The link transmission model with variable fundamental diagrams and initial conditions

Paper authored by Jeroen P.T. van der Gun, Adam J. Pel and Bart van Arem in 2019.

Journal article published in Transportmetrica B: Transport Dynamics, volume 7(1), pages 834–864 by Taylor & Francis in London, United Kingdom, ISSN 2168-0566.

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The link transmission model is a macroscopic network traffic flow simulation tool based on Lighthill-Whitham-Richards theory. While its efficiency and accuracy are superior to the well-known cell transmission model, applications of its current numerical formulations are limited by the inability to apply changes to the fundamental diagrams of links within a simulation and the need to start the simulation with an empty network. We resolve both limitations by developing a methodology for initialising the discrete-time link model with a non-empty initial condition and for computing within-link densities during the simulation, which can then serve as an initial condition for continued simulation with a new fundamental diagram. Since the computation of within-link densities is algebraic, no new numerical errors are introduced. Optional support for multiple commodities, subcritical delays and platoon dispersion, are retained. The resulting model is demonstrated on a motorway corridor network with variable speed limits and dynamic lane management.

Keywords: link transmission model, first-order model, Smulders fundamental diagram, traffic control, environmental conditions.

Citation: Van der Gun, J.P.T., Pel, A.J., Van Arem, B. (2019). The link transmission model with variable fundamental diagrams and initial conditions. Transportmetrica B: Transport Dynamics, vol. 7(1), pp. 834–864. London, United Kingdom: Taylor & Francis. ISSN 2168-0566. doi:10.1080/21680566.2018.1517060