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has been cited by the following article:

• TITLE: Improved Car-Following Model Considering Modified Backward Optimal Velocity and Velocity Difference with Backward-Looking Effect

  AUTHORS: Md. Anowar Hossain, K. M. Ariful Kabir, Jun Tanimoto

  KEYWORDS: Realistic Backward Optimal Velocity, Standerized Backward Maximum Speed, Honked Effect, Backward-Looking Effect, Car-Following Modelling

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.2, February 20, 2021

  ABSTRACT: In this paper, a new traffic flow model called the forward-backward velocity difference (FBVD) model based on the full velocity difference model is proposed to investigate the backward-looking effect by applying a modified backward optimal velocity using generalized backward maximum speed. The FBVD model belongs to the family of microscopic models that consider spatiotemporally continuous formulations. Neutral stability conditions of the discrete car-following model are derived using the linear stability theory. The stability analysis results prove that the modified backward optimal velocity has a significant positive effect in stabilizing the traffic flow. Through nonlinear analysis, a kink-antikink solution is derived from the modified Korteweg-de Vries equation of the FBVD model to explain traffic congestion of the model. The validity of this theoretical model is checked using numerical results, according to which traffic jams were found to have been significantly diminished by the introduction of the modified backward optimal velocity.