Modeling A Read-Write Version Of Texel: An Asynchronous Consensus Algorithm Without Rounds
In the previous post service I gave a model of atomic Texel, where a node tin atomically read all other nodes' determination together with update its ain decision. Here is a refined version of that, where a node tin atomically read the terra firma of *one* other node together with update its decision. This refined model shows why it is of import for the nodes to read from consistent cuts, together with how when multiple nodes are experimenting they tin violate this requirement, together with Agreement belongings is violated every bit a result.
Each node starts amongst t=FALSE (the determination is non finalized), pollSet= Procs \{self} (the node tin poll all nodes except self), together with tally=<<0,0>> (the number of votes from the polled nodes for "a" together with "b" is initally 0 together with 0).
Each node has iii actions that it tin select from together with execute every bit long every bit the node has non finalized its determination or crashed.
The get-go activity starts inwards Line 21. This activity is enabled if the node is inwards experimenting state. It picks (and removes) a node k from its pollSet. If k's determination is "a", it increases the tally for "a" together with if k's determination is "b", it increases the tally for "b". After this, if whatsoever of these tallies is a supporting decision, i.e., is greater than F (which agency it is a bulk of N-F nodes), thence the node adopts it every bit its ain decision.
Line 32 starts the mo action. If f, the actual number of crashes is yet less than F, the allowed number of classes, thence a procedure tin crash, past times setting its determination to crash permanently.
Line 36 starts the 3rd action. If a node finds that its electrical flow determination is shared past times at to the lowest degree N-F processes, thence that determination is "anchored", together with the node tin finalize its determination past times setting its t=TRUE. If no such anchor is inwards place, together with the node is non inwards experimenting state, the node switches to experimenting terra firma (resetting pollSet together with tally). By experimenting again, the node tin potentially modify its determination to closed to other supporting decision, which may atomic number 82 to progress together with finalization of consensus.
Here are the steps to the violation of Agreement. Initially the determination array of nodes is "a","b","b","a".
To attain the security violation, nosotros should disallow concurrent experimentation when it may atomic number 82 to reading from inconsistent snapshots. This is possible past times making the reads preemptive/destructive. (If, instead of using preemptive reads, nosotros elbow grease constraining the nodes to read from solely non-experimenting nodes, deadlock would happen.) In the higher upward trace, when node 2 reads from node 1, this should convey halted node 1's already ongoing experiment. This is slow to accomplish past times extending/modifying the model above, together with when I fixed this problem, I institute that security is e'er satisfied for N>=3*F+1. (I don't render that model, because I am considering assigning modeling Texel together with Ben-Or every bit a TLA+ projection inwards my distributed systems class.)
In that same setup (with <a,b,b,b>), if I arrive F=1, liveness is satisfied, because no node volition re-create a, every bit it volition necessitate to run across closed to other node amongst a earlier passing threshold. So, inwards this case, increasing F did assistance for liveness. This suggests that mayhap nosotros should innovate closed to other gratis parameter to serve every bit threshold for value adoption, together with non necktie that strictly to F the potential number of faults.
By restricting the occupation to binary (with solely 2 values) consensus together with amongst proper choice of the threshold for adoption, Texel may solve the occupation of having a minority value circulating inwards the organisation forever together with breaking progress. But fifty-fifty then, nosotros convey closed to other progress violation problem. When nosotros innovate experiment cancellation to satisfy the Agreement property, nodes that conk on interfering together with canceling each others' experiments volition violate progress.
This is closed to other house where having a leader for consensus provides advantage. The leader past times Definition reads from a consistent state, every bit for that circular the other nodes are passive. When you lot convey each node polling for itself, coordinate these distributed transactions to read from attain clean consistent states becomes really hard (maybe requires consensus itself).
Picking upward from the thread of previous give-and-take on comparison Texel together with Paxos, hither are pros together with cons of appointing a leader node for solving consensus.
There may locomote symmetry, together with no clear winner, when at that topographic point are multiple initial values nowadays inwards the system. Using a leader breaks the symmetry, because nodes conk amongst whatever the leader proposes every bit the vote to determine on. So using a leader, you lot tin solve to a greater extent than than simply binary consensus. Even amongst binary consensus, every bit nosotros convey seen inwards Texel, liveness tin yet locomote jeopardized due to experiment cancellation. And inwards Ben-Or, liveness is facilitated past times jolting the organisation past times using random changes of closed to values, thence that the organisation volition eventually probabilistically converge to a consensus. On the other hand, using a leader boosts liveness inwards the presence of multiple initial values. (Errr... when things conk right. See below.)
