Abstract
AbstractWe discuss the dynamic traffic network equilibrium system problem. We introduce the equilibrium definition based on Wardrop's principles when there are some internal relationships between different kinds of goods which transported through the same traffic network. Moreover, we also prove that the equilibrium conditions of this problem can be equivalently expressed as a system of evolutionary variational inequalities. By using the fixed point theory and projected dynamic system theory, we get the existence and uniqueness of the solution for this equilibrium problem. Finally, a numerical example is given to illustrate our results.
Highlights
The problem of users of a congested transportation network seeking to determine their travel paths of minimal cost from origins to their respective destinations is a classical network equilibrium problem
Since the transportation costs of certain kind of goods is related with the flow of itself, and related with the flow of other kinds of goods, the equilibrium problem when some kinds of goods are transported through the same traffic network should be considered
We study the dynamic traffic equilibrium system based on Wardrop’s principles and propose a basic model for the new equilibrium problem
Summary
The problem of users of a congested transportation network seeking to determine their travel paths of minimal cost from origins to their respective destinations is a classical network equilibrium problem. Fixed Point Theory and Applications stated as Wardrop’s principles and the Kuhn-Tucker conditions of a particular optimization problem under some symmetry assumptions In this case, the equilibrium flows could be obtained as the solution of a mathematical programming problem. Dafermos and Sparrow 5 coined the terms “user-optimized” and “system-optimized” transportation networks to distinguish between two distinct situations in which users act unilaterally, in their own selfinterest, in selecting their routes, and in which users select routes according to what is optimal from a societal point of view, in that the total costs in the system are minimized In the latter problem, marginal costs rather than average costs are employed. We introduce the equilibrium definition about this problem based on Wardrop’s principles and propose a mathematical model about this traffic equilibrium problem in dynamic networks.
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