A Fast Algorithm for Signal Timing Optimization in Corridors using Semi-explicit Solutions to Hamilton-Jacobi Equations

This article introduces a new formulation for optimizing traffic signal timing over long arterials. In this formulation, the arterial is modeled by a stretch of highway, on which traffic flow is described by the Lighthill Whitham Richards (LWR) model. The authors introduce an equivalent Hamilton-Jacobi formulation of the problem, in which the red phases of the traffic signals are described as internal conditions corresponding to a zero flow (fixed bottlenecks), though the parameters associated with these internal conditions (duration, initial value and initial time) are not known. The authors then show that these internal conditions can be dynamically incorporated into the computation of the solution, using a property known as inf-morphism. The authors propose an algorithm to automatically compute the parameters associated with these internal conditions, given a set of known initial and boundary conditions corresponding to the initial state of the arterial, the upstream demand and the downstream supply. Since the solutions associated with internal conditions can be computed analytically, this algorithm is extremely fast in performing a forward simulation of the traffic conditions associated with a given signal timing strategy. The authors then show that this fast simulation scheme can be integrated in a control loop to compute the best timing strategy associated with a given set of initial and boundary conditions. A numerical implementation is shown, and the extension of this formulation to transportation networks is discussed.

• Supplemental Notes:
  • This paper was sponsored by TRB committee AHB45 Standing Committee on Traffic Flow Theory and Characteristics.
• Corporate Authors:

  Transportation Research Board

  500 Fifth Street, NW
  Washington, DC  United States  20001
• Authors:
  • Simoni, Michele D
  • Claudel, Christian G
• Conference:
  • Transportation Research Board 96th Annual Meeting
  • Location: Washington DC, United States
  • Date: 2017-1-8 to 2017-1-12
• Date: 2017

Language

• English

Media Info

• Media Type: Digital/other
• Features: Figures; References; Tables;
• Pagination: 15p
• Monograph Title: TRB 96th Annual Meeting Compendium of Papers

Subject/Index Terms

• TRT Terms: Algorithms; Arterial highways; Bottlenecks; Control loops; Optimization; Traffic signal phases; Traffic signal timing; Traffic simulation
• Identifier Terms: Lighthill-Whitham-Richards traffic flow model
• Subject Areas: Highways; Operations and Traffic Management; Planning and Forecasting;

Filing Info

• Accession Number: 01628767
• Record Type: Publication
• Report/Paper Numbers: 17-04652
• Files: TRIS, TRB, ATRI
• Created Date: Mar 13 2017 9:12AM