Generalized Quasi-Variational Inequalities and Traffic Equilibrium Problem

Abstract

The model that expresses the traffic equilibrium problem in terms of Quasi-Variational Inequalities is improved taking into account that: i) the cost function may be discontinuous; ii) the cost function may be considered as a multifunction. Existence theorems in such directions are given with examples and considerations, based on a direct computational method, that justify this approach.In Sect. 3, we prove an existence theorem for the generalized Quasi-Variational Inequality which comes from this improved approach. Shortly, we recall that one of the possible model for a traffic network with fixed 45 F. Giannessi et al. (eds.), Variational Inequalities and Network Equilibrium Problems

On well-posedness for parametric vector quasiequilibrium problems with moving cones

“…Contributing to the development of traffic network problems, Smith [41] derived a spotlight point by claiming that the Wardrop equilibrium flows of a network are expressed as solutions of the corresponding variational inequality. Because of diverse practical situations, these demands may depend on the equilibrium vector flows which were considered in [20], [36]; the so-called elastic network problems, and then the Wardrop equilibrium flows of the elastic network problem are obtained as solutions of the corresponding quasivariational inequality.…”

“…Let us recall the mathematical model of the elastic traffic network problem studied in [2], [6], [20], [36]. Let N the set of nodes and L that of arcs (or links).…”

“…Now assume that the perturbation on the traffic is expressed by a parameter λ of a metric space Λ. Suppose that the travel demands g j of the O/D pair W j depend on λ ∈ Λ and also on the equilibrium vector flow H as interpreted in [20], [36]. We denote the travel vector demand by g = (g 1 , .…”

Optimal control of generalized multiobjective games with application to traffic networks modeling

“…In this section, we present an application of results obtained in Section 3 to controlled systems for traffic networks. We will recall the formulation of the traffic network problem, which was considered by many authors (see, e.g., [5, 9, 10, 13, 19, 25, 33, 46] and the references therein). Consider a transportation network $$G=(M, N)$$, where M denotes the set of nodes and N denotes the set of links (or arcs).…”

Evolutionary Quasi-Variational Inequalities and the Dynamic Multiclass Network Equilibrium Problem

“…It is beyond the scope of this article to give a survey of all relevant results, therefore, we address the reader only to some of them. We refer, for example, to [2][3][4][5][6][7] for an overview on theory and to [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] for some applications to equilibrium problems.…”