This work proposes an innovative car-following model that incorporates driver’s sensory memory and the preceding vehicle’s optimal velocity within the framework of the full velocity difference (FVD) model. First, the traffic stability criterion is calculated through the use of the theory of linear stability. Using a reductive perturbation technique, we construct the mKdV (modified Korteweg-de Vries) equation. Second, as the system approaches the critical point, the soliton of kink-antikink type obtained from the mKdV equation describes the traveling-wave behavior of jammed traffic. An analysis is also performed on the congestion magnitude and the energy expended. Finally, computational modeling is used to validate the theoretical findings, and the results show that the revised model is useful. According to numerical experiments and analytical derivations, the proposed model increases the optimal velocity coefficient, reduces memory requirements, mitigates traffic jam, strengthens traffic flow stability, and reduces kinetic energy fluctuations.
- Open Access
- Article
Modeling Following Behavior Using Driver Memory and Leader’s Optimal Speed
- Limei Liu *,
- Xia Li,
- Yang Chen
Author Information
Received: 05 May 2026 | Revised: 07 Jul 2026 | Accepted: 14 Aug 2026 | Published: 20 Oct 2026
Abstract
Graphical Abstract
Keywords
FVD model | driver’s sensory memory | mKdV equation | numerical simulations
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