Thank you!
One thing that makes it a little hard for me to follow your notation is that I am unclear on the definitions of beta and lamda. Beta is the rate of block additions to the "main chain" and lamda is the rate of block additions which have some potential to wind up in the main chain if they are accepted. At least, that is my reading of it.
However, there is no point in which a block becomes 100% canonized in the main chain (well, other than checkpointing). It is therefore hard to make a rigorous definition of beta. After all, the block chain is a probabilistic not a deterministic solution to the distributed consensus problem. It seems that the difference between lamda and beta is also called the orphan rate, a term you choose to not use, possibly because you are afraid people will accuse you of suggesting we put orphans to work in the mines
One thing that makes it a little hard for me to follow your notation is that I am unclear on the definitions of beta and lamda. Beta is the rate of block additions to the "main chain" and lamda is the rate of block additions which have some potential to wind up in the main chain if they are accepted. At least, that is my reading of it.
However, there is no point in which a block becomes 100% canonized in the main chain (well, other than checkpointing). It is therefore hard to make a rigorous definition of beta. After all, the block chain is a probabilistic not a deterministic solution to the distributed consensus problem. It seems that the difference between lamda and beta is also called the orphan rate, a term you choose to not use, possibly because you are afraid people will accuse you of suggesting we put orphans to work in the mines
You are right, the chain is never really fixed. But think of it this way: under the standard protocol, a chain only gets replaced by a longer one. We thus only look at the length of the longest chain (ignoring which one it actually is) and check the rate of events that make it grow (this could include a switch to a different chain).
Another comment is that some of the maths you develop could also be useful in analysis of shares in a mining pool.
Thanks! That's an interesting comment that we did not consider. I suppose you refer to issues related to stale shares?