Performance Evaluation of Cross-Chain Systems Based on Notary Mechanism

The application of blockchain technology in large-scale sustainable scenarios requires advancement. Therefore, high-performance cross-chain infrastructure is essential for domains like green supply chain management and peer-to-peer renewable energy trading. This study proposes an integrated modeling framework, whose core innovation is the combination of Phase-Type (PH) distribution, the GI/PH/1 queuing model, and quasi-birth-and-death (QBD) process theory to systematically describe the multi-stage service and dynamic interactions in a notary-based cross-chain system. This framework overcomes the limitations of traditional models that rely on oversimplified service assumptions. By utilizing matrix-analytic methods, it enables the precise quantification of key performance metrics, such as system throughput, response time, and rejection rate. This research provides a unified, scalable theoretical tool for cross-chain performance evaluation and establishes a methodological foundation for optimizing system resource allocation and sustainable infrastructure design.