  The growing number of applications for distributed ledger technologies is
driving both industry and academia to solve the limitations of blockchain,
particularly its scalability issues. Recent distributed ledger technologies
have replaced the blockchain linear structure with a more flexible directed
acyclic graph in an attempt to accommodate a higher throughput. Despite the
fast-growing diffusion of directed acyclic graph based distributed ledger
technologies, researchers lack a basic understanding of their behavior. In this
paper we analyze the Tangle, a directed acyclic graph that is used (with
certain modifications) in various protocols such as IOTA, Byteball, Avalanche
or SPECTRE. Our contribution is threefold. First, we run simulations in a
continuous-time model to examine tip count stability and cumulative weight
evolution while varying the rate of incoming transactions. In particular we
confirm analytical predictions on the number of tips with uniform random tip
selection strategy. Second, we show how different tip selection algorithms
affect the growth of the Tangle. Moreover, we explain these differences by
analyzing the spread of exit probabilities of random walks. Our findings
confirm analytically derived predictions and provide novel insights on the
different phases of growth of cumulative weight as well as on the average time
difference for a transaction to receive its first approval when using distinct
tip selection algorithms. Lastly, we analyze simulation overhead and
performance as a function of Tangle size and compare results for different tip
selection algorithms.
