Abstract—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’s 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.


Directed Acyclic Graph (DAG) based Distributed Ledger Technology (DLT) has recently emerged as an attractive approach for distributed ledger applications in the smart mobility domain [1]. While distributed ledgers based on Blockchain technology are probably the most well known [3]-[5], others have been developed that are of interest in a control theoretic context. The objective of this paper is to analyse one such alternative ledger structure; namely, the IOTA Foundation’s DAG-based distributed ledger, known as the Tangle.

To date, applications of DLTs have primarily focussed on two main areas: (i) as a peer-to-peer value transfer e.g. cryptocurrency(e.g., see [6][7]); and (ii) for tracking goods and services in a trustworthy manner in complex supply chains(e.g., [8]). More recently, DLT has been applied in smart city applications, specifically where the issues of social compliance and the enforcement of social contracts are at the forefront [1][9] (e.g. discouraging traffic from breaking regulations, parking for a limited amount of time in restricted areas, etc.). For these types of applications DLT is seen as an interest-ing enabling mechanism for a number of reasons.

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