Design of Covid-19 testing queues

In the event of a virus outbreak such as Covid-19, testing is key. However, long waiting lines at testing facilities often discourage individuals from getting tested. This paper utilizes queueing-game-theoretic models to study how testing facilities should set scheduling and pricing policies to incentivize individuals to test, with the goal to identify the most cases of infection. Our findings are as follows. First, under the first-in-first-out discipline (FIFO), the common practice of making testing free attracts the most testees but may not catch the most cases. Charging a testing fee may surprisingly increase case detection. Second, even though people who show symptoms are more likely to carry the virus, prioritizing these individuals over asymptomatic ones (another common practice) may let more cases go undetected than FIFO testing does. Third, we characterize the optimal scheduling and pricing policy. To maximize case detection, testing can be made free but one should also (partially) prioritize individuals with symptoms when testing demand is high and switch to (partially) prioritize the asymptomatic when testing demand is moderately low.