When a difficulty change reaches the upper or lower bound (4x current), what is the implied impact on time per block?

Question

Can someone work out the math that occurs with Bitcoin and Litecoin when the target changes to the hard coded minimum and maximum value, with respect to time?

In other words, if a lot of hashpower is added to the network and target increases by 4x, that is the upper bound. How many blocks can be created right before the throttle of 4x is taken by the network?

I'm trying to calculate the affect throttling has on the number of blocks generated per hour.

Question

What is the average time per block, right before the network adjusts to the 4x limit, when the hash power is added to the network?

If I were to guess, right before that 4x limit was reached, 1 block is generated every 2.5 minutes for Bitcoin, and 1 block every 45 seconds for litecoin.

Furthermore any hashpower added (or removed) beyond the 4x multipler will not cause a network adjustment and infinitely many blocks may be created in that interval.

Why I want to know this...

If a lot of hashpower is added to the Litecoin network, which already generates blocks (one every 2.5 minutes) then there will be more blocks generated, increasing the risk of a chain split.

I ultimately want to understand how the chain split will cause wasted computation by peers as their blocks are discarded by the longest chain.

Answer 1

The network doesn't "throttle" the blocks found. Rather, it simply doesn't change the difficulty by a factor of more than x4 in every adjustment (which is once every 2016 blocks). There is no limit on the rate of block generation.

Let's say you were in an equilibrium where a block is found every 10 minutes. Right after a difficulty adjustment, more power joins the network and the hashrate is x100 the original. The difficulty didn't change yet so now a block will be found every 6 seconds. This will go on for 2016 blocks (~3 hours) and then the difficulty will go up by x4. Now a block will be found every 24 seconds; after 2016 more blocks (~13 hours) the difficulty will go up again by x4. Then a block will be found every 96 seconds, for 53 hours; then a block will be found every 384 seconds, for 215 hours; then the hardcoded limit will not be active, the difficulty will go up by a factor of (600/384), and now a block will be found every 10 minutes.

In those times that the total hashrate is too high for the current difficulty, the level of forking will be as if the time constant was shorter. So forking will indeed be high if the total hashrate has just rapidly increased.