Abstract
We examine the use of a Geometric Distribution for pre-calculating the publication deadlines of blocks in a simulation of proof-of-work Blockchain. Specifically, we focus on Discrete-Event Simulation, where the simulator identifies events to be simulated, calculates their deadlines, places them in an Event Queue ordered by deadline, and processes them sequentially. In Blockchain, these events include the publication and reception of a block by each Miner. While a Geometric Distribution allows the calculation of block publication deadlines in the absence of Difficulty updates, in the case of evolving Difficulty, it must be extended to a non-homogeneous Geometric Distribution. To address this issue, we introduce the Geometric Distribution with a Variable Probability, a non-homogeneous Geometric Distribution that enables the calculation of block publication deadlines in the presence of Difficulty Regulation—a distinctive feature of proof-of-work Blockchain. We then present the architecture and operating principles of a Discrete-Event Simulator based on this distribution, along with simulation results that validate our approach.