Root
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Conference Proceedings
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6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
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TOWARDS AN OPTIMAL ALGORITHM FOR COMPUTING FIXED POINTS:
DYNAMICAL SYSTEMS APPROACH, WITH APPLICATIONS TO TRANSPORTATION
ENGINEERING
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In many practical problems, it is desirable to find an equilibrium.

For example, equilibria are important in transportation engineering.

Many urban areas suffer from traffic congestion. Intuitively, it may

seem that a road expansion (e.g., the opening of a new road) should

always improve the traffic conditions. However, in reality, a new

road can actually worsen traffic congestion. It is therefore

extremely important that before we start a road expansion project,

we first predict the effect of this project on traffic congestion.

When a new road is built, some traffic moves to this road to avoid

congestion on the other roads; this causes congestion on the new

road, which, in its turn, leads drivers to go back to their previous

routes, etc. What we want to estimate is the resulting equilibrium.

In many problems -- e.g., in many transportation problems -- natural

iterations do not converge. It turns out that the convergence of the

corresponding fixed point iterations can be improved if we consider

these iterations as an approximation to the appropriate dynamical

system.

For example, equilibria are important in transportation engineering.

Many urban areas suffer from traffic congestion. Intuitively, it may

seem that a road expansion (e.g., the opening of a new road) should

always improve the traffic conditions. However, in reality, a new

road can actually worsen traffic congestion. It is therefore

extremely important that before we start a road expansion project,

we first predict the effect of this project on traffic congestion.

When a new road is built, some traffic moves to this road to avoid

congestion on the other roads; this causes congestion on the new

road, which, in its turn, leads drivers to go back to their previous

routes, etc. What we want to estimate is the resulting equilibrium.

In many problems -- e.g., in many transportation problems -- natural

iterations do not converge. It turns out that the convergence of the

corresponding fixed point iterations can be improved if we consider

these iterations as an approximation to the appropriate dynamical

system.