Year: 2025
Type: article
Abstract: A microscopic particle model for hysteretic vehicular traffic flow is considered. The model is a system of possibly infinitely many ODEs for the positions of the cars, whose velocity depends not only on the discrete density in relation to the car ahead, but also on the sign of the acceleration, allowing hysteresis behaviors. This model's traveling wave profiles lead to a system of infinitely many delayed differential equations. Necessary and sufficient conditions are provided for the existence of traveling wave profiles in this microscopic hysteretic traffic model. The traveling wave profile is unique up to a shift. Both deceleration and acceleration shock profiles are observed, aligning with real-world traffic flow patterns. The existence of these shock types allows the construction of stop-and-go wave solutions.
DOI: 10.3934/dcds.2025064
Authors: Haitao Fan, Wen Shen
Institutions: Georgetown University, Pennsylvania State University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410377366