A Theoretical Model Characterizing Tangle Evolution in IOTA Blockchain Network

IOTA blockchain system is lightweight without heavy proof-of-work mining phases, which is considered a promising service platform of Internet of Things applications. IOTA organizes ledger data in a directed acyclic graph (DAG), called Tangle, rather a chain structure as in traditional blockchains. With arriving messages, IOTA tangle grows in a special way, as multiple messages can be attached to the tangle at different locations in parallel. Hence, the network dynamics of an operational IOTA system would justify a thorough study, which is currently unexplored in the literature. In this article, we present the first theoretical modeling for the evolving IOTA tangle based on stochastic analysis. After analyzing snapshots of the real-world IOTA ledger data, our key finding suggests that IOTA tangle follows a rather atypical double Pareto Lognormal (dPLN) degree distribution. In contrast, typical power-law and exponential distributions do not accurately reflect the fact. For model parameter estimation, we further realize that using generic optimization solvers cannot yield quality fitting results. Thus, we design an alternative algorithm based on expectation-maximization (EM) framework. We evaluate the proposed model and fitting algorithm with official data provided by the IOTA Foundation. Quantitative comparisons confirm the fitting quality of our proposed model and algorithm. The whole analysis reveals a deeper understanding of the internal mechanism of the IOTA network.