Data-Fitted Second-Order Macroscopic Production Models

Starting from discrete event simulations based on sampled data we simulate the interplay between product density and flux. Data-fitting helps to determine the right parameters for clearing functions to close first and second order conservation laws. For the first order case well-known relations from M/M/1-queuing theory can be reproduced and numerically extended to transient behavior. To include more information from the data into the model, a second equation is introduced leading to a second order production model which is close to the Aw-Rascle-Zhang model known from traffic flow. Numerical comparisons show similarities and, in particular, differences of the modeling approaches. AMS subject classifications: 90B30, 35L65, 91B74