Mathematical Modelling of Oscillatory Dynamics in Circular Traffic Systems
By: Craig S Wright
Potential Business Impact:
Cars automatically avoid traffic jams by thinking ahead.
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without relying on simulation, we derive a series of coupled delay differential equations to model vehicular interactions. By introducing a mnemonic-based symbolic system, we establish a mathematical framework incorporating stochastic initial conditions, non-uniform reaction times, and cognitive lag. A full linear stability analysis is conducted using Fourier decomposition and modal perturbation techniques. Our results identify critical thresholds for harmonic induction, delineate the bounds of safe following distances, and reveal hysteresis in driver overcorrection. The analysis concludes with implications for autonomous vehicle control and potential suppression strategies for oscillatory instability. All derivations are purely symbolic and analytically proven.
Similar Papers
A multi-class non-local macroscopic model with time delay for mixed autonomous / human-driven traffic
Analysis of PDEs
Makes traffic flow smoother with self-driving cars.
Nonlinear Oscillatory Response of Automated Vehicle Car-following: Theoretical Analysis with Traffic State and Control Input Limits
Systems and Control
Helps self-driving cars avoid traffic jams.
A Comparative Study of Oscillatory Perturbations in Car-Following Models
Systems and Control
Keeps self-driving cars driving safely together.