In this paper, we make explicit the connection between projected dynamical systems on Hilbert spaces and evolutionary variational inequalities. We give a novel formulation that unifies the underlying constraint sets for such inequalities, which arise in time-dependent traffic network, spatial price, and a variety of financial equilibrium problems. We emphasize the importance of the results in a...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

In large-scale communication networks, like the Internet, it is usually impossible to globally manage network traffic. In the absence of global control it is typically assumed in traffic modeling that network users follow the most rational approach, that is, they behave selfishly to optimize their own individual welfare. This motivates the analysis of network traffic using models from Game Theo...

Background Equilibrium is a central concept in numerous disciplines including economics, management science/operations research, and engineering. Methodologies that have been applied to the formulation , qualitative analysis, and computation of equilibria have included • systems of equations, • optimization theory, • complementarity theory, and • fixed point theory. Variational inequality theor...

We consider competition between two decentralized supply chains network under demand uncertainty. Each chain consists of one risk-averse manufacturer and a group of risk-averse retailers. These two chains present substitutable products to the geographical dispensed markets. The markets’ demands are contingent upon prices, service levels, and advertising efforts of two supply chains. We formulat...

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditio...

One of the main goals in a transportation planning process is to achieve solutions for two classical problems: the traffic assignment problem, which minimizes the total travel delay among all travelers, and the toll pricing problem which settles, based on data derived from the first problem, the tolls that would collectively benefit all travelers and would lead to a user equilibrium solution. A...

The Transit Assignment Problem for congested public transport systems based on the formulation of De Cea and Fernandez (1993) has asymmetric cost functions that can be solved, among others methods, by the diagonalización procedure. In this work, an implementation of the origin based algorithm proposed by Bar-Gera (1999) is used to solve the convex problems generated by the diagonalización proce...

Pigou's problem has many applications in real life scenarios like traffic networks, graph theory, data transfer internet etc. The two player classical network an unique Nash equilibrium with the Price of Stability and Anarchy agreeing each other. situation changes for $k-$person $n$ being total number people. If we fix behaviour $(n-2)$ people assume that $k-$persons take path $P_2$ where $k<(n...