Paxos Algorithm Overview

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Questions and Answers

What is the main problem that the Paxos algorithm addresses?

  • Remove all non-Byzantine faults
  • Increase message transmission speed
  • Ensure all processors are always operational
  • Define a total order of clients’ requests (correct)

Paxos ensures the system can progress with any majority of processors functioning.

True (A)

What is the core function of the Paxos algorithm?

Consensus algorithm

Paxos addresses issues caused by __________ failures and recoveries.

<p>crash</p> Signup and view all the answers

Match the following concepts related to Paxos with their descriptions:

<p>Crash failures = Systems stopping unexpectedly Byzantine failures = Arbitrary faults causing incorrect behavior Total order = A defined sequence of operations Partial synchrony = Certain timing assumptions about message delivery</p> Signup and view all the answers

What is the primary purpose of vector clocks in distributed systems?

<p>Ensure causal ordering of commands (A)</p> Signup and view all the answers

Causal requests are propagated in the background in distributed systems.

<p>True (A)</p> Signup and view all the answers

Who is the author of 'The Part-Time Parliament'?

<p>Leslie Lamport</p> Signup and view all the answers

The Paxos algorithm is described in terms of a ___________ on an ancient Greek island.

<p>parliament</p> Signup and view all the answers

Match the following individuals with their contributions related to Paxos:

<p>Leslie Lamport = Authored 'The Part-Time Parliament' Butler Lampson = Helped in publishing Paxos Roberto De Prisco = Revisited the Paxos Algorithm Ken Birman = Editor of TOCS during Lamport's publication</p> Signup and view all the answers

What year did Leslie Lamport submit his paper to TOCS?

<p>1990 (B)</p> Signup and view all the answers

The referees of Lamport's paper considered it very important.

<p>False (B)</p> Signup and view all the answers

Which publication included 'The Part-Time Parliament'?

<p>ACM Transactions on Computer Systems</p> Signup and view all the answers

What is the main purpose of replication in distributed systems?

<p>To provide fault tolerance and availability (B)</p> Signup and view all the answers

In a replicated state machine, all replicas execute the input commands in different orders.

<p>False (B)</p> Signup and view all the answers

What is the characteristic that mandates determinism in replicated state machines?

<p>Error masking</p> Signup and view all the answers

A replicated state machine is also called a __________ approach.

<p>state machine</p> Signup and view all the answers

Match the following types of replication with their descriptions:

<p>Active replication = All replicas execute the same commands in the same order Passive replication = Only designated primary server executes the commands Semi-active replication = Combines aspects of both active and passive Lazy replication = Updates are propagated after a delay</p> Signup and view all the answers

What is a key property that all servers must share in a replicated state machine?

<p>Agreement on command execution (D)</p> Signup and view all the answers

Fault tolerance is more challenging to achieve with active replication compared to passive replication.

<p>False (B)</p> Signup and view all the answers

What does the term 'total order' refer to in the context of replicated state machines?

<p>The requirement that all servers execute commands in the same order</p> Signup and view all the answers

In a distributed system, a client perceives the service as coming from a single __________.

<p>server</p> Signup and view all the answers

Which of the following describes the initial state condition (SMR1) for replicated state machines?

<p>All servers start in the same state (A)</p> Signup and view all the answers

For crash model input dissemination, how many replicas are generally needed?

<p>2f + 1 (B)</p> Signup and view all the answers

Output consolidation in a BFT model requires 2f + 1 replicas.

<p>True (A)</p> Signup and view all the answers

What is another name for primary-backup replication?

<p>Passive replication</p> Signup and view all the answers

In the event of a primary failure, a ______ takes over in primary-backup replication.

<p>backup</p> Signup and view all the answers

Match the type of replication with its description:

<p>Primary-backup = Leader executes and decides order Semi-active = All replicas execute but leader defines order Lazy = Replicas allowed to diverge for performance Active = All replicas execute and respond independently</p> Signup and view all the answers

What is the main issue with non-deterministic replicas?

<p>Their state may diverge despite executing the same inputs. (C)</p> Signup and view all the answers

In prime-backup replication, only the Primary receives requests from clients.

<p>True (A)</p> Signup and view all the answers

What is the potential consequence of a backup taking over after a primary failure?

