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On the modelling and management of traffic

Published online by Cambridge University Press:  23 February 2011

Rinaldo M. Colombo ,
Paola Goatin  and
Massimiliano D. Rosini
Rinaldo M. Colombo
Affiliation:
Dipartimento di Matematica, Università degli studi di Brescia, Italia. [email protected]
Paola Goatin
Affiliation:
INRIA Sophia Antipolis – Méditerranée, EPI OPALE, France. [email protected]
Massimiliano D. Rosini
Affiliation:
ICM, Uniwersytet Warszawski, Polska. [email protected]
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Abstract

Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific cases are dealt with in detail through ad hoc numerical integrations. These are here obtained implementing the wave front tracking algorithm, which appears to be very precise in computing, for instance, the exit times.

Keywords

Optimal control of conservation lawsconstrained hyperbolic PDEstraffic modelling
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 5 , September 2011 , pp. 853 - 872
Copyright
© EDP Sciences, SMAI, 2011

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