Since this is a social problem, you can add a complication that the response time has an impact on the throughput. If people call for an appointment, and find

Since this is a social problem, you can add a complication that the response time has an impact on the throughput. If people call for an appointment, and find they have openings this afternoon and tomorrow morning, they'll be more likely to go to the doctor. If they find that the earliest appointments are 12 weeks out (as I did when trying to schedule a physical before a recent trip to Asia - ended up skipping the appointment), they're going to go elsewhere. If you're viewing the queue as a sort of plumbing system, this can be approximated as backpressure.