I can't really go into specifics, I'm more just looking for terms that I can research to get on the right track. Classes of model/processes etc.
A close analogy to my problem:
I need to optimally place exits in a building such that in an emergency people can get out as quickly as possible.
I'm pretty sure that I need to be looking into Queuing models. My knowledge of Queuing Theory is very limited, only touched on it in a stochastic calculus back in college.
The key points of the model are that spatial distance matters, variable population density throughout the building matters, and people have the option to choose different exits.
I can try to provide more information if that would be helpful, but I'd really appreciate some suggestions of types of queuing models (or another field) that incorporate these points.