I hope I never have to go into your hospital
I presume the Queue classes do something similar to the Java® classes of the same name. So your priority queue will need some sort of sorting to do with the urgency of the situation, so you will need some way to compare time to live. But with the ordinary queues, what is going to happen? You are going to get people out of it in the same order they went in: remember a queue is usually FIFO. What are you going to do? Go through the whole queue and find the people with the shortest time to live?
Your methods are far too long. One of them is over 120 lines. That suggests either you should rethink the whole logic for that method, or it needs to be divided into lots of smaller methods, (or both).