An anisotropic continuum model considering bi-directional information impact

• An anisotropic continuum model is proposed under the bi-directional looking context.
• Anisotropy is preserved only when backward weight ratio is in an appropriate range.
• Condition of avoiding wrong-way travels is consistent with anisotropic condition.
• Positive holding effect and negative pushing effect of backward looking are observed.
• Traffic flow wave performance is related to microscopic driving behaviors.

In traffic flow with naturalistic driving only, stimulus information pre-dominantly comes from the preceding vehicles with drivers occasionally responding to the following vehicles through the inspection of rear-view mirrors. Such one-sided information propagation may potentially be altered in future connected vehicle environment. This brings new motivations of modeling vehicle dynamics under bi-directional information propagation. In this study, stemming from microscopic bi-directional car-following models, a continuum traffic flow model is put forward that incorporates the bi-directional information impact macroscopically but can still preserve the anisotropic characteristics of traffic flow and avoid non-physical phenomenon such as wrong-way travels. We then analyze the properties of the continuum model and respectively illustrate the condition that guarantees the anisotropy, eradicates the negative travel speed, preserves the traveling waves and keeps the linear stability. Through a series of numerical experiments, it is concluded that (1) under the bi-directional looking context only when the backward weight ratio belongs to an appropriate range then the anisotropic property can be maintained; (2) forward-propagating traffic density waves and standing waves emerge with the increasing consideration ratio for backward information; (3) the more aggressive driving behaviors for the forward direction can delay the backward-propagating and speed up the forward-propagating of traffic density waves; (4) positive holding effect and negative pushing effect of backward looking can also be observed under different backward weight ratios; and (5) traffic flow stability varies with different proportion of backward traffic information contribution and such stability impact is sensitive to the initial traffic density condition. This proposed continuum model may contribute to future development of traffic control and coordination in future connected vehicle environment.