<p>Long takeover-glitch</p> Signup and view all the answers

The primary in primary-backup replication ensures that backups receive state updates before sending a reply to the ______.

<p>client</p> Signup and view all the answers

What fault model allows the Primary to send updates without waiting for confirmations from Backups?

<p>Reliable network (A)</p> Signup and view all the answers

In semi-active replication, the leader executes all commands and followers wait for the leader's command.

<p>True (A)</p> Signup and view all the answers

How does lazy replication handle replica consistency?

<p>Replicas are allowed to diverge and consistency is guaranteed when the system is idle.</p> Signup and view all the answers

Total order broadcast is used to ensure a deterministic order in ______ replication.

<p>semi-active</p> Signup and view all the answers

What triggers a backup to elect a new primary?

<p>Detecting a failure of the current primary (B)</p> Signup and view all the answers

What is the role of the leader in the Paxos algorithm?

<p>To assign sequence numbers to clients' requests (D)</p> Signup and view all the answers

A new leader is elected only when the current leader is confirmed to be crashed.

<p>False (B)</p> Signup and view all the answers

What is needed for progress in the Paxos algorithm?

<p>Quorum of servers</p> Signup and view all the answers

In the Paxos algorithm, a server accepts a sequence number when it receives _____ ACCEPT messages.

<p>N + 1</p> Signup and view all the answers

Match the following Paxos roles with their functions:

<p>Proposers = Submit requests to be processed Acceptors = Accept proposed requests Learners = Learn the outcome of accepted proposals Leader = Coordinates the request sequence</p> Signup and view all the answers

What happens if multiple leaders are active at the same time?

<p>They may commit identical messages multiple times (B)</p> Signup and view all the answers

The Paxos algorithm can execute two different requests with the same sequence number.

<p>False (B)</p> Signup and view all the answers

What happens when a server crashes and recovers?

<p>Restores its state from the disk and initiates leader election.</p> Signup and view all the answers

When a timer expires, a server suspects the leader is faulty and sends a _____ message.

<p>VIEW-CHANGE</p> Signup and view all the answers

What is the purpose of the PREPARE message sent by a new leader?

<p>To ask for the last request accepted by other servers (B)</p> Signup and view all the answers

Once a leader is elected, it can always stay as the leader without any failures.

<p>False (B)</p> Signup and view all the answers

How does the Paxos algorithm ensure liveness?

<p>Through the ability to elect a leader and achieve quorum.</p> Signup and view all the answers

The algorithm guarantees that execution happens in order of the _____ number.

<p>sequence</p> Signup and view all the answers

Match the following terms to their definitions:

<p>Quorum = A minimum number of votes required for progress Leader election = The process of selecting a new leader when needed Recovery = Restoring a server's state after a failure Message timeout = The duration after which a leader is suspected faulty</p> Signup and view all the answers

Flashcards

Client-Server Model in Replication

A model for distributing services, where multiple servers provide the same service, and clients interact with it as if talking to a single entity.

State in Replication

In replication, a set of variables representing the current state of the system.

State Machine Approach

A way to organize computations where commands are applied sequentially, and each command modifies the system's state and generates outputs.

Replicated State Machine (RSM)

A type of replication where multiple servers start with the same state and execute the same sequence of commands in the same order, ensuring consistent behavior and outputs.

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Error Masking in RSM

The ability to hide failures from users by having multiple replicas handle requests, providing a seamless service even if some replicas fail.

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Determinism in RSM

A key requirement for RSM, ensuring that the same sequence of commands always produces the same state and outputs, regardless of the replica processing it.

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Total Order of Commands in RSM

Ensuring that all replicas receive commands in the same order, crucial for RSM to guarantee consistent outputs.

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Atomic Broadcast

A concept in distributed systems where a message is delivered to all members of a group simultaneously, guaranteeing that they all receive the same message in the same order.

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SMR1: Initial State

A property of replicated state machines requiring that all replicas start with the same initial state, forming the basis for consistent behavior.

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SMR2: Agreement

A property of replicated state machines requiring that all replicas execute the same set of commands, ensuring consistency.

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Paxos

A distributed consensus algorithm invented by Leslie Lamport, named after the Greek Island Paxos, used to reach agreement among multiple nodes in a system, even if some nodes fail.

