Trex2: Paxos Algorithm Strong consistency for cluster replication on the Java JVM

TL;DR

This repository contains a Java library that implements the Paxos algorithm as described in Leslie Lamport's 2001 paper Paxos Made Simple

To use this library:

• You will need to implement the Journal interface to persist the state of the algorithm. This can be tables (or documents or key-values) in the database that your application uses.
• At this time you will need to setup the cluster membership manually. You will need to assign a unique node identifier to each node in the cluster.
• This library is designed to be transport agnostic. Examples of plugging in network transport are not complete.

At this time the exhaustive brute force tests are not yet all written so it is not recommended for production use. A release candidate will be made when the exhaustive tests mentioned in this readme are implemented.

Introduction

The ambition of this documentation is to:

1. Provide sufficient detail about the invariants described in the original paper to transcribe them into rigorous tests.
2. Clarify that the approach taken in this implementation is based on a careful and thorough reading of the original papers, watching Lamport's videos, and careful research about other implementations.
3. Provide sufficient detail around the "learning" messages used by this implementation to understand that they are minimal and do not harm correctness.
4. Provide enough documentation so that someone can carefully study the code, the tests, and the papers to verify this implementation with far less overall effort than it would take them to write any equivalent implementation.
5. Explicitly explain the design decisions in this implementation.

As of today, the proceeding list is aspirational. When the exhaustive tests are written, I will invite peer review and possibly offer a nominal bug bounty (which would be a folly I would surely come to regret instantly).

Cluster Replication With Paxos

To replicate the state of any service, we need to apply the same stream of commands to each server in the same order. The paper states (p. 8):

A simple way to implement a distributed system is as a collection of clients that issue commands to a central server. The server can be described as a deterministic state machine that performs client commands in some sequence. The state machine has a current state; it performs a step by taking as input a command and producing an output and a new state.

For example, in a key-value store, commands might be put(k,v), get(k) or remove(k) operations. These commands form the "values" that must be applied consistently at each server in the cluster.

The paper explicitly states that Paxos has a leader (p. 6):

The algorithm chooses a leader, which plays the roles of the distinguished proposer and the distinguished learner.

This means command values are forwarded to the leader, and the leader assigns the order of the command values.

A common misconception is failing to recognize that Paxos is inherently Multi-Paxos. The paper states (p. 10):

A newly chosen leader executes phase 1 for infinitely many instances of the consensus algorithm. Using the same proposal number for all instances, it can do this by sending a single reasonably short message to the other servers.

This enables the algorithm to enter a steady state of streaming only accept messages until a leader crashes or becomes network-isolated. Only then are prepare messages necessary for simultaneous leader election and crash recovery.

The description below refers to server processes as "nodes" within a cluster. This helps to disambiguate the code running the algorithm from the physical server or host process. This repository provides a core library with a node class TrexNode solely responsible for running the core Paxos algorithm.

The Paxos Algorithm

This description will explain it in the following order:

• First, explain that promises apply to both core message types.
• Second, explain the steady state of the algorithm, which uses only accept messages.
• Third, explain how nodes may efficiently learn which values have been fixed.
• Fourth, explain the leader take-over protocol, which is the most complex step that uses both prepare and accept messages.
• Fifth, explain the durable state requirements.
• Sixth, define the invariants of this implementation.
• Seventh, provide a footnote on leader duels.

First: Promises, Promises

The core algorithm uses only two protocol messages, prepare(_,N) and accept(_,N,_)) where N is called a ballot number or a proposal number. Nodes promise to reject protocol messages associated with a lower number than the last N they did not reject. This means each node stores the highest N it has previously acknowledged.

If you have studied Paxos before, you may be surprised to learn that nodes must make promises to both message types. Lamport talks about this fact in a video lecture. He describes it as the only ambiguity in his 2001 paper Paxos Made Simple. He explains that this detail is included in his formal TLA+ specification of the Paxos Algorithm.

The number N must be unique to a given node for the algorithm to be correct. Lamport writes (p. 8):

Different proposers choose their numbers from disjoint sets of numbers, so two different proposers never issue a proposal with the same number.

This is achieved by encoding the node identifier in each Ns lower bits. This library uses a record with a signature similar to this:

public record BallotNumber(int counter, byte nodeIdentifier) implements Comparable<BallotNumber> {
}

The compareTo method treats the four-byte counter as having the most significant bits and the single-byte nodeIndentifier as having the least significant bits. The cluster operator must ensure they assign unique nodeIdentifier values to every node added to the cluster.

In this implementation, nodes never recycle their numbers. They increment their counter each time they attempt to lead. This avoids the need to retransmit values when fixing slots, as explained below.

Second: Steady State Galloping

The objective is to fix the same command value V into the same command log stream index S, known as a log slot, at each node in the cluster. When the network is healthy, and servers have undertaken crash recovery, an uncontested leader sends a stream of commands using accept(S,N,V) messages where:

• S is a log index slot the leader assigns to the command value.
• N is a node's unique ballot number.
• V is a command value.

