Paxos Algorithm Overview
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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

    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</p> Signup and view all the answers

    Causal requests are propagated in the background in distributed systems.

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

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

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

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

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

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

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

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

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

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

    <p>True</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.</p> Signup and view all the answers

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

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

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

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

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

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

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

    <p>False</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

    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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