A Stochastic Petri Net Approach for Evaluating Resource Utilization and Costs in Cloud-Hosted ZK-Rollups

Abstract

Leading blockchain platforms like Ethereum face significant scalability challenges while striving to balance high transaction throughput, security, and decentralization. Layer-2 solutions, especially Zero-Knowledge (ZK) Rollups, tackle this issue by processing transactions off-chain and submitting concise validity proofs to the main network. This approach preserves security while improving throughput. Despite these technical advantages, optimizing the underlying infrastructure remains a complex task for node operators. This paper presents a formal modeling approach using Stochastic Petri Nets (SPNs) to assess the operational behavior of ZK-Rollups, particularly addressing deployment challenges in public cloud environments. The proposed model is calibrated using empirical parameters from the zkSync Era protocol to ensure realistic performance representation. Using a Design of Experiments (DoE) methodology, we analyze key infrastructure metrics systematically, including resource utilization, transaction wait times, and daily operational costs under various system configurations. Case studies demonstrate that increasing Layer-2 transaction volume can reduce service providers’ daily operational costs by up to $\mathbf{2 5 \%}$ through more efficient batch usage. However, results indicate a significant tradeoff between cost efficiency and responsiveness, as larger batch sizes may double user waiting times. Additionally, we analyze the relationship between server utilization and capacity, demonstrating that typical deployments are frequently overprovisioned and compromise system stability.