Citation

Vishnoi SC, Claudel CG. IEEE Trans. Intel. Transp. Syst. 2022; 23(7): 7441-7456.

Copyright

(Copyright © 2022, IEEE (Institute of Electrical and Electronics Engineers))

DOI

10.1109/TITS.2021.3069971

PMID

unavailable

Abstract

This paper presents a novel optimization formulation to solve the problem of variable speed limit control on road networks modeled by the Lighthill-Whitham-Richards (LWR) partial differential equation. It also presents some mathematical rules that allow for a reduction in the size and computational time of the optimization problem. Using the analytical solutions to the LWR model, an optimization problem is formulated for the variable speed limit and ramp metering control of traffic on highway networks using the Lax-Hopf algorithm. The resulting problem, which is non-linear in the decision variables, is transformed into a Mixed Integer Linear Program. An example is presented to show the effectiveness of the approach, including its application to a real-world highway network with multiple ramp connections. The possibility of linear relaxation of integer variables in the problem is also considered. Lastly, the method is compared to a classical Link Transmission Model formulation of the variable speed limit control problem.

Language: en

Keywords

Boundary conditions; Computational modeling; Lax-Hopf method; Mathematical model; mixed integer linear programming; network control; Optimization; Real-time systems; Road transportation; Transforms; variable speed limits