The Intelligent Driver Model with stochasticity – New insights into traffic flow oscillations

Abstract

Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds (action points), and external acceleration noise. However, the relative importance of these factors in a given situation remains unclear. We bring light into this question by adding external noise and action points to the Intelligent Driver Model and other car-following models thereby obtaining a minimal model containing all three oscillation mechanisms. We show analytically that even in the subcritical regime of linearly stable flow (order parameter ǫ < 0), external white noise leads to spatiotemporal speed correlations "anticipating" the waves of the linearly unstable regime. Sufficiently far away from the threshold, the amplitude scales with (−ǫ) −0.5 . By means of simulations and comparisons with experimental car platoons and bicycle traffic, we show that external noise and indifference regions with action points have essentially equivalent effects. Furthermore, flow instabilities dominate the oscillations on freeways while external noise or action points prevail at low desired speeds such as vehicular city or bicycle traffic. For bicycle traffic, noise can lead to fully developed waves even for single-file traffic in the subcritical regime.

Langevin method for a continuous stochastic car-following model and its stability conditions

“…string stability) are still missing for general stochastic car-following models. Our approach advances the model of Laval et al (2014) and Treiber and Kesting (2017) as following:…”

Simulating bicycle traffic by the intelligent-driver model-Reproducing the traffic-wave characteristics observed in a bicycle-following experiment

“…Validation by cross comparison implies determining the error measures for a certain test data set by simulating the model with the parameters calibrated to the disjunct "learning" data set [9]. For each experiment (5,10,15,18,20 and 33 participants, respectively), we have separately calculated the calibration-validation matrix whose elements M i j give the error measure √ S abs for the trajectory pair j as obtained from the model calibrated to the trajectory pair i. The diagonal element M ii are the calibration errors whereas the off-diagonal elements M ji , j = i, give a superposition of the validation error and the inter-driver variation of follower j with respect to follower i.…”

Analysis of V2V Messages for Car-Following Behavior with the Traffic Jerk Effect

“…According to Equations (14) and (24), the tra c ow stability distribution is shown in Figures 4(a) and 4(b), respectively. In Figure 4(a), the space above the neutral stable surface is the stable space, and the space below is the unstable space.…”

“…In actual tra c scenarios, vehicles o en undergo sudden acceleration changes, and this e ect is called tra c jerk. is kind of disturbance easily spreads upstream in tra c, resulting in phantom tra c jams [22][23][24]. In recent years, many scholars have studied various tra c ow models that consider tra c jerk.…”