Paper authored by Jeroen P.T. van der Gun, Adam J. Pel and Bart van Arem in 2017.
Journal article published in Transportation Research Part B: Methodological, volume 98, pages 154–178 by Elsevier in Amsterdam, The Netherlands, ISSN 0191-2615.
The original Link Transmission Model as formulated by Yperman et al. (2006) simulates traffic according to Lighthill–Whitham–Richards theory with a very small numerical error, yet only supports triangular fundamental diagrams. This paper relaxes that restriction in two steps. Firstly, we extend the model to handle any continuous concave fundamental diagram, and prove that this extension is still consistent with Lighthill–Whitham–Richards theory. Secondly, we extend the theory and model to handle a capacity drop, explicitly looking into the handling of both the onset and release of congestion. The final model is still first-order and suitable for general networks. Numerical examples show that it qualitatively improves on the original model due to uniquely featuring complex traffic patterns including stop-and-go waves, with crisp shockwaves between traffic states, as well as acceleration fans.
Keywords: Link Transmission Model, Lighthill-Whitham-Richards theory, first-order model, capacity drop, node model, stop-and-go wave.
Citation: Van der Gun, J.P.T., Pel, A.J., Van Arem, B. (2017). Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops. Transportation Research Part B: Methodological, vol. 98, pp. 154–178. Amsterdam, The Netherlands: Elsevier. ISSN 0191-2615. doi:10.1016/j.trb.2016.12.011