Quote from: TierNolan on January 29, 2014, 11:38:00 PM

Quote from: Mike Hearn on January 29, 2014, 05:05:49 PM

We can solve the issue another way, by finding methods to reduce the fees (smartfees etc).

How low do you think they would go? Wasn't there a calculation somewhere about the potential block orphan probability vs extra bandwidth. That set the current (or one of the previous) fees.

Not sure where the other estimate is, but here's mine:

Using the CDF of the exponential distribution to estimate the probability of a block being orphaned during its propagation, the expected orphan "cost"* is approximately

c ~= r(1-exp(-t/T)) ~= rt/T

where r is the block reward, T is the block period, and t is the fractional hashing power-weighted mean time to get the block to the rest of the miners. (Not too hard to show this precisely.) The latter approximation is valid since t/T ~= 5/600 << 1**.

Then the marginal cost to add a transaction is

dc ~= r dt/T

where dt is the marginal increase in block propagation time.

Assuming a functional fee market between users and miners, and a profit margin of m for the miner, then the fee paid is

f = (1 + m) dc ~= (1 + m) r dt/T

Note that since f doesn't depend on t, only dt, the latency "cost"* is built into the basic "cost"* of mining a block, and shouldn't affect fees, ultimately. Thus, supposing the transaction has been well-propagated in advance, so that only the first D bytes of the txid needs to be broadcast, and assuming the (weighted) mean number of hops to the other miners is n and the mean bandwidth on these paths is B, then we have roughly (with some underlying assumptions)

dt ~= nD/B

So

f ~= (1 + m) D/T n/B r

Plugging in some rough estimates:

r ~= 25 BTC
T ~= 600s
m ~= 0.06
n ~= 5
D ~= 5 bytes
B ~- 1 Mb/s

=> f ~= 0.000009 BTC

At today's exchange rate of ~800 USD/BTC, this is 0.7 cents.

With a high-bandwidth, well-connected minernet, n/B, and thus f, could probably be reduced by one or two orders of magnitude***. This could always be used to counteract any crazy rise in the exchange rate, though it may be considered somewhat of a degradation of decentralization.

* "cost" is in quotations because it's not really a cost per se, but a reduction in expected revenue
** http://bitcoinstats.com/network/propagation/

*** Edit: actually, hashing and lookup times would become the bottleneck at this point:

dt ~= nD/B ~= 3*5*8/10⁸ s ~= 10^-6 s

and this is ~ the time to do a SHA256 hash.