On the other hand, trusting a leader to complete a circular introduces a problem. What if the leader is dead? (2PC blocking problem!) In fellowship to avoid getting stuck forever, nodes should role a failure detector. Then, upon suspicion of the leader's death, whatsoever node tin start a novel circular to atomic number 82 the residuum of the nodes. But what if the suspicion is wrong? The FLP impossibility effect strikes again! Fortunately, at that topographic point is a way to circumvent the impossibility effect past times postponing liveness together with yet preserving safety. For example, Paxos preserves security fifty-fifty amongst multiple leaders concurrently trying to atomic number 82 rounds.
Another drawback amongst having a leader is, if northward is large, the leader is a functioning bottleneck inwards the deterministic together with instant consensus protocols, similar Paxos.
The model
This builds together with extends over the previous model. northward stands for number of nodes, together with F denotes the number of nodes that tin crash. We role f to conk on rail of actual number of nodes that crash. In add-on to the *decision* array that tracks the determination of each node, nosotros at in i trial convey an *exp* array that denotes the experimentation condition of each node. Initially each node is inwards the experimenting state.Each node starts amongst t=FALSE (the determination is non finalized), pollSet= Procs \{self} (the node tin poll all nodes except self), together with tally=<<0,0>> (the number of votes from the polled nodes for "a" together with "b" is initally 0 together with 0).
Each node has iii actions that it tin select from together with execute every bit long every bit the node has non finalized its determination or crashed.
The get-go activity starts inwards Line 21. This activity is enabled if the node is inwards experimenting state. It picks (and removes) a node k from its pollSet. If k's determination is "a", it increases the tally for "a" together with if k's determination is "b", it increases the tally for "b". After this, if whatsoever of these tallies is a supporting decision, i.e., is greater than F (which agency it is a bulk of N-F nodes), thence the node adopts it every bit its ain decision.
Line 32 starts the mo action. If f, the actual number of crashes is yet less than F, the allowed number of classes, thence a procedure tin crash, past times setting its determination to crash permanently.
Line 36 starts the 3rd action. If a node finds that its electrical flow determination is shared past times at to the lowest degree N-F processes, thence that determination is "anchored", together with the node tin finalize its determination past times setting its t=TRUE. If no such anchor is inwards place, together with the node is non inwards experimenting state, the node switches to experimenting terra firma (resetting pollSet together with tally). By experimenting again, the node tin potentially modify its determination to closed to other supporting decision, which may atomic number 82 to progress together with finalization of consensus.
Safety violation
When I model-check this protocol for N=4, F=1, this model violates the Agreement property. Two nodes tin finalize their decisions amongst dissimilar values, because they experiment concurrently, together with i of them reads from an inconsistent cut. In the line below node 2 builds its supporting determination on an inconsistent snapshot involving 1, which changes its terra firma subsequently beingness read past times 2.Here are the steps to the violation of Agreement. Initially the determination array of nodes is "a","b","b","a".
- Node 1 reads from node 2 the value "b".
- Node 2 reads from node 1 the value "a". (Note that 2 nodes are concurrently experimenting together with reading terra firma from each other which volition teach inconsistent soon.)
- Node 1 reads from node 3 the value "b", together with since tally for "b" is to a greater extent than than F=1, node 1 changes its determination to "b", together with concludes its experimentation.
- Node 1 finalizes its determination of "b", because it sees an anchored quorum (cardinality >= N-F) for "b".
- Node 2 reads node iv the value "a", together with since tally for "a" is to a greater extent than than F=1 (including the at in i trial invalid vote from Node 1), node 2 changes its determination to "a", together with concludes its experimentation.
- Node 3 reads from node 2 the value "a".
- Node 3 reads node iv the value "a", together with since tally for "a" is to a greater extent than than F=1, node 3 changes its determination to "a", together with concludes its experimentation.
