Christopher King

Andrew Cullen, Pietro Ferraro, Christopher King et al.

Recently, Directed Acyclic Graph (DAG) based Distributed Ledgers have been proposed for various applications in the smart mobility domain [1]. While many application studies have been described in the literature, an open problem in the DLT community concerns the lack of mathematical models describing their behaviour, and their validation. Building on a previous work in [1], we present, in this paper, a fluid based approximation for the IOTA Foundation DAG based DLT that incorporates varying transaction delays. This extension, namely the inclusion of varying delays, is important for feedback control applications (such as transactive control [2]). Extensive simulations are presented to illustrate the efficacy of our approach.

Andrew Cullen, Pietro Ferraro, Christopher King et al.

Directed Acyclic Graph (DAG) based Distributed Ledgers can be useful in a number of applications in the IoT domain. A distributed ledger should serve as an immutable and irreversible record of transactions, however, a DAG structure is a more complicated mathematical object than its blockchain counterparts, and as a result, providing guarantees of immutability and irreversibility is more involved. In this paper, we analyse a commonly discussed attack scenario known as a parasite chain attack for the IOTA Foundation DAG based ledger. We analyse the efficacy of IOTA core MCMC algorithm using a matrix model and present an extension which improves the ledger resistance to these attacks.

Pietro Ferraro, Christopher King, Robert Shorten

Directed Acylic Graphs (DAGs) are emerging as an attractive alternative to traditional blockchain architectures for distributed ledger technology (DLT). In particular DAG ledgers with stochastic attachment mechanisms potentially offer many advantages over blockchain, including scalability and faster transaction speeds. However, the random nature of the attachment mechanism coupled with the requirement of protection against double-spend transactions leaves open the possibility that not all transactions will be eventually validated. Such transactions are said to be orphaned, and will never be validated. Our principal contribution is to propose a simple modification to the attachment mechanism for the Tangle (the IOTA DAG architecture). This modification ensures that all transactions are validated in finite time, and preserves essential features of the popular Monte-Carlo selection algorithm. In order to demonstrate these results we derive a fluid approximation for the Tangle (in the limit of infinite arrival rate) and prove that this fluid model exhibits the desired behavior. We also present simulations which validate the results for finite arrival rates.