@Peter R check out figure 4 and 5 in my paper that I just I PMed you. It plots the theoretical probability against actual data collected from the Relay Network. So we are right. I think that the difference is that the graph in http://hashingit.com/analysis/34-bitcoin-traffic-bulletin is plotting "cumulative probability", basically its plotting:@Peter R.

Indeed, I just read it and tried to figure it out, but I do not understand this either. It is a Poisson process, memory-less, so timing between blocks and transactions shouldn't matter - you should simply get the 600s exponential PDF for when a transaction is included in a block. Assuming no load.

y = Integral from t=0, infinity of (poisson probability )

Where we are are just plotting the poisson probability

In other words, they are summing the probabilities from 0 to x...

EDIT: oops, I see that they are plotting 2 different y axis now. But I think that the difference is that this is the probability of particular transaction confirmation, not that any block is found. So this transaction needs to propagate throughout the network and be incorporated into the block that mining pools are working on. This is very different than the Poisson process of block discovery.

EDIT2: The red line actually looks a lot like the block discovery probability if you remove 1-txn blocks. At least in shape if not in magnitude... that makes sense to me.

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