TITLE: Queues in Tandem and Random Growth Models

ABSTRACT: Imagine the following hellish scenario. You are standing in line at the airport security gate, at which point you are the n-th person waiting to go through the security guard. As soon as you pass, you realize that the queue persists, because there's a second security point right after the first one! You go through that as well, and horrified you understand that there are many security points, one after the other and you need to go through all of them. The important question at this point is to decide if you can make your flight. We will answer that. In the process, we will connect the above model with a disease propagation model (like a mindless zombie invasion), one lane highway traffic, and more realistic queuing models where the servers (or guards) get tired as the day progresses.