Mathematical Model of an Industrial Distributed Ledger as a Queueing System with Multiple Tickets of Unlimited Depth

Abstract

The paper proposes a technique for the mathematical description of a distributed ledger in industrial applications as a queuing system. A conceptual model of an industrial distributed ledger is represented, determining the main structural elements of the distributed ledger topology such as network nodes, distributed ledger nodes, and distributed ledger services to verify transactions. The distribution functions of random variables typical of this process are determined and represented. The approximation of the tickets distribution via the Erlang arrivals is performed to obtain the most accurate value. The conditions for building the infinitesimal matrix are determined considering the specifics of information processes in the distributed ledger. Normalization conditions are formed. The main integral characteristic exponents required to analyze a distributed ledger as a queuing system are given. To determine the main integral characteristic exponents of the industrial distributed ledger system, a simulation model was developed in the AnyLogic environment.