...
I'm going to copy the formula you posted earlier to make sure I get it -
For simplicity I will define:
BlkSize = (1+B) M
NBaseReward = R
basePenalty (for a given B) = P
BNewReward (for a given B) = R
BI'm assuming that B is the current block? Is it the size of the block in bytes? kb? I think its the 1 + B that is throwing me off. Does that just mean "the next block"?
The penalty for a given B becomes:
P
B = R
baseB
2While the new reward for a given B becomes:
R
B = R
base(1 - B
2)
The first derivative of P
B with respect to B is
dP
B /
dB = 2R
baseB
I apologize that I can't parse the equations. Its even worse as I type now with the bbcode or whatever formatting it is.
So if I'm reading this right, you're using hashrate as an indicator of the size of the network? Or just use something other than blocksize scaling / penalty formula for the first two tiers?
I apologize for being obtuse in my understanding.
The way that I understand things is that we need a way to match the internal cost (xmr) with the external value of xmr for adding data to the blockchain. With the multi-tiered system you propose, something is used to adjust the xmr cost for the first two tiers, and then for tiers 3,4,5 , it uses a component of the block size penalty. I think what I'm not getting is that as the network becomes more valuable, the internal xmr cost has to go down to maintain the usability of the network. Now, if the change in the transaction fee is coupled to a transaction priority system and is dependent on the block penalty... wouldn't all those things imply that the transaction fee is increasing?
No apologies needed. You are not being obtuse, in fact, on the contrary, you are being very helpful. These are far from easy concepts to understand and explain. Furthermore I am not aware of any other crypto currency that has even seriously looked at these issues let alone proposed a solution or set of solutions, even though these are issues that every crypto currency faces.
You are of course correct. that "we need a way to match the internal cost (xmr) with the external value of xmr for adding data to the blockchain".
Monero however imposes a significant linear correlation between the internal cost (xmr) and the external value of adding data to the blockchain by virtue of the penalty function for blocksize scaling. I say linear because for a given base reward the cost in xmr adding a particular transaction of a given size in KB to a particular part of the penalty area falls liniarly with the the median of the blocksize. For example if M
N is 10x larger the cost per transaction falls by a factor of 10 since there are 10x as many transactions paying for a given amount of penalty. In this example I am assuming the transactions are all of the same size for simplicity.
B is the
relative increase in the block size over the median blocksize, It can range from 0 (no increase) to 1 (100% increase / doubling of the blocksize). The critical point here is that B attracts the same penalty in XMR for an increase in blocksize from say 1 MB to 1,1 MB than for say 1 GB to say 1.1 GB, since in both cases B = 0.1. In the latter case there are 1024x more transactions to absorb the cost of the penalty so the cost per transaction falls by a factor of 1024. Again I am assuming for simplicity the same distribution by size of transactions in the 1.1 MB and 1.1 GB blocks.
Now here is where it can get interesting. If the natural relationship between network value and network size is say M
N log (M
N) rather than M
N then it is possible for the cost of a transaction, in real terms, in the penalty area to rise with log (M
N) at least for a period of time. This can happen if for example market responds to this difference by optimizing transactions in order to minimize paying the penalty. This would occur because all transactions do not have the same priority. It is for this reason that there can be a very significant merit to use a different scaling formula (difficulty adjusted for block reward) for the low tier fee levels than for the high tier fee levels where the fees are effectively set by the base reward and median blocksize.