Chaotic jam and phase transitions in a lattice model with density dependent passing

In real traffic dynamics, passing has a significant impact on the traffic flow. Passing/Overtaking is primarily influ-enced by the traffic density in the surroundings, therefore considering passing as constant is impractical. In this paper, we proposed a lattice hydrodynamic model with the consideration of density dependent passing for a uni-directional single lane highway to examine the traffic system more realistically. Due to various experimental in-vestigations, the passing behavior is considered similar to the flow-density curve. The passing increases with the density and after achieving a maximum at a critical value, it decreases. Thus, implementing the idea to model density dependent passing similar to the optimal velocity function. The impact of density dependent passing on the lattice model is investigated through linear stability analysis and it is shown that with an increase in pass-ing, the stability region reduces significantly. Using nonlinear analysis, the kink-antikink solution of the mKdV equation is obtained to describe the propagating behavior of the density wave near the critical point. For the small values of passing, there is a phase transition from the kink jam region to the free flow region, with decreas-ing sensitivity. On the other hand, for large values of passing, the phase transition occurs from the uniform to the kink jam region through the chaotic jam region, with increasing delay time. The influence of parameters involved in density dependent passing is investigated theoretically as well as numerically.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This study proposed a lattice hydrodynamic model with density dependent passing for a uni-directional single lane highway to examine the traffic system realistically. The increase in passing led to a significant reduction in the stability region of the lattice model. Phase transitions from different regions to the kink jam region were observed with varying levels of passing.