On the modelling and management of traffic

Rinaldo M. Colombo; Paola Goatin; Massimiliano D. Rosini

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 5, page 853-872
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Colombo, Rinaldo M., Goatin, Paola, and Rosini, Massimiliano D.. "On the modelling and management of traffic." ESAIM: Mathematical Modelling and Numerical Analysis 45.5 (2011): 853-872. <http://eudml.org/doc/197555>.

@article{Colombo2011,
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. },
author = {Colombo, Rinaldo M., Goatin, Paola, Rosini, Massimiliano D.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Optimal control of conservation laws; constrained hyperbolic PDEs; traffic modelling; optimal control of conservation laws; constrained hyperbolic pdes},
language = {eng},
month = {2},
number = {5},
pages = {853-872},
publisher = {EDP Sciences},
title = {On the modelling and management of traffic},
url = {http://eudml.org/doc/197555},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Colombo, Rinaldo M.
AU - Goatin, Paola
AU - Rosini, Massimiliano D.
TI - On the modelling and management of traffic
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/2//
PB - EDP Sciences
VL - 45
IS - 5
SP - 853
EP - 872
AB - 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.
LA - eng
KW - Optimal control of conservation laws; constrained hyperbolic PDEs; traffic modelling; optimal control of conservation laws; constrained hyperbolic pdes
UR - http://eudml.org/doc/197555
ER -

References

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