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Two-Phase Commit

A technique in Paxos where a proposer (leader) gathers votes from acceptors (nodes) before committing a new value. This ensures that only values supported by a majority of acceptors are applied.

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Proposer

In Paxos, a proposer that attempts to generate consensus, similar to a leader in a distributed system.

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Acceptor

In Paxos, a node that can vote on proposed values, playing a role in reaching consensus in the distributed system.

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Replication

A mechanism for replicating data across multiple nodes in a distributed system, achieving fault tolerance and high availability.

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Consensus

A critical concept in Paxos, denoting a state where all participating nodes have reached a consensus on a proposed value.

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Fault tolerance

A system where nodes may be unavailable or may fail, but the system must still function correctly.

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High availability

A property of a system where it remains operational even if some of its components or nodes fail.

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Crash Failures

A type of failure model where nodes can crash and recover, but they do not exhibit malicious behavior. They simply stop working and may later resume.

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Total Order of Clients' Requests

A replication technique that ensures all replicas receive messages in the same order, even if some replicas fail or experience delays. This is essential for maintaining consistency in replicated state machines.

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Partial Synchrony

A system where the timing of messages and events is not perfectly predictable. Even with timeouts, there are uncertainties in network delays and processor speeds.

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Paxos for System Builders (PSB)

A variant of the Paxos algorithm designed to be more practical for system builders. It addresses issues not covered in the original paper, making it more implementable in real-world systems.

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Replicated State Machine

A distributed system architecture where multiple servers maintain identical copies of the system's state and process client requests. All servers execute the same commands, ensuring consistency and fault tolerance.

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Number of Replicas

The number of servers needed in replicated systems depends on the fault model and the type of consistency required. More replicas provide higher fault tolerance but may increase performance overhead.

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Primary Back-up Replication

A distributed system design where a single server (the primary) is responsible for processing requests and maintaining the system's state, while backups passively replicate the primary's actions. Primary failure results in a backup taking over.

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Active Replication

A distributed system design where multiple servers (leaders) can actively process requests and maintain the system's state. Leaders communicate with each other to ensure consistency. Faster fault tolerance but more complex to manage.

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Preemption in Active Replication

In active replication, a leader can be replaced by a backup during a failure. This switch is referred to as preemption, and it ensures that the system remains operational without significant downtime. This is a key advantage of active replication over passive replication.

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Semi-active Replication

A type of replication where all replicas execute received commands but the leader defines the order. This allows for per-message deterministic preemption, where urgent commands can overtake others. It provides faster response time for urgent operations.

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Lazy Replication

A replication approach where replicas are allowed to diverge temporarily for performance optimization. This approach trades consistency for efficiency. Full consistency is only guaranteed when the system is idle.

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Fault Tolerance in Replicated Systems

The ability of a system to continue operating correctly even if some components fail. Replication plays a crucial role in achieving fault tolerance by providing redundant copies of data and functionality.

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Non-deterministic Replica Behavior

A replicated system is considered non-deterministic if its state and behavior are influenced by factors beyond the sequence of commands it executes, such as local parameters, scheduling decisions, or random number generation. This can lead to inconsistencies between replicas, making it difficult to maintain consistency.

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Input Dissemination

The process of forwarding messages to all replicas in a replicated system. This step is crucial for ensuring consistency by ensuring that all replicas receive and execute the same commands.

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Output Consolidation

The process of aggregating the output from multiple replicas in a replicated system into a single result. This step is critical for achieving consistency by validating and merging the outputs from different replicas.

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Crash Fault Model

A type of fault model where servers may experience failures like crashing or being temporarily disconnected, but communication is reliable, ensuring that messages sent eventually reach their destinations. This model requires fewer replicas than the Byzantine fault model.

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Byzantine Fault Model

A type of fault model where servers may exhibit malicious behavior, including sending incorrect information or acting in a way that violates protocol rules. This model requires more replicas than the crash fault model to achieve consensus and fault tolerance.

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Leader in Paxos

The server responsible for assigning sequence numbers to client requests in the Paxos algorithm.

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Quorum in Paxos

The number of servers required to make progress in Paxos, typically calculated as N+1/2, where N is the total number of servers.

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Committing a Message in Paxos

The leader periodically attempts to commit a message by broadcasting it to all servers in the system.

