Linearized Theory of Traffic Flow
  The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena. Specifically, the scenarios examined involve a smooth velocity field in stop-and-go traffic, a discontinuous velocity field with shock waves in a traffic light problem, and discontinuous displacement fields in a problem where a single platoon of vehicles splits into two, and later merges back into one. 
Tal Cohen and Rohan Abeyaratne
physics.soc-ph