Eigenvalue and Eigenvector Analysis of Stability for a Line of Traffic

Many authors have recognized that traffic under the traditional car-following model (CFM) is subject to flow instabilities. A recent model achieves stability using bilateral control (BCM)—by looking both forward and backward [1]. (Looking back may be difficult or distracting for human drivers, but is not a problem for sensors.) We analyze the underlying systems of differential equations by studying their eigenvalues and eigenvectors under various boundary conditions. Simulations further confirm that bilateral control can avoid instabilities and reduce the chance of collisions.