nor Q2’s intersect with
each other
○ Q1 + Q2 > N (N is the number of acceptors)
Observation

25. Example
P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C: (10, 1)
X: 1
P:
C:
X: 2
P: 10
C:
Proposer, Acceptor Proposer, Acceptor
Acceptor
? ?
Acceptor Acceptor
Q1: 4
Q2: 2
P: 10
C:
P: 10
C: (10, 1)

26. Example
P: the highest promised proposal number
C: the last accepted proposal
X: the value a proposer want to propose
? ?
?
P: 10
C: (10, 1)
X: 1
P:
C:
X: 2
P: 10
C:
Proposer, Acceptor Proposer, Acceptor
Acceptor
? ?
Acceptor Acceptor
Q1: 4
Q2: 2
P: 10
C:
P: 10
C: (10, 1)
Prepare(11)
Prepare(11)
Prepare(11)

27. Implications
● Majority Quorums
● Simple Quorums
● Grid Quorums

28. Implications - Majority Quorums
● Majority Quorums: use quorums of size N/2 + 1
● When the number of acceptors N is even
○ We can safely reduce the size of Q2 by one from N/2 + 1 to N/2

29. Implications - Simple Quorums
● Simple Quorums: any acceptor is able to participate in a quorum and each
acceptor’s participation is counted equally
○ a straightforward generalization of majority quorums
● Paxos requires that all quorums intersect
● In FPaxos (Flexible Paxos) simple quorums require only that quorums from different
phases intersect
○ Q1 + Q2 > N (N is the number of acceptors)
○ for a given size of Q2 and number of acceptors N, the minimum size of our
first phase quorum is Q1 = N − Q2 + 1

30. Implications - Grid Quorums
● Grid Quorums: arrange the N nodes into a matrix of N1 columns by N2 rows,
where N1 ×N2 = N
● Paxos requires that all quorums intersect
○ then it requires one row and one column to form a quorum
● In FPaxos, we can safely reduce our quorums to one row of size N1 for Q1 and one
column of size N2 for Q2
Paxos FPaxos

31. Benchmark
● 64 bytes per request
● A single linux VM with a single core and 1GB of RAM
● use mininet to simulate a 10 Mbps network with 20 ms round trip time

32. Any Questions ?
Thank You!