# 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

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topColombo, 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 -

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