Performance Analysis of Direct Acyclic Graph-Based Ledgers in Low-to-High Load Regime

Direct acyclic graph (DAG)-based ledgers and distributed consensus algorithms have been proposed for use in the Internet of Things (IoT). The DAG-based ledgers have many advantages over single-chain blockchains, such as low resource consumption, low transaction fee, high transaction throughput, and short confirmation delay. However, the scalability of the DAG consensus has not been comprehensively verified on a large scale. This paper explores the scalability of DAG consensus within the low-to-high load regime (L2HR) using the tangle model, where L2HR characterizes the transition from a phase of low network load to another phase of high network load. In particular, we determine the average number of tips in the tangle in L2HR when adopting the uniform random tip selection (URTS) and rigorously prove that using the tangle model, the average number of tips at the end of L2HR converges to a constant. We also analyze the probability that a transaction in L2HR becomes an abandoned tip, the approximate average time required for the network load to transition from low load regime (LR) to high load regime (HR), and the average time required for a tip being approved for the first time in L2HR. All analytics are verified by numerical simulations.