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Leader Election in Paxos

A mechanism in Paxos where a new leader is chosen when the current leader is suspected to have failed. This involves a number of steps, like sending VIEW-CHANGE messages, and electing a new leader.

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VIEW-CHANGE Message in Paxos

A message type in Paxos used to initiate leader election. It is sent by a server to all other servers when it suspects the current leader is faulty.

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Preparing Next Sequence Number in Paxos

The process of the new leader in Paxos gathering information about the last sequence number assigned by the previous leader, to ensure the ordering of requests.

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PREPARE Message in Paxos

A message type in Paxos sent by the new leader to all servers, querying them for the highest sequence number they have accepted.

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PREPARE-OK Message in Paxos

A message type in Paxos sent by a server in response to a PREPARE message, indicating the highest sequence number it has accepted.

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Study Notes

Algorithmic Foundation - Distributed Algorithms

  • Chapter 6 covers Basics of Replication and Paxos.

Chapter Overview

  • Replication:
    • State machine and active replication
    • Passive and primary backup replication
    • Semi-active and lazy replication
  • Paxos:
    • Background
    • Algorithm

Replication

  • Client-server model:

    • Service provided by server(s) is replicated across several servers
    • Client interacts as if it's contacting a single server
    • If a replica fails, the service continues unaffected.

  • Replicated State Machine:

    • Active replication approach
    • All servers start in the same initial state
    • All replicas execute the same commands in the same order
    • Same sequence of state/output

  • Replicated state machine:

    • Error masking
    • Deterministic
    • Message ordering (total order of commands to replicas)

  • Properties that specify the problem:

    • SMR1 Initial state (all servers start in the same state)
    • SMR2 Agreement (all servers execute the same commands)
    • SMR3 Total order (all servers execute the commands in the same order)

  • Agreement and total order implies atomic broadcast

  • Broadcast to whom? Only to servers involved

  • Client-server protocol:

    • Send to all servers then all atomically broadcast OR
    • Send to one server, then it broadcasts, and if no reply in timeout, broadcast to more servers
    • Servers send output to client which consolidates it.

  • Number of servers:

    • Crash model: Typically 2f + 1 replicas (f + 1 in specific cases)
    • BFT model: Typically 3f + 1 replicas
    • In crash model, f + 1 replicas ensure correct output (single reply required)
    • In BFT model, 2f + 1 replicas guarantee majority voting

  • Problems with replicated computation:

    • Non-deterministic component (state and behavior depend on local parameters)
    • Non-deterministic programming constructs
    • Scheduling decisions
    • Shared resources
    • Clocks, random numbers

Replication - Primary Backup

  • Also known as passive replication

  • Only primary executes commands and determines order

  • Uses leader-election algorithm (no atomic broadcast)

  • Supports preemption and non-determinism (active replication doesn't support this)

  • State is transferred to back-ups

  • Backups log commands until a checkpoint is received.

  • Primary fails: Backup takes over

  • Potentially long takeover glitch

  • Non-ordered message diffusion

  • Algorithm (Primary):

    • Execute the request
    • Forward state updates (if any) to backups
    • Send reply to client

  • Algorithm (Backups):

    • Store request in log
    • Update state and handle corresponding request based on log.
    • Detect primary failure; elect a new primary
    • Execute and reply to any requests in the log (if elected as new primary).

  • Fault model is important - reliable network or network commits omission faults (state update messages might get lost). Client confirmation needed from backups.

  • Alternative

    • Use total-order broadcast for requests and assume deterministic replicas.
      -Sufficient to send state updates only periodically.

Replication - Semi-active

  • All servers execute, but leader defines the order first
  • Supports per-message deterministic preemption (e.g., urgent command messages).
  • Commands transferred to followers.
  • Leader informs followers of the next command or command sequence
  • Leader fails: Follower takes over
  • Short takeover-glitch
  • Non-ordered message diffusion (needs leader election algorithm)

Replication - Lazy (optimistic)

  • Replicas eventually become consistent if everything goes well.

  • Trade consistency for performance.

  • Allows client requests to different copies.

  • Replicas allowed to diverge in inconsistent states.

  • Full consistency only guaranteed when the system is idle.

  • Addressing conflicts

  • Vector clocks used to ensure causal ordering and handle those commands that don't need total order.

  • Synchronization among replicas when total order is needed

  • Causal requests are processed in the background.

