Bounded acceleration traffic flow models: A unified approach

Analytical solutions are presented for (i) an accelerating rarefaction wave on a homogeneous road, where traffic is still in equilibrium in the acceleration zone, and (ii) an inhomogeneous road with varying speed limits, where an accelerating standing wave is continuous over an acceleration zone and traffic states are non-equilibrium but stationary. We find that traffic states with bounded acceleration can be equilibrium or not and stationary or not, and bounded acceleration does not lead to capacity drop with variable speed limits. These theoretical results are verified with numerical solutions of corresponding lead-vehicle problems. This study provides a theoretical foundation of applying variable speed limits to eliminate capacity drop at lane-drop, sag, tunnel, and other bottlenecks. In the future we are interested in extending such bounded acceleration models for other bottlenecks with inhomogeneous jam densities and time gaps.