- Node 2 finalizes its determination of "a", because it sees an anchored quorum (cardinality >= N-F) for "a". This determination violates Agreement, because Node 1 has finalized its determination to "b", together with nosotros convey conflicting decisions.
To attain the security violation, nosotros should disallow concurrent experimentation when it may atomic number 82 to reading from inconsistent snapshots. This is possible past times making the reads preemptive/destructive. (If, instead of using preemptive reads, nosotros elbow grease constraining the nodes to read from solely non-experimenting nodes, deadlock would happen.) In the higher upward trace, when node 2 reads from node 1, this should convey halted node 1's already ongoing experiment. This is slow to accomplish past times extending/modifying the model above, together with when I fixed this problem, I institute that security is e'er satisfied for N>=3*F+1. (I don't render that model, because I am considering assigning modeling Texel together with Ben-Or every bit a TLA+ projection inwards my distributed systems class.)
Liveness violation
Liveness is too an interesting story. Even amongst F=0 together with starting terra firma of <<"a","b","b","b">>, nosotros tin convey a liveness violation. With F=0, reading from i node is plenty to modify your vote. So the value of "a" may locomote circulated inwards the system, since it tin conk on getting adopted past times closed to other minority of processes. The organisation may non locomote able to anchor the bulk value every bit the consensus value, together with every bit a effect cannot finalize a decision. Side note: When you lot appoint a leader for consensus (as inwards Paxos) this vote looping does non conk an issue, because the leader volition interruption the symmetry past times dictating the value it picks (or a suitable value) to the other nodes for adoption.In that same setup (with <a,b,b,b>), if I arrive F=1, liveness is satisfied, because no node volition re-create a, every bit it volition necessitate to run across closed to other node amongst a earlier passing threshold. So, inwards this case, increasing F did assistance for liveness. This suggests that mayhap nosotros should innovate closed to other gratis parameter to serve every bit threshold for value adoption, together with non necktie that strictly to F the potential number of faults.
By restricting the occupation to binary (with solely 2 values) consensus together with amongst proper choice of the threshold for adoption, Texel may solve the occupation of having a minority value circulating inwards the organisation forever together with breaking progress. But fifty-fifty then, nosotros convey closed to other progress violation problem. When nosotros innovate experiment cancellation to satisfy the Agreement property, nodes that conk on interfering together with canceling each others' experiments volition violate progress.
This is closed to other house where having a leader for consensus provides advantage. The leader past times Definition reads from a consistent state, every bit for that circular the other nodes are passive. When you lot convey each node polling for itself, coordinate these distributed transactions to read from attain clean consistent states becomes really hard (maybe requires consensus itself).
MAD questions
1. What are the advantages together with disadvantages of appointing a leader for solving consensus?Picking upward from the thread of previous give-and-take on comparison Texel together with Paxos, hither are pros together with cons of appointing a leader node for solving consensus.
There may locomote symmetry, together with no clear winner, when at that topographic point are multiple initial values nowadays inwards the system. Using a leader breaks the symmetry, because nodes conk amongst whatever the leader proposes every bit the vote to determine on. So using a leader, you lot tin solve to a greater extent than than simply binary consensus. Even amongst binary consensus, every bit nosotros convey seen inwards Texel, liveness tin yet locomote jeopardized due to experiment cancellation. And inwards Ben-Or, liveness is facilitated past times jolting the organisation past times using random changes of closed to values, thence that the organisation volition eventually probabilistically converge to a consensus. On the other hand, using a leader boosts liveness inwards the presence of multiple initial values. (Errr... when things conk right. See below.)
On the other hand, trusting a leader to complete a circular introduces a problem. What if the leader is dead? (2PC blocking problem!) In fellowship to avoid getting stuck forever, nodes should role a failure detector. Then, upon suspicion of the leader's death, whatsoever node tin start a novel circular to atomic number 82 the residuum of the nodes. But what if the suspicion is wrong? The FLP impossibility effect strikes again! Fortunately, at that topographic point is a way to circumvent the impossibility effect past times postponing liveness together with yet preserving safety. For example, Paxos preserves security fifty-fifty amongst multiple leaders concurrently trying to atomic number 82 rounds.
Another drawback amongst having a leader is, if northward is large, the leader is a functioning bottleneck inwards the deterministic together with instant consensus protocols, similar Paxos.
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