Paxos

  • Background:

    • From Leslie Lamport's paper
    • Part time Parliament (used to popularize the consensus problem idea).
    • Published with many delays.

  • Literature:

    • Lamport's work and other papers
    • Various papers/publications on Paxos

Paxos - Why Paxos Matters

  • Solves active replication despite any number of crash failures and recoveries.
  • Main problem: define a total order of client requests.
  • Core is a consensus algorithm.
  • Variations/improvements by Lamport and others.

Paxos - System Model

  • Links do not corrupt messages but may omit some.
  • Handles crash failures and recoveries
  • Algorithm is safe even if the system is asynchronous

Paxos - Main Concept

  • Fixed number of servers
  • Leader assigns sequence numbers to client requests
  • If leader suspected of crashing, a new one is elected.
  • Quorum is needed for progress ([N/2] + 1 servers)
  • Algorithm considered proposers, acceptors, learners; alternative (PSB): all roles played by all servers.

Paxos - Main Concept: More Details

  • Leader periodically commits messages.
  • Operation failures due to crashed processes or lost messages.
  • If leader changes, the new leader uses a new view number.
  • Unreliable failure detection might lead to multiple active leaders.
  • Algorithm ensures messages committed by multiple leaders are identical.

Paxos - Normal Case Operation

  • Client sends update to leader
  • Leader sends proposal to other servers
  • Servers respond with accept messages
  • Client gets reply after the update is executed.
  • Proposal messages contain the sequence number

Paxos - Normal Case Operation: (Continued)

  • Sequence number is accepted when [N/2] + 1 accept messages are received.
  • Execution is done in order of sequence numbers.
  • Network may reorder messages, early requests wait for late ones.
  • Servers may crash and recover.
  • On recovery, servers know their state.
  • Leader must synchronize to disk before sending proposals
  • Other servers must sync to disk before sending accepts.

Paxos - Leader Failure

  • Leader election is necessary
  • Prepare next sequence number (finding the last sequence number assigned by previous leader is critical).

Paxos - Leader Failure: Election

  • Server restarts timer after each request execution.
  • If timer expires (no requests), server suspects leader and sends a view-change message.
  • ViewChange message includes the next view number.
  • When receiving [N/2] + 1 view-change messages, a new leader is selected (V mod N).
  • Partial synchronous time model, Timeout increased each time.

Paxos - Leader Failure: Prepare Next Sequence Number

  • After election, new leader sends prepare message to all servers.
  • Asking for the last request they accepted.
  • Servers reply with prepare-ok (promising not to accept earlier proposals).
  • This step ensures that proposal is not conflicting with something previously accepted.
  • This is done immediately before syncing to disk.

Paxos - Leader Failure: Prepare Next Sequence Number (Continued)

  • Leader receives replies from majority of servers.
  • Leader picks the highest sequence number, adds 1 and sets it as the next.
  • Moves to normal case operation

Paxos - Leader Change

  • Example of leader sending proposal and subsequently crashing.
  • S1 and S2 execute request and S1 becomes the new leader.

Paxos - Missing Requests

  • Messages may be omitted so a server may receive request r without r - 1
  • Execution is stopped for pending messages which are missing

Paxos - Recovery

  • When a server recovers it restores its state from disk and starts leader election.
  • May wait time to restart requests.

Paxos - Ensuring Safety

  • Not possible to execute 2 different requests with the same sequence number in the same view.
  • At least [N/2] + 1 servers have to accept (incl. 1 propose)
  • Not possible to execute a request without executing previous requests imposed by local servers.

Paxos - Ensuring Liveness

  • Progress depends on ability to elect a leader and quorum ([N/2]+1).
  • Network stability requirement of the leader election protocol (defined formally)

Paxos - Implementation

  • Issues such as UDP+IP multicast or TCP/IP, flow control, timeouts ("large" or "short"), and aggregation (batching)
  • Some results with PSB.

Paxos - Implementation: Throughput (without aggregation)

  • Figures showing update throughput (updates/sec) versus number of clients, for different numbers of servers.

Paxos - Implementation: Throughput (with aggregation)

  • Figures showing update throughput with aggregation, versus number of clients, for different numbers of servers.

Paxos - Implementation: Latency

  • Figures showing update latency (seconds or milliseconds) versus number of clients, for different numbers of servers.

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