Volume 45, Number 5, September-October 2011
|Page(s)||853 - 872|
|Published online||23 February 2011|
On the modelling and management of traffic
Dipartimento di Matematica, Università degli studi
di Brescia, Italia. firstname.lastname@example.org
2 INRIA Sophia Antipolis – Méditerranée, EPI OPALE, France. email@example.com
3 ICM, Uniwersytet Warszawski, Polska. firstname.lastname@example.org
Revised: 24 November 2010
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.
Mathematics Subject Classification: 35L65 / 90B20
Key words: Optimal control of conservation laws / constrained hyperbolic PDEs / traffic modelling
© EDP Sciences, SMAI, 2011
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