Quote from: ProfMac on May 14, 2014, 03:48:46 PM

The question is, what does "stable" look like. Large numbers of addresses enter the queue from relatively small recent earnings. Many of these have had a long time elapse since their last payout, and they get put at the top of the queue.

One of my accounts has almost 2 BTC in the unpaid shares (I forget their name for these). A few lucky blocks will pay those unpaid shares to me. There are several things going on. It would be interesting to write a program to model "steady state" using realistic account data. That data is pretty available from Eligius.

I believe that the queue will ALWAYS increase.

Imagine, if the queue is 3 block deep. Under normal circumstances, the queue slowy grows as user submit shares and ear reward at the same rate that Eligius finds the block, thus one block per 2 hours currently. In that case, indeed, in steady state, the queue slowly grows one block, then a block is found, it decreases one block, and repeats.

However, luck is not considered here: with luck, blocks may be found faster or slower than shares are submitted (share submission rate is fairly constant compared to block rate). Thus, the pool may sometimes blocks faster, and the queue shrinks, and may sometimes find the longer, and the queue increses. Over the long time it averages, but this introduces variance. But even in case of incredible luck, the pool cannot have a negative block queue length. It that were to happen (the queue is completely emptied) then the found shares are put aside for a manual payment, so when thing will "average", those lucky blocks will not take part of the averaging, and will push the average queue length up. (until they are manually paid)

In a more mathematical analysis, if we "start" the pool at a queue of length 0, it will grow fast initially, as the the odds it finds a block faster that the submitted shares is high. But when it will be a few blocks deep, that queue provides a "cushion" that makes unlikely the queue will empty again. The longest the queue, the unlikelyest it will empty. But the odd is never 0, only decreasingly small... So it will ALWAYS empty again sometimes, but in longer and longer intervals, and each times it empties, it will grow a bit. One can then calculate that the expected growth of the cue is that it's length will be proportionnal to the square root of the time elapsed since the last time it was emptied. The exact proportionnality factor will depend on network difficuly, hashrate of the pool, etc... (For the mathematically inclined, sqrt(ht) (where h is the hashrate and t the time) is the standart deviation of a poisson distribution, the distribution that describes the bitcoin behavior. Correct me if i've made a mistake.)

I did not consider the fact that user can set a treshold. That increases the odds that the queue will empty up, because it is entirely possible that the pool has more that 25 BTC worth of unpaid shares as a whole, but that no user has crossed it's treshold. (I believe it maintains the square root proportionality rule, just with an increased factor.)

But the main reason the queue grows longer than 10 blocks on eligius is when failsafe mode triggers.