Chapter 6 Wenbing Zhao Department of Electrical and Computer Engineering Cleveland State University Building Dependable Distributed Systems Building Dependable Distributed Systems, Copyright Wenbing Zhao 1

Wenbing Zhao Outline Distributed consensus and Paxos algorithms  Distributed consensus problem  Classic Paxos  Multi-Paxos

Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao Distributed Consensus Distributed consensus is a fundamental problem in distributed computing  Ensure replica consistency Asynchronous distributed system  No upper bound on processing time  No upper bound on clock drift rate  No upper bound on networking delay In an asynchronous distributed system, you cannot tell a crashed process from a slow one, even if you can assume that messages are sequenced and retransmitted (arbitrary numbers of times), so they eventually get through

Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao FLP Impossibility Results FLP (Fischer, Lynch and Paterson) Impossibility result  A single faulty process can prevent consensus  Because a slow process is indistinguishable from a crashed one Chandra/Toueg Showed that FLP Impossibility applies to many problems, not just consensus  In particular, they show that FLP applies to group membership, reliable multicast  So these practical problems are impossible to solve in asynchronous systems  They also look at the weakest condition under which consensus can be solved Ways to bypass the impossibility result  Use unreliable failure detector  Use a randomized consensus algorithm

Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao Distributed Consensus Older generation of consensus algorithms rely on the use of an unreliable failure detector to exclude failed processes from the consensus consideration  Difficult to understand and harder to prove for correctness The Paxos algorithm introduced by Lamport  Separate safety and liveness properties  “Paxos is among the simplest and most obvious of distributed algorithm” by Lamport  Consensus can be reached during periods of synchrony  No consensus is possible if system very asynchronous, but guarantees no disagreement

Consensus Problem Safety:  Only a value that has been proposed may be chosen  If a value is chosen by a process, then the same value must be chosen by any other process that has chosen a value  If a process learns a value, then the value must have been chosen by some process Liveness:  Some proposed value is eventually chosen and, if a value has been chosen, then a process can eventually learn the value Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm – Consensus for Asynchronous Distributed Systems Contribution: separately consider safety and liveness issues. Safety can be guaranteed and liveness is ensured during period of synchrony Participants of the algorithm are divided into three categories  Proposers: those who propose values  Accepters: those who decide which value to choose  Learners: those who are interested in learning the value chosen Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm How to choose a value  Use a single acceptor: straightforward but not fault tolerant  Use a number of acceptors: a value is chosen if the majority of the acceptors have accepted it Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao Accepted does not mean chosen. However, if a value has been chosen, it must have been accepted first

The Paxos Algorithm Requirements for choosing a value  P1. An acceptor must accept the first proposal that it receives  P2. If a proposal with value v is chosen, then every higher- numbered proposal that is chosen has value v Since the proposal numbers are totally ordered, P2 guarantees the safety property Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm How to guarantee P2?  P2a: If a proposal with value v is chosen, then every higher-numbered proposal accepted by any acceptor has value v But what if an acceptor that has never accepted v accepted a proposal with v’?  P2b: if a proposal with value v is chosen, then every higher-numbered proposal issued by any proposer has value v P2b implies P2a, which implies P2 Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm How to ensure P2b? P2c: For any v and n, if a proposal with value v and number n is issued, then there is a set S consisting of a majority of acceptors such that either  (a) no acceptor in S has accepted any proposal numbered less than n, or  (b) v is the value of the highest-numbered proposal among all proposals numbered less than n accepted by the acceptors in S Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm To ensure P2c, an acceptor must promise:  It will not accept any more proposals numbered less than n, once it has accepted a proposal n Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm Phase 1.  (a) A proposer selects a proposal number n and sends a prepare request with number n to a majority of acceptors.  (b) If an acceptor receives a prepare request with number n greater than that of any prepare request to which it has already responded, then it responds to the request with a promise not to accept any more proposals numbered less than n and with the highest-numbered proposal (if any) that it has accepted. Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm Phase 2.  (a) If the proposer receives a response to its prepare requests (numbered n) from a majority of acceptors, then it sends an accept request to each of those acceptors for a proposal numbered n with a value v, where v is the value of the highest-numbered proposal among the responses, or is any value if the responses reported no proposals.  (b) If an acceptor receives an accept request for a proposal numbered n, it accepts the proposal unless it has already responded to a prepare request having a number greater than n. Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

