The Exactly Solvable Simplest Model for Queue Dynamics
  We present an exactly solvable model for queue dynamics. Our model is very simple but provides the essential property for such dynamics. As an example, the model has the traveling cluster solution as well as the homogeneous flow solution. The model is the limiting case of Optimal Velocity (OV) model, which is proposed for the car following model to induce traffic jam spontaneously. 
Y. Sugiyama (City College of Mie, Japan), H. Yamada (Nagoya   University,Japan)