My reply to the TSA would be that there is a branch of applied mathematics called "Queueing Thoery". It has proven very useful in assessing lengths of queues in retail, fast food restaurants, airline ticket counters, and so forth. It could also be applied to security lines. :-:

Queueing theory works very well in practice and requires minimal inputs (arrival rate, number of security checkpoints open, and it will give you the estimated queue length at any time). Then, you run simulations and/or different scenarios to find the acceptable queue length.

But then you might need people with more than a high school education wearing neat, blue uniforms!