Variable speed limits in the link transmission model using an information propagation method

•Variable speed limits in continuous time link transmission model.•Variable fundamental diagram support in macroscopic dynamic network loading.•Alternative solution method to a specific type of moving bottleneck via a transition node model.•Explicit propagation of speed limit information in space–time.•Distinction between physical and realised fundamental diagrams. Traffic management on (smart) motorways is becoming increasingly important to extract the most out of the limited capacity that is available, especially during peak periods. Accurate modelling of traffic management measures in traffic flow simulation is therefore paramount to make accurate short, and/or long-term predictions, to aid offline and online applications. In this work we propose a novel macroscopic network loading model that supports variable speed limits (VSL). Most existing aggregate network loading models that support VSL impose speed limits instantaneously across the entire road section, ignoring the fact that only vehicles passing the speed limit sign are aware of the new limit (either by a driver seeing the signal, or in case of autonomous/connected vehicles via infrastructure-to vehicle-technology), this leads to a discrepancy between model and reality that one ideally would want to avoid. Another challenge that arises is that current state-of-the-art macroscopic network loading models, such as the link transmission model (LTM), do not track the internal state of the link while constructing their solution. This is especially useful in large-scale (macroscopic) simulations where its increased efficiency is valued highly. Unfortunately, this desirable property makes modelling traffic management measures such as VSL much more challenging. Virtually all existing methods to date rely on tracking the link’s internal state to support VSL. Therefore, very few methods exist that offer proper support for VSL in LTM. At the same time, the methods that do exist have various limitations. In this work we propose a continuous-time LTM model that address these limitations, yields exact solutions, and supports VSL. The proposed solution method is an extension of the event-based LTM of Bliemer and Raadsen (2019) and Raadsen and Bliemer (2019) which can be considered a special case with a single speed limit. Three case studies are provided to demonstrate feasibility and general applicability of the proposed method and solution algorithm.