Add servers and the line shortens — but not smoothly. As the desks fill toward capacity, the wait doesn't rise, it explodes. Slide the arrival and service rates, drag across the desks to add or remove servers, and watch how close to the edge you dare run the shop.
A textbook M/M/c queue: Poisson arrivals at rate λ, c servers each at rate μ, utilisation ρ = λ/(cμ). The chance an arrival must wait is the Erlang-C formula; the average wait Wq = P(wait)/(cμ − λ); the average queue length Lq = λ·Wq (Little's Law). All computed live — slide λ and μ, drag to set the servers, and as ρ → 1 the wait diverges to infinity. Standard, real queueing theory.
Real service systems break M/M/c's assumptions — arrivals cluster, service times aren't exponential, customers balk and abandon, and demand swings by hour. The instrument is the exact classical model; treat the minutes as the shape of congestion, not a forecast for a specific counter.