I am reading "paxos" on wiki, and it reads: "Rounds fail when multiple Proposers send conflicting Prepare messages, or when the Proposer does not receive a Quorum of responses (Promise or Accepted). In these cases, another round must be started with a higher proposal number." But I don't understand how the proposer tells the difference between its proposal not being approved and it just takes more time for the message to transmit?
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If you are interested in learning Paxos it is very helpful to implement it. There is a university that had open sourced it's class on implementing Paxos where they provide a testing framework and you simply write the code. The course work gets progressively harder working up to a full key-value store running Paxos. The project on github.com is DSLabs which so described here blog.acolyer.org/2019/04/17/…
– simbo1905
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One of the tricky parts to understanding Paxos is that the original paper and most others, including the wiki, do not describe a full protocol capable of real-world use. They only focus on the algorithmic necessities. For example, they say that a proposer must choose a number "n" higher than any previously used number. But they say nothing about how to actually go about doing that, the kinds of failures that can happen, or how to resolve the situation if two proposers simultaneously try to use the same proposal number (as in both choosing n=2). That actually completely breaks the protocol and would lead to incorrect results but I'm not sure I've ever seen that specifically called out. I guess it's just supposed to be "obvious".
Specifically to your question, there's no perfect way to tell the difference using the raw algorithm. Practical implementations typically go the extra mile by sending a Nack message to the Proposer rather than just silently ignoring it. There are plenty of other tricks that can be used but all of them, including the nacks, come with varying downsides. Which approach is best generally depends on both the kind of application employing Paxos and the environment it's intended to run in.
If you're interested, I put together a much longer-winded description of Paxos that includes many of issues practical implementations must address in addition to the core components. It covers this issue along with several others.
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Specific to your question it isn't possible for a proposer to distinguish between lost messages, delayed messages, crashed acceptors or stalled acceptors. In each case you get no response. Typically an implementation will timeout on getting less than a quorum response and resend the proposal on the assumption messages were dropped or acceptors are rebooting.
Often implementations add "nack" messages as negative acknowledgement as an optimisation to speed up recovery. The proposer only gets "nack" responses from nodes that are reachable that have accepted a higher promise. The ”nack” can show both the highest promise and also the highest instance known to be fixed. How this helps will be outlined below.
I wrote an implementation of Paxos called TRex with some of these techniques sticking as closely as possible to the description of the algorithm in the paper Paxos Made Simple. I wrote up a description of the practical considerations of timeouts and nacks on a blog post.
One of the interesting techniques it uses is for a timed out node to make the first proposal with a very low number. This will always get "nack" messages. Why? Consider a three node cluster where one network link breaks between a stable proposer and one other node. The other node will timeout and issue a prepare. If it issues a high prepare it will get a promise from the third node. This will interrupt the stable leader. You then have symmetry where the two nodes that cannot message one another can fight with the leadership swapping with no forward progress.
To avoid this a timed out node can start with a low prepare. It can then look at the "nack" messages to learn from the third node that there is a leader who is making progress. It will see this as the highest instance known to be fixed in the nack will be greater than the local value. The timed out node can then not issue a high prepare and instead ask the third node to send it the latest fixed and accepted values. With that enhancement a timed out node can now distinguish between a stable proposer crashing or the connection failing. Such ”nack” based techniques don't affect the correctness of the implementation they are only an optimisation to ensure fast failover and forward progress.
