Related papers: The dynamic system of the traffic assignment probl…
Transportation and traffic are currently undergoing a rapid increase in terms of both scale and complexity. At the same time, an increasing share of traffic participants are being transformed into agents driven or supported by artificial…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
In this second part of our research we used the models presented in \emph{Modeling a vehicular traffic network. Part I} \cite{ogm1} to perform an analysis of the urban traffic as recorded by cameras distributed in a chosen sector of Tigre,…
While motion planning approaches for automated driving often focus on safety and mathematical optimality with respect to technical parameters, they barely consider convenience, perceived safety for the passenger and comprehensibility for…
The article provides an overview of the latest developments on control approaches for connected and automated vehicles along with their effectiveness on energy and transportation efficiency.
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
The Logit lane assignment model has been introduced recently in order to describe multi-lane traffic flow from a macroscopic point of view. The model is based on the idea that each available lane has a specific utility for each driver, who…
In this paper we analyze mathematically how human factors can be effectively incorporated into the analysis and control of complex systems. As an example, we focus our discussion around one of the key problems in the Intelligent…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
Traffic prediction plays an essential role in intelligent transportation system. Accurate traffic prediction can assist route planing, guide vehicle dispatching, and mitigate traffic congestion. This problem is challenging due to the…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
Traffic assignment analyzes traffic flows in road networks that emerge due to traveler interaction. Traditionally, travelers are assumed to use private cars, so road costs grow with the number of users due to congestion. However, in…
This historical introduction is in two parts. The first is reprinted with permission from ``A century of mathematics in America, Part II,'' Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the…
Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)
This paper is a follow-up work about the artificial ecosystem model: number soup (Liu and Sumpter, J. Royal Soc. Interface, 2017). It elaborates more details about this model and points out future directions.
This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.
In this note, we propose a case study of freeway traffic flow modeled as a hybrid system. We describe two general classes of networks that model flow along a freeway with merging onramps. The admission rate of traffic flow from each onramp…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.
We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…