Currently, confirmation rate of transactions is sitting at about 30-40%.
What goes into determining this number and why is it so low?
What sort of technical adjustments can be made to improve this? In an ideal situation, what confirmation rate would IOTA aim to have, if 100% isn't feasible?
IOTA tip selection mechanism is based on a weighted random walk. A parameter α>0 dictates how important a transaction’s cumulative weight is. The transition probability P is proportional to , where
is the difference between the cumulative weights of the site and the tip. If the tip is a lazy tip,
will be big and P will be small. Thus, it is less probable that a lazy tip will be selected (which is an important characteristic of a good tip selection mechanism).
If α is very small, it is an unweighted walk which does not punish lazy tips. If α is very big, it is a super-weighted walk, where too many transactions will be left behind and need to be reattached, which leads to decreased confirmation rate.
So, the parameter α is a major dictator of confirmation rate. Unfortunately, how we can improve it and what an ideal confirmation rate is are still speculative questions as of today. We are still unsure, and further research needs to be done before we can reach a conclusion.
Adding to Zass' answer, the best fit to α is being studied by IF, so far what we have is the upper bound of α, that means if we want a good confirmation rate in the network the α value can't be higher than that. Right now they are searching for the lower bound, which is more complicated because a low α permits malicious behaviours. You can read more about that here on the IOTA blog and in this IOTA foundation whitepaper, "Probability of being left behind and probability of becoming permanent tip in the Tangle".
[Source: The whitepaper mentioned above.]
The probability of a transaction getting left behind, for various values of α and λ. λ is the rate of transactions, measured in units of transactions per h. Essentially h is the average time it takes to perform proof of work. Assuming it takes one minute to perform PoW (which is more or less the case), then λ is in transactions per minute.