The value V is fixed at slot S when a mathematical majority of nodes journal the value V into their log. No matter how many leaders attempt to assign a value to the same slot S, they will all assign the same V using different unique N values. How that works is described below.

We can call this steady-state galloping, as things move at top speed using a different stride pattern than when walking (or trotting). A leader will self-accept and transmit the message to the other two nodes in a three-node cluster. It only needs one message response to learn that a mathematical majority of nodes in the cluster have accepted the value. That is the minimum number of message exchanges required to ensure that the value V is fixed. Better yet, our leader can stream accept messages continuously without awaiting a response to each message.

This library uses code similar to the following as the accept message and its acknowledgement:

public record Command( String uuid,
                       byte[] operationBytes){}

public record BallotNumber(int counter, byte nodeIdentifier) {}

public record Accept( long logIndex,
                      BallotNumber number,
                      Command command ) {}

public record AcceptResponse(
    long logIndex,
    BallotNumber number,
    boolean vote ){}

The boolean vote implies each node may respond with either a positive acknowledgement or a negative acknowledgement. This implementation includes negative acknowledgements to both prepare and accept messages. When a leader receives a majority negative response, it abdicates.

Third: Learning Which Values Are Fixed

Any value V journaled into slot S by a mathematical majority of nodes will never change. Cloud environments typically only support point-to-point messaging. This means that AcceptResponse messages are only sent to the leader. As the leader is the first to learn which values are fixed, Lamport calls it the “distinguished learner”.

The leader can send a short fixed(S,N) message to inform the other nodes when a value has been fixed. This message can piggyback at the front of the subsequent outbound accept message network packet. Due to lost messaging, a leader may learn which slots are fixed out of sequential order. In this implementation leaders only send fixed messages in sequential slot order.

Leaders must always increment their counter to create a fresh N each time they attempt to lead. That ensures that each fixed(S,N) refers to a unique accept(S,N,V) message. If any node does not have the matching accept(S,N,V) in its journal, it must request retransmission. This implementation uses a catchup message to request the retransmission of missed accept messages.

This implementation uses code similar to the following to allow nodes other than the leader to learn which values have been fixed:

public record Fixed(
    BallotNumber number,
    long fixedLogIndex) {
}

public record Catchup(long highestFixedIndex) {
}

public record CatchupResponse( List<Accept> catchup ) {}

Each node learns which value V is fixed into each sequential slot S. Each node will then up-call the command value V to the host application.

Fourth: The Leader Takeover Protocol

On leader election (p. 7):

A reliable algorithm for electing a proposer must use either randomness or realtime — for example, by using timeouts. However, safety is ensured regardless of the success or failure of the election.

This library implements leader failure detection by heartbeating fixed messages. Leader election is then by random timeouts. The core algorithm is in a single class TrexNode class. The timeout logic is in the TrexEngine class. This allows you to use a different failure detection library if you like.

When a node times out it attempts to run the leader takeover protocol:

1. The new leader sends prepare(N,S) for all slots any prior leader has attempted to fix
2. For each slot nodes respond with promise messages containing any unfixed {S,N,V} tuples else only {S,N} when it has no value in that slot.
3. For each slot the leader selects the V that was associated with the highest N value from a majority of responses. If there was no value known at that slot by a majority then the new leader can safely use its own command value V at that slot.
4. For each slot the leader sends fresh accept(S,N',V) messages with chosen command V using its own higher N' for each slot.

That description says that the leader takeover protocol is to run the full algorithm for many slots. This can happen in parallel for many slots. The only question is what is the range of slots that we need to recover. It is the range of slots up to the maximum slot any node has journalled a value. We can ask a majority of nodes the highest slot at which they have accepted a value.

This library uses code similar to the following for the prepare message and its acknowledgement:

public record Prepare( long logIndex,
                       BallotNumber number ) {}

public record PrepareResponse(
    long logIndex,
    Optional<Accept> highestUnfixed,
    long highestAccepted,
    boolean vote ) {}

We use highestAccepted value to learn the full range of slots that any past leader has attempted to fix.

Again, whenever a node receives either a prepare or accept message protocol message with a higher N that it replies to positively, it has promised to reject any further protocol messages with a lower N. Again, when a leader learns that a slot is fixed in sequence, it will issue a fixed(S,N). Again, if it gets a majority negative acknowledgement for any slot, it abdicates.

In this implementation, a new leader first issues a prepare for the slot immediately after the highest slot it knows was fixed. The new leader instantaneously sends the response message to itself and instantaneously responds, which is a message that includes its own highestAccepted. When it gets a majority positive response, it computes max(highestAccepted) to know all the slots it must recover. It then streams prepare messages for the full range of slots.

Intuitively, we can think of the first message as a leader election. Hence, we call N a ballot number, and we consider the responses to be votes. In a three-node cluster, a leader only needs to exchange one message to be elected.