The Paxos Algorithm Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao

Importance of Keeping Promises (for not accepting older proposal) Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao Not a problem if a value has been chosen

Importance of Keeping Promises (for not accepting older proposal) Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao Safety violated without promise with competing proposers

Importance of Keeping Promises (for not accepting older proposal) Building Dependable Distributed Systems, Copyright Wenbing Zhao Wenbing Zhao Safety is ensured by the promise with competing proposers

Multi-Paxos: Paxos for State Machine Replication Client: partially assumes the role of a proposer Server replicas: acceptors Value to be agreed on: total ordering of requests sent by clients Total ordering accomplished by running a sequence of instances of Paxos  Each instance is assigned a sequence number, representing the total ordering of the request that is chosen  Value to be chosen: the request chosen for the instance Building Dependable Distributed Systems, Copyright Wenbing Zhao 19

Multi-Paxos: Paxos for State Machine Replication Client: partially assumes the role of a proposer  Only propose a value (i.e., request it sends) without the corresponding proposal number  A server replica, the primary, decides on the proposal number Primary: essentially the proposer in Paxos  Propose a sequence number – request binding  Propagate value chosen (i.e., total ordering info) to other replicas (i.e., learners) Initial membership is known with a sole primary  First phase can be omitted during normal operation  When the primary is suspected, a new primary is elected (view change) Building Dependable Distributed Systems, Copyright Wenbing Zhao 20

Multi-Paxos: Paxos for State Machine Replication Normal operation of Multi-Paxos Building Dependable Distributed Systems, Copyright Wenbing Zhao 21

Multi-Paxos: Checkpointing and Garbage Collection Paxos is open-ended: it never terminates  A proposer is allowed to initiate a new proposal even if every acceptor has accepted a proposal  An acceptor must remember the last proposal that it has accepted and the latest proposal number it has accepted In Multi-Paxos, every replica must remember such info for every instance of Paxos: Need infinite memory Solution: periodic checkpointing, e.g., once for every n requests  Garbage collect logs after taking each checkpoint  Request or control msg needed by a slow replica may not be available anymore after a checkpoint => state transfer Building Dependable Distributed Systems, Copyright Wenbing Zhao 22

Multi-Paxos: Leader Election and View Change Leader election: can be done using a full Paxos instance New primary needs to determine if a value has been chosen in each incomplete instance of Paxos Leader election and history determination can be done in a simple full paxos: view change Building Dependable Distributed Systems, Copyright Wenbing Zhao 23

Multi-Paxos: View Change A set of 2f+1 replicas, replica id: 0,1,…,2f History of system: a sequence of views  Each view: one and only one primary  Initially replica 0 assumes the primary role for v=0  Subsequently, replicas take the primary role in a round-robin fashion To ensure liveness  A replica starts a view change timer on the initiation of each instance of Paxos  If the replica does not learn the request chosen before timer expires => suspect the primary Building Dependable Distributed Systems, Copyright Wenbing Zhao 24

View Change On suspecting the primary, a replica broadcasts a view change message to all Current primary, if it is wrongly suspected, joins the view change anyway (i.e., it steps down from primary role) A replica joins the view change even if it’s view change timer has not expired yet On joining view change, a replica stops accepting normal control msgs and respond to only checkpointing and view change msgs Building Dependable Distributed Systems, Copyright Wenbing Zhao 25

