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Nash equilibria for a model of traffic flow with several groups of drivers

Alberto Bressan, Ke Han (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κi drivers, sharing the same departure and arrival costs ϕi(t),ψi(t). For any given population sizes κ1,...,κn, we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure...

On the modelling and management of traffic

Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific cases are...

On the modelling and management of traffic

Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific cases...

p-Median problems in a fuzzy environment.

David Kutangila-Mayoya, José Luis Verdegay (2005)

Mathware and Soft Computing

In this paper a formulation for the fuzzy p-median model in a fuzzy environment is presented. The model allows to find optimal locations of p facilities and their related cost when data related to the node demands and the edge distances are imprecise and uncertain and also to know the degree of certainty of the solution. For the sake of illustration, the proposed model is applied in a reduced map of Kinshasa (Democratic Republic of Congo) obtaining results which are rather than realistic ones.

Steady state and scaling limit for a traffic congestion model

Ilie Grigorescu, Min Kang (2010)

ESAIM: Probability and Statistics

In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...

Synchronized traffic plans and stability of optima

Marc Bernot, Alessio Figalli (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The irrigation problem is the problem of finding an efficient way to transport a measure μ+ onto a measure μ-. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, Publ. Mat.49 (2005) 417–451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical cost functional...

The inverse carrier problem

Grant B. Gustafson, Miroslav Laitoch (2002)

Czechoslovak Mathematical Journal

The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.

Traffic plans.

Marc Bernot, Vicent Caselles, Jean-Michel Morel (2005)

Publicacions Matemàtiques

In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure y+ onto a measure y- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,. ..) but it is no more realistic when we want to specify who goes where, like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approathes...

Un problema simple de decisión y un problema de espera.

Luis A. Santaló (1985)

Trabajos de Estadística e Investigación Operativa

El viaje de P a Q se puede hacer por diferentes líneas de autobuses que pasan por P según una ley de Poisson dada y tienen distintas velocidades. En esta nota analizamos la estrategia óptima para un pasajero que llega al azar a la parada P y desea trasladarse a Q en un tiempo mínimo. Al final (n.5) consideramos un problema de espera para autobuses que no siguen una distribución de Poisson.

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