Analysis of Gaussian vs. Triangular Profiles for traffic flow modeling

The present work provides a comprehensive comparative analysis between two advanced traffic density profiles — the Enhanced Gaussian Profile with Dynamic skewness and sigmoidal Spread, and the Novel Modified Triangular Profile with Interacting Peaks and Adaptive Heights — within the framework of the fractional Lighthill–Whitham–Richards (FLWR), which is an extension of the classical LWR model (Lighthill and Whitham, 1955; Richards, 1956; Sun and Zhang, 2011). The improved Gaussian Profile includes time-dependent skewness and spread, allowing it to dynamically adapt to changes in traffic conditions. On the other hand, the Modified Triangular Profile represents complex interactions between several congestion peaks (Newell, 1993; Treiber et al., 2000), similar to the multi-peak congestion phenomenon (Helbing, 2001; Kerner, 2004). The Von Neumann Stability Analysis (von Neumann and Richtmyer, 1950; von Neumann and Richtmyer, 1947) is employed and applied to both profiles to assess their stability under various traffic scenarios, providing valuable insights into the conditions under which each model remains robust. We conducted a comparison between simulated traffic density data and real-world measurements to evaluate the accuracy and applicability of each profile. Our findings reveal a significant disparity in how these profiles capture small differences in traffic flow, particularly in situations that involve sudden changes in traffic patterns or external factors like weather conditions. This study not only enhances our understanding of traffic density modeling but also offers a framework for selecting acceptable traffic profiles based on specific real-world scenarios. The findings are essential for enhancing traffic management systems and designing more effective road networks (Richards, 1956; Mainardi, 2010; van der Houwen and Gijzen, 2010).