Abstract
Due to the serious impact of border control measures during the ongoing novel coronavirus (COVID-19) epidemic, new difficulties and challenges have been brought to the border lines of most countries and regions. Focusing on the post-COVID global economic recovery, we develop a computing method for studying the health inspection process based on a three-color risk screening management mechanism at border crossing checkpoints. In this article, to manage the cross-border risk efficiently during the epidemic prevention and control, we formulate a queueing model with hierarchical health inspection channels. The structural characteristics and properties of this three-level queueing model are also analyzed by studying the health inspection process with risk classification. Furthermore, we conduct a series of sensitivity analysis on several performance measures for the studied queueing system. In the numerical results, we figure out the monotonicity, convexity and complicated patterns of the derived formulas.