Large Scale Performance Assessment of the Lighthill-Whitham-Richards Model on a Smart Motorway

Abstract

In this work, we present a large scale assessment of the Lighthill-Whitham-Richards (LWR) model for a modern smart motorway. We use 36 days of loop-level sensor data from the National Traffic Information Service (NTIS) for 29 sections of the M25 motorway around London. The model is tested on 48,697 different test scenarios each consisting of a sequence of at least 3 consecutive loop sensors. Data from the first and last loop sensors are used as boundary data and the model is used to predict the data measured by the interior loops. We find consistent performance across different sections of road, with mean absolute percentage errors typically being below 10% for traffic density. Furthermore, we find accidents and obstructions lead to significantly greater uncertainty in performance when compared to other events. Changing a speed limit during the simulation typically leads a doubling of the prediction error. The relationship between domain length and error is also quantified. We see the smallest domains have around 4% error, whilst the largest have 12%. Finally, the model performs poorly in the extreme lows and highs of congestion and the distributions of errors have very heavy tails.