View change View change msg contains  New view #  Seq# of last stable checkpoint  A set of accepted records since last stable checkpoint Each record consists of view#, seq#, request msg On receiving f+1 view change msgs, new primary sends new view msg  Include a set of accept msgs Include all accepted msgs as part of view change msg When a gap in seq# is detected, create an accept request with no op A replica accepts new view msg if it has not installed a newer view Building Dependable Distributed Systems, Copyright Wenbing Zhao 26

Dynamic Paxos Designed to accommodate reconfiguration Extension majority concept to quorum Classic Paxos => uses static quorum Dynamic quorum: quorum size may change dynamically Cheap Paxos uses dynamic quorum Building Dependable Distributed Systems, Copyright Wenbing Zhao 27

Dynamic Paxos Fewer replicas are required by using spare replicas and reconfiguration provided no other fault during reconfiguration Without reconfiguration, 3f+1 replicas can only tolerate up to 3f/2 faulty replicas 2f+1 active replicas, plus f spares can tolerate up to 3f-1 faulty replicas via substitution and reconfiguration  As long as 1 active replica and 1 spare are operating Building Dependable Distributed Systems, Copyright Wenbing Zhao 28

Dynamic Paxos Reconfiguration request must be totally ordered with respect to regular application requests A reconf request includes both new membership and quorum definition Replicas in the new membership should not accept msgs unrelated to reconf from replicas that have been excluded from the membership  External replicas should not be allowed to participate the consensus step  Replica mistakenly excluded can join via recofiguration Building Dependable Distributed Systems, Copyright Wenbing Zhao 29

Building Dependable Distributed Systems, Copyright Wenbing Zhao 30

Building Dependable Distributed Systems, Copyright Wenbing Zhao 31

Cheap Paxos Cheap Paxos is a special instance of Dynamic Paxos Aims to minimize involvement of spare replicas Enable the use of f+1 active replicas to tolerate f faults, provided that sufficient spares are available (f or more)  Active replicas are referred to as main replicas  Spare replicas are referred to as auxiliary replicas Building Dependable Distributed Systems, Copyright Wenbing Zhao 32

Cheap Paxos Primary quorum  Consists of all active replicas Secondary quorum  Must be formed by the majority of combined replicas  Consists of at least one main replica => Ensures intersection between primary and secondary quorums Question: what if only one active replica left? Building Dependable Distributed Systems, Copyright Wenbing Zhao 33

Building Dependable Distributed Systems, Copyright Wenbing Zhao 34

Building Dependable Distributed Systems, Copyright Wenbing Zhao 35

Cheap Paxos Upon detection of the failure of an active replica, a reconfiguration request is issued  New primary quorum still consists of all surviving active replicas When reconfig request is executed, switch to new configuration Auxiliary replicas are not bothered unless a reconfiguration is necessary What if the primary fails => view change Building Dependable Distributed Systems, Copyright Wenbing Zhao 36

Cheap Paxos: View Change For history information: new primary must collect info from every active replica except the old primary For approval of the primary role, the new primary must collect votes from all surviving active replicas plus one or more auxiliary replica => a secondary quorum The secondary quorum is used to complete all Paxos instances started by old primary but not yet completed Building Dependable Distributed Systems, Copyright Wenbing Zhao 37

Cheap Paxos Replicas in secondary quorum must propagate their knowledge to all replicas prior to moving back to primary quorum  So that auxiliary replicas do not have to keep all requests and control msgs How to achieve this  Primary notifies its latest state to all replicas not in secondary quorum  Main replica (if it is not in secondary quorum) requests for retransmission of missing msgs  Auxiliary replica keeps new info from primary and purge old data, and ack to the primary  Primary resumes ordering requests after it receives ack from every replica Building Dependable Distributed Systems, Copyright Wenbing Zhao 38

