Abstract
Many scholars have conducted research on the traffic oscillations and reproduced the growth pattern by establishing stochastic models and simulations. However, the growth pattern of oscillations caused by uncertainty have not been thoroughly studied. Recently, a frequency domain stability analysis method was proposed to analyze the discrete stochastic model. This paper extends this analysis to a continuous situation based on frequency domain tools (e.g., Laplace transform) by introducing a continuous bandlimited white noise. The analytical expression for the evolution of speed standard deviation has been derived. Our study of a homogeneous case reveals an interesting phenomenon: when |G(ω)|∞<1, the speed variance will converge to a constant value, which only depends on the self-disturbance of vehicles. The simulation results verified that the continuous models and corresponding discrete model tend to be consistent when the discrete time step tends to the infinitesimal. Overall, this paper makes up for the deficiency of previous studies on continuous oscillations in car-following theory and can potentially be used to develop new control strategies to help dampen traffic oscillations.
Highlights
Stability Analysis of ContinuousIn the last century, the research on traffic flow mainly focused on the classical models.The early exploration in this field can be traced back to 1953
This paper presents an analytical expression for the evolution of speed standard deviation under a continuous first-order model
We simulatively show that when the discrete interval δ→0, the transfer function of the discrete model and continuous model converge to each other; when frequency F→∞, the noise term of discrete function and continuous function converge to each other
Summary
The research on traffic flow mainly focused on the classical models. Nagatani [8–10] and Sawada [11] extended the car-following model with a next-nearest neighbor interaction These classic models have clear and elegant stability properties, the growth pattern of oscillation is inconsistent with the field experiment, in which the speed standard deviation of each vehicle developed concavely. [30]that proposed the frequency-domain stability methodor putIn forward another view the traffic oscillations are caused notanalysis by the model for linear stochastic car-following extending traditional frequency heterogeneous behavior, but by themodels, disturbance of thethe drivers/vehicles itself.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
