analysis of iota tangle stability in high transaction rates

The future of the iot requires new payment methods that can handle millions of transactions per second. iota cryptocurrency aims at providing such a solution. it uses a consensus algorithm based on directed acyclic graphs (dag) called tangle. a tip selection algorithm (tsa) is a part of tangle that determines which unconfirmed blocks (tips) should be confirmed by new blocks. there is always a chance that a small number of valid blocks never get confirmed and become stale. if a significant part of the blocks becomes stale, the tangle is considered unstable. in this paper, we mathematically prove that a tsa is stable at all transaction rates if and only if the probability of selecting all tips is at least 1/2n in which n is the total number of tips. accordingly, we demonstrate that the current iota tsa would not be stable at high transaction rates.