Related papers: Traffic assignment models. Numerical aspects
Managing all the mobility and transportation services with autonomous vehicles for users of a smart city requires determining the assignment of the vehicles to the users and their routing in conjunction with their speed. Such decisions must…
In this note, I review entropy-regularized Monge-Kantorovich problem in Optimal Transport, and derive the gradients of several popular algorithms popular in Computational Optimal Transport, including the Sinkhorn algorithms, Wasserstein…
The rapid urbanization and increasing traffic have serious social, economic, and environmental impact on metropolitan areas worldwide. It is of a great importance to understand the complex interplay of road networks and traffic conditions.…
In this work we widespread statistical physics (chemical kinetic stochastic) approach to the investigation of macrosystems, arise in economic, sociology and traffic flow theory. The main line is a definition of equilibrium of macrosystem as…
This paper considers the optimization-based traffic allocation problem among multiple end points in connectionless networks. The network utility function is modeled as a non-concave function, since it is the best description of the quality…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
A classic network tomography problem is estimation of properties of the distribution of route traffic volumes based on counts taken on the network links. We consider inference for a general class of models for integer-valued traffic. Model…
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…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
Traffic data imputation is a critical preprocessing step in intelligent transportation systems, underpinning the reliability of downstream transportation services. Despite substantial progress in imputation models, model selection and…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…
We discuss a class of coupled systems of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution are proven via…
We study the interdependence between transportation and power systems considering decentralized renewable generators and electric vehicles (EVs). We formulate the problem in a stochastic multi-agent optimization framework considering the…