A Macroscopic Model for Platooning in Highway Traffic

Abstract

We consider a model describing the presence of a platoon of vehicles moving in the traffic flow. The model consists of a coupled PDE-ODE system describing the interaction between the platoon and the surrounding traffic flow. The scalar conservation law takes into account the main traffic evolution, while the ODEs describe the trajectories of the initial and final points of the platoon, whose length can vary in time. The presence of the platoon acts as a road capacity reduction, resulting in a space-time discontinuous flux function. We describe the solutions of Riemann problems and design a finite volume numerical scheme sharply capturing non-classical discontinuities. Some numerical tests are presented to show the effectiveness of the method.

Traffic Control Via Platoons of Intelligent Vehicles for Saving Fuel Consumption in Freeway Systems

“…The technical constraint (6) comes from an admissibility condition on the feasibility of the corresponding Riemann problems, see [18]. The speed of the upstream point v u is allowed to assume a negative value if new vehicles can join the platoon, thus moving the end point backwards.…”

“…In correspondence of the initial and final points of the platoon, a discontinuity in the flow arises and a solution to the scalar conservation law with moving discontinuities needs to be studied. A numerical scheme able to precisely capture the density discontinuities has been proposed in [18], where a conservative reconstruction strategy is adopted. For both the upstream and downstream endpoints of the platoon, we consider the discontinuities moving with speeds v u (k) and v d (k).…”

“…Let us focus on the cell i d (k) in which the downstream front-end point z d (k) is located at time step k. We expect a density discontinuity to appear in the cell and at each time step we consider the Riemann-type initial datum ρ l = ρ i d −1 (k) and ρ r = ρ i d +1 (k). The Riemann problem is then solved as detailed in [18] and we obtain the two solution density valuesρ α andρ, that correspond to the values of density that appear in cell i d upstream and downstream the position z d (k). The density ρ i d (k) can be then replaced by a convex combination of the two values by defining d i d such that…”

“…Their speeds were controlled by means of a Model Predictive Control (MPC) to reduce travel times of drivers. The PDE-ODE model presented in [8] considering a punctual moving bottleneck has been recently extended in [18] to capture platoons of vehicles having a physical length that can change in time, depending on the number of vehicles composing it and their spacing, so that the length can here be taken as an additional control variable. The main contribution of this paper is the design of a multi-variable model predictive control to regulate the speeds of both end-points of the platoon (therefore controlling its speed and length) with the aim of reducing congestion and fuel consumption of the overall traffic flow.…”

A Hybrid Queuing Model for Coordinated Vehicle Platooning on Mixed-Autonomy Highways: Training and Validation

“…The vehicle discharge rate is upper-bounded by the highway capacity. The HQM can be viewed as a simplification of a class of more sophisticated models for mixed-autonomy traffic, which are designed for more detailed analysis or control purposes [10,14,15,16]. The HQM can be further abstracted and used for higher-level decisions such as routing [17].…”