Related papers: Mathematical Modelling of Oscillatory Dynamics in …

We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some…

With the emergence of autonomous vehicles, it is important to understand their impact on the transportation system. However, conventional traffic simulations are time-consuming. In this paper, we introduce an analytical traffic model for…

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…

In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…

Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds…

In two intersecting many-particle streams, one can often find the emergence of oscillatory patterns. Here, we investigate the interaction of pedestrians with vehicles, when they try to cross a road. A numerical study of this coupled…

In this paper, we develop a mechanical system inspired microscopic traffic model to characterize the longitudinal interaction dynamics among a chain of vehicles. In particular, we extend our prior work on mass-spring-damper-clutch based…

In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…

In this contribution, we introduce a general class of car-following models with an input-state-output port-Hamiltonian structure. We derive stability conditions and long-term behavior of the finite system with periodic boundaries and…

This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty.…

We study the dynamics of vehicular traffic in a loop using a car-following model with the consideration of volume exclusions. In particular, we solve the steady state for the single-cluster case and derive fundamental diagrams, exhibiting…

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…

The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of…

This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…

At an unmanaged intersection, it is important to understand how much traffic delay may be caused as a result of microscopic vehicle interactions. Conventional traffic simulations that explicitly track these interactions are time-consuming.…

We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii)…

We consider a discrete-time dynamical system in a car-following context. The system was recently introduced to parsimoniously model human driving behavior based on utility maximization. The parameters of the model were calibrated using…

We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical…

Understanding the mechanisms responsible for the emergence and evolution of oscillations in traffic flow has been subject to intensive research by the traffic flow theory community. In our previous work, we proposed a new mechanism to…