Comparison of Speed-Density Models in the Age of Connected and Automated Vehicles

Fundamental diagrams (FDs) present the relationship between flow, speed, and density, and give some valuable information about traffic features such as capacity, congested and uncongested situations, and so forth. On the other hand, high accuracy speed-density models can produce more efficient FDs. Although numerous speed-density models are presented in the literature, there are very few models for connected and autonomous vehicles (CAVs). One of the recent spend-density models that takes into account the penetration rate of CAVs is provided by Lu et al. However, the estimation power of this model has not been tested against other speed-density models, and it has not been applied to high-speed networks such as freeways. Thus, this paper made a comparison between the Lu speed-density model and a well-known speed-density model (Papageorgiou) in freeway and grid networks. Different CAV behaviors (aggressive, normal, and conservative) are evaluated in this comparison. The comparison has been made between two speed-density models using the mean absolute percentage error (MAPE) and a t-test. The MAPE and t-test results show that differences between the two speed-density models are not significant in two case studies and that Lu is a powerful speed-density model to estimate speed compared with a well-known speed-density model. For the sake of comparing the above-mentioned models, this paper investigates the impact of CAVs on capacity based on FDs. The results suggest that the magnitude of the impacts of CAVs on road capacity (capacity increment percentage) which are obtained from two speed-density models are very close to each other. Also, the extent to which CAVs affect road capacity is highly dependent on their behavior.