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 and Analysis of Mixed Flow of Cars and Powered Two Wheelers

International audienceIn modern cities, a rapid increase of motorcycles and other types of Powered Two-Wheelers (PTWs) is observed as an answer to long commuting in traffic jams and complex urban navigation. Such increasing penetration rate of PTWs creates mixed traffic flow conditions with unique characteristics that are not well understood at present. Our objective is to develop an analytical traffic flow model that reflects the mutual impacts of PTWs and Cars. Unlike cars, PTWs filter between cars, have unique dynamics, and do not respect lane discipline, therefore requiring a different modeling approach than traditional " Passenger Car Equivalent " or " Follow the Leader ". Instead, this work follows an approach that models the flow of PTWs similarly to a fluid in a porous medium, where PTWs " percolate " between cars depending on the gap between them. Our contributions are as follows: (I) a characterization of the distribution of the spacing between vehicles by the densities of PTWs and cars; (II) a definition of the equilibrium speed of each class as a function of the densities of PTWs and cars; (III) a mathematical analysis of the model's properties (IV) an impact analysis of the gradual penetration of PTWs on cars and on heterogeneous traffic flow characteristics

Traffic State Estimation via a Particle Filter Over a Reduced Measurement Space

Traffic control and vehicle route planning require accurate estimates of the traffic state in order to be successfully implemented. This estimation problem can be solved by using particle filters in conjunction with macroscopic traffic models such as the stochastic compositional model. The accuracy of the estimates can be decreased for road segments where there are no measurements available. However, the inclusion of measurements for all segment boundaries carries a computational cost associated with the evaluation of the likelihood function required by the particle filter. To solve this problem, this paper proposes using the column based matrix decomposition method to select the most significant locations in the road network. This results in the particle filter being applied over a reduced measurement space, allowing a trade-off between computational efficiency and estimation accuracy to be achieved. A performance evaluation based on a simulated stretch of road is provided to validate the proposed method. It shows that by selecting half the original number of measurements, the computational time is reduced by approximately 9% without significantly decreasing the estimation accuracy. A more significant improvement in terms of savings in computational complexity can be expected when considering larger urban road networks

Traffic State Estimation via a Particle Filter with Compressive Sensing and Historical Traffic Data

In this paper we look at the problem of estimating traffic states within segments of road using a particle filter and traffic measurements at the segment boundaries. When there are missing measurements the estimation accuracy can decrease. We propose two methods of solving this problem by estimating the missing measurements by assuming the current measurements will approach the mean of the historical measurements from a suitable time period. The proposed solutions come in the form of an l1 norm minimisation and a relevance vector machine type optimisation. Test scenarios involving simulated and real data verify that an accurate estimate of the traffic measurements can be achieved. These estimated missing measurements can then be used to help to improve traffic state estimation accuracy of the particle filter without a significant increase in computation time. For the real data used this can be up to a 23.44% improvement in RMSE values

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

Long-term degradation, damage and fracture in deep rock tunnels: A review on the effect of excavation methods

Rocks are frequently host materials for underground structures, particularly for deep Tunnels. Their behavior plays a fundamental role in the overall stability of these structures. In fact, the erection of deep tunnels imposes rocks excavations around the defined routes. These excavations are generally carried out by various methods of which the most used are Drill-and-Blast (DB) and Tunnel Boring Machine (TBM).  However, regardless of the tunnelling method used, the impacts such as the perturbation of the initial stress field in rocks and the release of the stored energy are always significant. The impacts produce damage, fractures and deformations which are generally time-dependent and influence the long-term stability of deep tunnels built in rocks. Thus, by considering the aforementioned excavation methods, this paper identifies, reviews and describes the relevant factors generated during and after rock excavations. Interestingly, such factors directly or indirectly influence the long-term stability and therefore the structural integrity of deep rock tunnels. In addition, some recommendations and proposals for future works are presented. This paper can provide useful references in understanding the degradations, damage and fractures generated by tunnelling methods and facilitate suitable actions to ensure long-term stability of deep underground structures