6 research outputs found
Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach
This paper presents scalable traffic stability analysis for both pure
autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic
flow models. Human vehicles are modeled by a non-equilibrium traffic flow
model, i.e., Aw-Rascle-Zhang (ARZ), which is unstable. AVs are modeled by the
mean field game which assumes AVs are rational agents with anticipation
capacities. It is shown from linear stability analysis and numerical
experiments that AVs help stabilize the traffic. Further, we quantify the
impact of AV's penetration rate and controller design on the traffic stability.
The results may provide insights for AV manufacturers and city planners.Comment: 6 page
Analysis of Heterogeneous Vehicular Traffic: Using Proportional Densities
An extended multi-class Aw-Rascle (AR) model with pressure term described as
a function of area occupancy defined in form of proportional densities is
presented. Two vehicle classes that is; cars and motorcycles are considered
based on an assumption that proportions of these form total traffic density.
Qualitative properties of the proposed equilibrium velocity is established.
Conditions under which the proposed model is stable are determine by linear
stability analysis. To compute numerical flux, the model is discretized by the
original Roe decomposition scheme, where Roe matrix, averaged data variables
and wave strengths are explicitly derived. The Roe matrix is shown to be
hyperbolic, consistent and conservative. From the numerical results, the effect
of motorcycles proportion on the flow of vehicle classes is determined. Results
obtained remain within limits therefore, the proposed model is realistic.Comment: 25 pages, comments are welcom
Modeling the impact of on-line navigation devices in traffic flows
International audienceWe consider a macroscopic multi-population traffic flow model on networks accounting for the presence of drivers (or autonomous vehicles) using navigation devices to minimize their instantaneous travel cost to destination. The strategic choices of each population differ in the degree of information about the system: while part of the agents knows only the structure of the network and minimizes the traveled distance, others are informed of the current traffic distribution, and can minimize their travel time avoiding the most congested areas. In particular, the different route choices are computed solving eikonal equations on the road network and they are implemented at road junctions. The impact on traffic flow efficiency is illustrated by numerical experiments. We show that, even if the use of routing devices contributes to alleviate congestion on the whole network, it also results in increased traffic on secondary roads. Moreover, the generalized use of real-time information can even deteriorate the efficiency of the network
Differential Models, Numerical Simulations and Applications
This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems