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.
Highlights
Traffic flow models have been a staple of the traffic engineering discipline for ground vehicles
This paper provides a traffic flow model for drones motivated by their unique characteristics, such as the 3D movement compared to the ground vehicles
We introduce the concept of density and capacity in a novel way in the area of microscopic traffic flow models
Summary
Traffic flow models have been a staple of the traffic engineering discipline for ground vehicles. We need computing tools for analyzing the behaviors of drones in the air and use the gained insights to improve the airway structures in UAV traffic control architectures (e.g., IoD) and provide additional capacity or services as the need for them becomes clear Among these tools are traffic flow models. If instead, we use an OMV model to represent the UAV traffic flow and velocity assignment, we effectively limit the movement of UAVs in an artificial way This is because while ground vehicles can overtake each other only by moving to the adjacent lanes, we do not have the same channel topology for UAVs in the air. This allows us to eliminate lanes and lane change models altogether
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