Speed limit and ramp meter control for traffic flow networks

Goatin, Paola; Göttlich, Simone; Kolb, Oliver · 2015 · OpenAlex-citations

DOI: 10.1080/0305215x.2015.1097099

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the optimal control of traffic flow networks by combining variable speed limits (VSL) and coordinated ramp metering. The authors aim to minimize total travel time and maximize system outflow within the framework of the Lighthill-Whitham-Richards (LWR) model, which describes traffic dynamics via scalar conservation laws. While previous studies often relied on linearized models or restricted analyses to single roads, this work provides a rigorous mathematical and computational treatment for complex network topologies, including highway interchanges. The motivation is to demonstrate how time-dependent speed limits and boundary controls at on-ramps can interact to prevent congestion and improve traffic efficiency. The methodology employs a "discretize-then-optimize" approach. The traffic network is modeled as a directed graph where edges represent roads and vertices represent junctions, with coupling conditions defined by demand and supply functions. The authors use a staggered Lax-Friedrichs scheme to discretize the governing partial differential equations in space and time. Control variables—piecewise constant maximal velocities for VSL and inflow rates for ramp metering—are integrated into the flux functions and boundary conditions. The resulting finite-dimensional nonlinear optimization problem is solved using Sequential Quadratic Programming (SQP). Gradient information required for the solver is efficiently computed using an adjoint-based optimization framework, which involves solving forward state equations and backward adjoint equations. Numerical experiments are conducted on a network topology inspired by the Frankfurter Kreuz interchange in Germany. The results demonstrate that optimizing VSL alone yields modest improvements, reducing total travel time by approximately 1.28% and increasing outflow by 0.03% compared to uncontrolled scenarios where speed limits remain at their upper bounds. The study analyzes the sensitivity of the solution to the number of control points and discretization parameters, showing convergence as control resolution increases. Additionally, the authors introduce a penalty term to smooth control variations, preventing unrealistic fluctuations in speed limits. The simulations confirm that VSL acts as an effective traffic guidance mechanism, maintaining high outflows and short travel times even when ramp metering alone is insufficient to prevent congestion. The significance of this work lies in its rigorous application of nonlinear control techniques to full LWR network models, bridging a gap in existing literature that often relied on simplified dynamics. By successfully combining VSL and ramp metering within an adjoint-based optimization framework, the paper provides a robust computational tool for traffic management. The findings suggest that coordinated control strategies can effectively navigate traffic flow through complex junctions, offering practical insights for implementing real-time traffic guidance systems on highway networks.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• speed management