A two-dimensional car-following model for two-dimensional traffic flow problems

Understanding the Lateral Dimension of Traffic: Measuring and Modeling Lane Discipline

“…In the aforementioned microscopic 2D social force model three forces were defined: (i) acceleration force f a , which is exclusively longitudinal and represents the desire of drivers to accelerate up to their free-flow velocity; (ii) lane force f l , which is exclusively lateral and controls lane discipline; and (iii) repulsive force f r , which is bidimensional and represents driver caution, leading drivers to keep their distance from other vehicles, especially when they approach or are already close ( 4, 26 ).…”

“…During the execution of a lane change, a vehicle affects both its current lane and its target lane ( 1 ). Its lateral position affects the comfort of surrounding vehicles ( 2 ) as well as that of its own occupants ( 3 ) and is related to the relaxation phenomenon through anticipation ( 4, 5 ). Standard deviation of lateral position has been studied as a road safety ( 6, 7 ) and a performance ( 8–10 ) metric.…”

“…In certain cases they have also taken account of lateral position during the lane-changing maneuver itself ( 24, 25 ). To the author’s knowledge, however, only one model, that developed by the author, has fully incorporated the lateral dimension into the context of multi-lane traffic ( 4, 5, 26 ). This formulation, called the two-dimensional microscopic traffic model (2D- μ TM), is based on a social force paradigm ( 27, 28 ) in which drivers are modeled as though their vehicles were subject to physical forces.…”

Cyber‐physical description and CPS‐based pinning approach of mixed traffic

“…The two‐dimensional car‐following model was proposed to describe the influence of surrounding vehicles[51]‐[53]. It is necessary to make some simplifying assumptions: there exists and only exists one virtual leader; the longitudinal and lateral movements of the vehicle are considered as independent with each other; the influence of $$\bm {F}^a(t)$$ is mostly longitudinal, thus we ignore its lateral influence, and let $$F^{ay}=0$$; the influence of $$\bm {F}^l(t)$$ is mostly lateral, thus we ignore its longitudinal influence, and let $$F^{lx}=0$$. …”

“…Since there are not many studies on the two‐dimensional car‐following model, the specific forms of $$\bm {F}^a(t)$$, $$\bm {F}^r(t)$$ and $$\bm {F}^l(t)$$ in this paper mostly refer to [51]. When a vehicle is a CAV, then we have $$\begin{equation} F^{ax}=(V-v^x(t))c_1.$$…”