A Density-Based and Lane-Free Microscopic Traffic Flow Model Applied to Unmanned Aerial Vehicles

Abstract

In this work, we introduce a microscopic traffic flow model called Scalar Capacity Model (SCM) which can be used to study the formation of traffic on an airway link for autonomous Unmanned Aerial Vehicles (UAVs) as well as for the ground vehicles on the road. Given the 3D trajectory of UAV flights (as opposed to the 2D trajectory of ground vehicles), the main novelty in our model is to eliminate the commonly used notion of lanes and replace it with a notion of density and capacity of flow, but in such a way that individual vehicle motions can still be modeled. We name this a Density/Capacity View (DCV) of the link capacity and how vehicles utilize it versus the traditional One/Multi-Lane View (OMV). An interesting feature of this model is exhibiting both passing and blocking regimes (analogous to multi-lane or single-lane) depending on the set scalar parameter for capacity. We show the model has linear local (platoon) and asymptotic linear stability. Additionally, we perform numerical simulations and show evidence for non-linear stability. Our traffic flow model is represented by a nonlinear differential equation which we transform into a linear form. This makes our model analytically solvable in the blocking regime and piece-wise analytically solvable in the passing regime. Finally, a key advantage of using our model over an OMV model for representing UAV’s flights is the removal of the artificial restriction on passing via only adjacent lanes. This will result in an improved and more realistic traffic flow for UAVs.