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.