Once elected a new leader immediately issues small prepare messages for the full range of slots. Intuitively the new leader is asking nodes to retransmit what they know about all past accept messages. The new leader then collaborates with an old leader by choosing their value. The mathematics of the Paxos algorithm guarantees that all leaders converge on choosing the same value at each slot.

Fifth, Durable State Requirements

The state of each node is similar to the following model:

public record Progress(BallotNumber highestPromised,
                       long fixedIndex) {
}

The progress of each node is its highest promised N and its highest fixed slot S. This is only thirteen bytes of data.

You must also provide an implementation of the journal interface which is similar to this definition:

public interface Journal {
  // this is only called at startup so you could trade write speed for read speed. 
  Progress loadProgress();

  // this is called on every message to persist a small amount of data so you would want to optimise this for write speed.
  void writeProgress(Progress progress);

  // this is called to write data to disk. when there are no crashes or isolated leaders this is write once per slot.
  void writeAccept(long logIndex, Accept accept);

  // this is called during crash recovery or to catchup other nodes and we can expect sequential access patterns. 
  Optional<Accept> readAccept(long logIndex);

  // if the host application is not explicitly managing database transactions this will be called to make all the writes durable. 
  void sync();

  // this is used during startup
  long highestAcceptedSlot();
}

Journal writes must be crash-proof (disk flush or equivalent). The journal's sync() is intended must first flush any commands into their slots and only then flush the progress. The general idea here is that your application probably already has a database, it is almost trivial to implement this interface on top of that database. You can specify that your host code will be managing transactions and the sync() method will not be called and you so you can supply a no-op method.

See the java doc on the Journal interface for more details.

Sixth, The invariants

This implementation enforces the following invariants at each node:

1. The fixed index increases sequentially (therefore, the up-call of {S,V} tuples must be sequential).
2. The promise number only increases (yet it may jump forward).
3. The promised ballot number can only change when processing a prepare or accept message.
4. The fixed index can only change when a leader sees a majority AcceptReponse message, a follower node sees a Fixed message or any node learns about a fixed message due to a CatchupResponse message.

The core of this implementation that ensures safety is written as inequalities comparing integer types. When we unit test the TrexNode class:

• It can only see messages that are less than, greater than, or equal to its promise.
• It can only see messages from another node with a node identifier that is less than, greater than, or equal to its own.
• It can only see messages with a fixed slot index that are less than, greater than, or equal to its own.
• The journal at any slot can have only no value, the no-operation value, or a client command value.
• The journal can either be continuous, have gaps, or not have reached a specific index when that index is learnt to be fixed.

If we consider just testing the prepare message:

1. The node can be in one of three TrexStates: FOLLOW, RECOVER, or LEAD.
2. The node can have a progress.highestPromised().counter() that is less than, greater than, or equal to the counter in the number of the sender.
3. The node can have a progress.highestPromised().highestFixedIndex() that is less than, greater than, or equal to the log index in the message.
4. The node can have a progress.highestPromised().nodeIdentifier() that is less than, greater than, or equal to the node identifier in the message.

We can exhaustively test this by generating a total of 3^4=81 test scenarios. We can also add into that list whether the v the journal at that slot hold either null, no-op, or a client command byte[]. This would give us a total of 3^5=243 test scenarios.

TO BE CONTINUED

Seventh, Leader Duels

The paper states (p. 7):

It’s easy to construct a scenario in which two proposers each keep issuing a sequence of proposals with increasing numbers, none of which are ever chosen.

One pathological scenario exists for a stable network where nodes repeated timeout in an unlucky order such:

• The first node to timeout has the lowest node identifier.
• The second node to timeouts does so before the first node can fix a value into the next slot.

Yet there is also the other scenario where the first node to timeout has the highest node identifier. Then the second node to timeout does not interrupt. If you were to set things up so that you had a 50% probability of two nodes timing out within the time it takes them to complete a full slot recovery you have great odds.

Every timeout you have two chances of success; that the first node to timeout has the highest node identifier, and if not that the lower node is not interrupted before it can complete a full cycle. The odds of success each attempt to elect a leader are 75%, 94%, 99%, ..

This implementation separates the core algorithm into TrexNode and the timeout logic into TrexEngine. It will allow you to use your own node failure detection or election mechanism if you do not like those odds.

See the wiki for a more detailed explanation of this topic.

Development Setup

./setup-hooks.sh

Releases

TBD

Tentative Roadmap

The list of tasks:

• Implement the Paxos Parliament Protocol for log replication.
• Write a test harness that injects rolling network partitions.
• Write property based tests to exhaustively verify correctness.
• Implement a trivial replicated k-v store.
• Implement cluster membership changes as UPaxos.
• Add optionality so that randomised timeouts can be replaced by some other leader failover detection and voting mechanism (e.g. JGroups).

Attribution

The TRex icon is Tyrannosaurus Rex by Raf Verbraeken from the Noun Project licensed under CC3.0