Related papers: Evolution models for mass transportation problems
We propose a framework for constructing microscopic traffic models from microscopic acceleration patterns that can in principle be experimental measured and proper averaged. The exact model thus obtained can be used to justify the…
We present a generative model of human mobility in which trajectories arise as realizations of a prescribed, time-dependent Markov dynamics defined on a spatial interaction network. The model constructs a hierarchical routing structure with…
In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the…
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity equation. When this source term is penalized based on the…
Consider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on the real line, and suppose the cost of matching two points satisfies the Monge condition. We introduce a notion of locally…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail,…
The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
Efficient traffic management is crucial for maintaining urban mobility, especially in densely populated areas where congestion, accidents, and delays can lead to frustrating and expensive commutes. However, existing prediction methods face…
The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…
In this paper we consider the problem of estimating emissions due to vehicular traffic on complex networks, and minimizing their effect by regulating traffic at junctions. For the traffic evolution, we consider a Generic Second Order Model,…
We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems in a gradient flow setting, and form the basis of our…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
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…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
In the present paper we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…