Derivation of Van Aerde Traffic Stream Model from Tandem-Queuing Theory

The relationship between the traffic stream flow, speed, and density can be described with a fundamental diagram. With a reasonable fundamental diagram, the maximum flow rate of motorways and the corresponding traffic quality can be estimated more accurately. According to different theories such as the car-following theory, queuing theory, or theory of fluid dynamics, different models for the fundamental diagram can be established. From queuing theory, several models can be found. However, the existing queuing models consider a roadway cross section as a stand-alone queuing counter, and thus the interaction between consecutive vehicles cannot be considered sufficiently. This paper presents a new model treating a road stretch as a series of many queuing counters. The new model yields a single-regime fundamental diagram that fully corresponds to the well-known Van Aerde model. In the Van Aerde model, the model parameters can be easily measured and calibrated using loop detector data. The application and calibration of the model are demonstrated with sample data sets and compared with other state-of-the-art traffic stream models. The results demonstrate the superiority of this model in capturing traffic stream behavior.