Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation. (August 2019)

• Record Type: Journal Article
• Authors: Bliemer, Michiel C.J.; Raadsen, Mark P.H.
• Is Part Of: Transportation research. Volume 126(2019)
• Page Start: 442
• Page End: 470
• Publication Date: 2019-08
• Subjects: Kinematic wave theory -- Link transmission model -- Nonlinear concave fundamental diagram -- On-the-fly linearization -- Simplified fanning -- Shockwave theory -- Event-based solution methods; Transportation -- Research -- Periodicals; Transportation -- Mathematical models -- Periodicals
• DOI: 10.1016/j.trb.2018.01.001
• Languages: English
• ISSNs: 0191-2615

Abstract

Highlights: Formulates continuous-time general link transmission model derived from Lax-Hopf formula. Two on-the-fly linearization techniques are proposed to simplify expansion fans, one is consistent with shockwave theory. Simplified fanning allows for exact non-entropic solutions or approximate entropic solutions to the kinematic wave model. Potential for fast event-based algorithms. Abstract: The kinematic wave theory is widely used to simulate traffic flows on road segments. Link transmission models are methods to find a solution to the kinematic wave model, however, their computational efficiency heavily relies on the shape of the fundamental diagram that is used as input. Despite the limitations and drawbacks of triangular and piecewise linear fundamental diagrams, they remain popular because they result in highly efficient algorithms. Using smooth nonlinear branches is often preferred in terms of realism and other desirable properties, but this comes at a significantly higher computational cost and requires time discretization to find an approximate solution. In this paper we consider a nonlinear fundamental diagram as input and propose on-the-fly multi-step linearization techniques to simplify expansion fans. This leads to two simplified link transmission models that can be solved exactly in continuous time under the assumption of piecewise stationary travel demand. One of the models simplifies to shockwave theory in case of a single step. We show that embedding shockwave theory in the link transmission model allows for finding an exact solution in continuous time and we discuss the potential for the design of efficient event-based algorithms for general networks.