Pooling and Balking: Decisions on COVID-19 Testing

Abstract

The most important issue in the prevention and mitigation of the COVID-19 pandemic is, perhaps, testing. To increase the convenience and efficiency of testing, many countries have set up walk-in testing sites. One fundamental decision for local governments or authorities to make is, should they build fewer centralized walk-in or drive-thru testing site (with more manpower and therefore a higher service rate) or more decentralized testing sites (each with less manpower and therefore a lower service rate)? To make this decision, one needs to understand the benefits and/or drawbacks of pooling incorporating people's balking behavior. In this short paper, we build classic queueing models to analytically characterize how system performance measures such as the expected waiting time, the expected queue length, and the balking probability change with the service rate, under different values of the implied utilization. These performance measures not only indicate the productivity and efficiency of testing operations, but also influence the safety and well-being of people and society.

Keywords: pooling; balking; waiting time; queue length