Quote from: stdset on July 06, 2013, 07:02:10 PM

Quote from: d'aniel on July 06, 2013, 09:31:32 AM

1 - e^(-t/T)

Good formula.
Let's extend our analysis a bit.
Let "x" be transaction rate, i.e. number of transactions per second. And "t0" - average transaction validation time, i.e. block validation time divided by number of transactions in that block, in the first approximation we can assume that "t0" doesn't depend on block size.

Than, number of transactions to be validated N = x*T
and time required for validation t = x*T*t0

Thus, orphans rate, expressed with theese variables: 1 - e^(-x*t0). We see, in first approximation it doesn't depend on T. Dependacy on T arises from network delays.

Ah yes, that's right. I actually deleted that post shortly after posting it because I noticed this for a second, but the brain fart won out in the end and I reposted it without fixing it

I should've just written it down explicitly like you did.

This formula is a first approximation, where it is assumed that miners rarely end up working on competing chains. As we lower T while keeping x fixed, we can intuitively see that the likelihood of races between miners increases, i.e. higher order terms in the orphan rate become important. As you mentioned, this is due to network delays. It's during these races that hashing power is wasted, so T should be set high enough to keep their frequency low.

I'll try and come up with the next order term for the orphan rate. This will be from the cases where another miner finds a block at roughly the same time as our miner, and gets it to some portion of the miners before our miner gets his block to them.

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I agree, that working on payment channels is important. But may be it would be beneficial for Bitcoin to adopt shorter block times. At least it definitely would eliminate that marketing issue.

Sure it would be "beneficial" to lower it to the "optimal" value, but practically speaking it's probably just cosmetic. If the problem is people misunderstanding the issue, then perhaps educating people is the better solution.