On the consistency of freeway macroscopic merging models

Many first-order macroscopic models for freeway traffic have been developed since the seminal work on the well-known Lighthill-Whitham-Richards, or LWR, continuous model. The asymmetric cell transmission model (ACTM) is a widely accepted macroscopic model integrated into a variety of freeway traffic control frameworks. The model is based on the original cell transmission model; modified merge equations make it computationally tractable for optimization of ramp metering. However, when the common simplistic calibration of the model is used, an infeasible merging behavior is observed at uncontrolled merges, and the resulting queue lengths are not accurately estimated. This paper proposes an elegant analytical relationship, based on traffic flow theory, for calibrating the two parameters involved in the ACTM merge model. The method ensures the physical consistency of the dynamics involved in queue processes in the proximity of a noncontrolled merge junction. This method should be an essential feature of any freeway traffic model.