A Multi-Tier Inspection Queueing System With Finite Capacity for Differentiated Border Control Measures

Both uniform quarantine and isolation measures, due to the COVID-19 pandemic, have brought forth unprecedented and severe socio-economic impacts. For the global post-COVID economic recovery, it is of great significance to explore scientific ways to reopen the borders with consideration of both risk and efficiency. With the development of international travel health certificate or digital travel pass, differentiated inspection and quarantine measures can be implemented to accelerate the recovery of international travel. In this paper, we study a multi-tier inspection queueing system with finite capacity based on a differentiated level of risk classification. A queueing analysis is conducted for the stochastic process of inspecting cross-border travelers under differentiated service for inspection and quarantine. Besides, we develop a computing method to determine the steady-state probability and several performance indices of the proposed queueing system, and an illustrative example is also set to introduce a step-by-step process for the method. Furthermore, we figure out the relationship between the model parameters and system performance of interest by means of a series of numerical experiments. In the data analysis, we also illustrate the monotonic and concave effects on the system performance, which can provide a visualized understanding of the trade-off between safety and efficiency in the studied multi-server queueing system with hierarchical inspection channels and finite capacity. Our findings can reveal some managerial insight into the border control problems, which could reconcile the efficiency with safety in the current epidemic prevention and control tasks.