Equation-Free Analysis of Macroscopic Behavior in Traffic and Pedestrian   Flow
  Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are explicitly given on the macroscopic level. This will facilitate a study of how the model behavior depends on parameter values including an understanding of transitions between different types of qualitative behavior. These methods are introduced and explained for traffic jam formation and emergence of oscillatory pedestrian counter flow in a corridor with a narrow door. 
Christian Marschler, Jan Sieber, Poul G. Hjorth and Jens Starke
math.DS