A performance evaluation method of queuing theory based on Cosmos cross-chain platform

To solve the interconnection between a large number of coexisting blockchains such as Bitcoin and Ethereum and other types of blockchains, more and more scholars have pay attention to the cross-chain technology in recent years. However, the cross-chain exchange of transactions also imposes stricter requirements on the concurrent running speed of blockchains, which indirectly affects the performance and security of cross-chain systems. Therefore, evaluating and optimizing cross-chain technologies is of great significance for forming new internet value models. Queuing theory has been widely used to model various blockchain transaction processes and provide replicable performance evaluation results. However, existing research has overlooked the limitations of cross-chain systems. Many research works focus on modeling, simulating, and analyzing the performance of traditional blockchain systems, rather than cross-regional blockchain processes. To fill this gap, our study takes Cosmos as an example and proposes a queuing theory model based on finite space, which is a typical cross-regional blockchain implemented through a relay mode. Several performance indicators, such as average queue length, transaction rejection probability, system throughput etc., are obtained through three-dimensional continuous time Markov process. Finally, we simulated the analytical solutions of relevant performance indicators through experiments to verify the proposed simulation model's effectiveness. This analysis method can be extended to other blockchain systems with similar cross-chain processes.