Title: Waves in a Spatial Queue: Stop-and-Go at Airport Security

Abstract: Imagine you are the $170$th person in line at an airport security checkpoint. As people reach the front of the line they are being processed steadily, at rate $1$ per unit time. But you move less frequently, and when you do move, you typically move several units of distance, where $1$ unit distance is the average distance between successive people standing in the line.

This phenomenon is easy to understand qualitatively. When a person leaves the checkpoint, the next person moves up to the checkpoint, the next person moves up and stops behind the now-first person, and so on, but this ''wave" of motion often does not extend through the entire long line; instead, some person will move only a short distance, and the person behind will decide not to move at all. Around the $k$'th position in line, there must be some number $a(k)$ representing both the average time between your moves and the average distance you do move. This talk describes a stochastic model in which in can be proved that $a(k)$ grows as order $k^{1/2}$. A more refined analysis (work in progress) suggests sharp asymptotics in terms of the coalescing Brownian motion model.