Latency performance modeling and analysis for cross-chain transaction processing

Cross-chain communication has become a key enabler of blockchain interoperability, but its end-to-end latency remains difficult to characterize analytically. Unlike single-chain transactions, cross-chain operations must traverse multiple processing stages across heterogeneous chains and relayers, so delay accumulates over the full communication cycle. Existing cross-chain queueing models typically capture such processing as a sequence of loosely connected service stages, but they do not explicitly model the coupled latency effect of the forward transfer path and the return acknowledgment path in IBC-style protocols. To address this gap, we develop a unified queueing model for cross-chain transaction latency that jointly characterizes the complete packet lifecycle, including source-chain submission, relay forwarding, destination-chain processing, and acknowledgment return. Based on this formulation, we derive closed-form latency expressions, characterize delay distributions, and extend the framework to capture bursty arrivals, service-time variability, and batched relayer behavior. Numerical and simulation results reveal how acknowledgment coupling, service heterogeneity, and batching jointly determine bottleneck formation and amplify end-to-end latency as load approaches capacity. These results provide a more faithful analytical foundation for cross-chain performance modeling and offer practical guidance for relay configuration and capacity provisioning in interoperable blockchain systems.