The impact of the predictive effect on traffic dynamics in a lattice model with passing
School of Mathematics, Thapar Institute of Engineering and Technology,
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Received in final form: 9 December 2019
Published online: 2 March 2020
In this paper, we study the impact of the predictive effect with passing for a unidirectional single-lane highway. The model is further analyzed theoretically by the means of stability analysis. The influence of the predictive effect is examined on traffic stream stability through linear stability analysis when passing is permitted. It is shown that the accurate expected behavior of the vehicles ahead can enhance the stability of traffic flow for any rate of passing. Using nonlinear stability analysis, we obtained the critical value of passing constant for which kink soliton solution of mKdV equation exist. When the passing constant is smaller than critical value, the jamming transition occurs between uniform flow and kink flow while for higher value of passing constant, the jamming transitions occur from uniform flow to kink density wave flow through a chaotic phase. Numerical simulation verifies the theoretical predictions which confirms that the traffic congestion can be suppressed efficiently by considering the predictive effect in a single-lane traffic system when passing is allowed.
Key words: Statistical and Nonlinear Physics
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020