Example Building Dependable Distributed Systems, Copyright Wenbing Zhao 39

Example Building Dependable Distributed Systems, Copyright Wenbing Zhao 40

Example Building Dependable Distributed Systems, Copyright Wenbing Zhao 41

Example Building Dependable Distributed Systems, Copyright Wenbing Zhao 42

Fast Paxos Multi-Paxos: use one round of P1 for all instances of Paxos Fast Paxos: aims to further reduce the cost of consensus by running one P2a for all instances of Paxos  Enables an acceptor to select a value (provide by a client) unilaterally and sends P2b to the primary  However, there is no free lunch => we need more replicas to tolerate f faulty nodes (> 2f+1 for sure)  We will also have to deal with collision recovery Building Dependable Distributed Systems, Copyright Wenbing Zhao 43

Fast Paxos: Basic Steps Fast Paxos runs in rounds and each round has up to two phases  In each round, 1 st phase: prepare phase to enable the coordinator to solicit the status and promises  2 nd phase for the coordinator to select a value to be voted on  When an acceptor responded to P1a in round i, it has participated the round I  When an acceptor sent P2b in response to P2a, it has casted its vote Building Dependable Distributed Systems, Copyright Wenbing Zhao 44

Fast Paxos: Basic Steps Start from an initial membership, phase 1 will always enable the coordinator to select any value for P2b  Need to run P1 once for all rounds  Need to run P2a once for all rounds => eliminate another communication step Classic round is used only when a consensus is not reached in the fast round  Due to coordinator faiure  Due to a collsion Building Dependable Distributed Systems, Copyright Wenbing Zhao 45

Fast Paxos: Normal Operation Building Dependable Distributed Systems, Copyright Wenbing Zhao 46

Fast Paxos: Collision Recovery In the presence of multiple clients, acceptors may chose different requests (values) The coordinator must collect from a quorum of replicas on their values and select the right value  On detecting a collision, i.e., the presence of multiple values, the coordinator initiates a Classic round  Phase 1 can be omitted in Classic round because the coordinator already collected enough info Building Dependable Distributed Systems, Copyright Wenbing Zhao 47

Fast Paxos: Quorum Requirement Quorum based on majority will not work  Coordinator cannot rule out any value in the presence of collision  Any value could have been chosen The coordinator must select a value that have been chosen or might have been chosen Intuition: coordinator selects a value only if it is present in the majority of the votes collected  Need to make sure that a value in the minority could not have been chosen Building Dependable Distributed Systems, Copyright Wenbing Zhao 48

Fast Paxos: Quorum Requirement How to ensure that a value in the minority could not have been chosen  First, it cannot be chosen in the same fast round => the majority value makes it impossible  Second, make sure two fast quorums (Rf) intersect in more than half of |Rf| acceptors  Third, make sure any fast quorum Rf, and any classic quorum Rc intersect in more than half of |Rc| acceptors Building Dependable Distributed Systems, Copyright Wenbing Zhao 49

Fast Paxos: Quorum Requirement Let total number of acceptors be n, number of faults tolerated in a fast round e, and # of faults tolerated in a classic round f Derive inequalities (n-f)+(n-f)-n>0 (n-e)+(n-e)-n>(n-e)/2 (n-e)+(n-f)-n>(n-f)/2 Reduce to  n > 2f and n > 2e+f Building Dependable Distributed Systems, Copyright Wenbing Zhao 50

Fast Paxos: Quorum Requirement First quorum formation: maximize e => e=f, n> 3f => |Rc| = n-f > 2f => n = 3f+1 Second quorum formation: maximize f  f < n/2  e <= n/4  If e=1, n=4; |Rf| = |Rc| = 3 Building Dependable Distributed Systems, Copyright Wenbing Zhao 51

Fast Quorum: Coordinator Value Selection Rule If no acceptor has casted any vote, the coordinator gets to select any value for P2b If only a single value in the votes, select that value If multiple values, select that one that is in the majority, if one is present. Otherwise, select any value Building Dependable Distributed Systems, Copyright Wenbing Zhao 52