Quasi-Variational Inequalities in Transportation Networks

Abstract

This paper aims to consider user equilibrium problems in transportation networks in the most complete and realistic situations. In fact, the presented model allows for the dependence of data on time, the presence of elastic travel demands, the capacity restrictions and delay effects. The equilibrium conditions for such a model are given and the equivalent formulation in terms of a quasi-variational inequality is discussed. Moreover, a theorem for the existence of solutions is shown and a numerical example is provided. Finally, some questions of stability are studied.

Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term

“…In fact, the integral term represents the displacement, namely the delay, of the equilibrium solution commodity shipments due to the previous equilibrium state. Therefore, delay effects are not only regarded as perturbation factors for the constraint set (see [37] in connection with traffic network problems) but can also be interpreted as adjustment factors of operators.…”

Double-layered dynamics: A unified theory of projected dynamical systems and evolutionary variational inequalities

“…The same framework has been used also by Scrimali in [42], who studied a special convex set K which depends on the solution of the evolutionary variational inequality, and gives rise to an evolutionary quasivariational inequality. In Gwinner [19], the author presents a survey on several classes of time-dependent variational inequalities.…”

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.…”