Seminar Details
2005-10-11 (14.00 pm) : Quasi-variational inequalities applied to traffic network equilibrium problems
At Auditoire Euler
Organized by Mathematical Engineering
Speaker :
Laura Scrimali (INMA)
Abstract :
We consider equilibrium problems in transportation
networks when data explicitly depend on time. We
deal with a class of models in which travel demands are
affected by the equilibrium distribution itself. The user
optimal assignment problem is examined in the framework of
the variational inequality theory. In particular, due to the
variable demand requirements, the problem is formulated as a
quasi-variational inequality. We then give some sufficient
conditions for the existence of solutions, supposing that users
obtain information about the flow propagation instantaneously.
The case in which information travels at a finite speed, thus
involving delays in the conservation of flows condition, is also examined.
Moreover, we show some results of sensitivity analysis, in order to
investigate the behaviour of solutions when some changes in model
parameters occur. Finally, a numerical method based on a projection-type
procedure is discussed