Differential Load Modeling and Multiobjective Optimization of BFT Consensus Parameters in Hyperledger Besu

Abstract

The article proposes a mathematical model for analysing the performance of a Hyperledger Besu-based permissioned blockchain network under a Byzantine Fault Tolerant (BFT) consensus protocol. Using a system of differential equations characterised by a time-varying transaction arrival rate $lambda(t)$, we derive conditions for stable network operation, showing in particular that the system remains stable (i.e., avoids overload) if $lambda < mu$, $mu$ denotes the processing rate. Building on these theoretical foundations and formal results (lemmas and theorems), we formulate a multiobjective optimisation problem for tuning key consensus parameters (such as block interval and consensus timeout). Three performance criteria are considered: block finalisation latency ($F_1$), throughput ($F_2$), and the deviation of validator participation a target level ($F_3$). The formulation seeks to minimise latency and participation deviation while maximising throughput, under a quorum constraint requiring that the fraction of participating validators $p(x)$ meets a threshold $q(n)$ (e.g., at least two-thirds of the $n$ validators). Solving this problem yields concrete recommendations for optimal configuration, indicating that an ideal participation target $p^*$ lies between 0.85 and 0.95 and that a moderate number of validators provides the best performance balance. The results offer practical guidance for network configuration and represent a novel integration of stability analysis with multiobjective optimisation in the context of BFT consensus protocols.