LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)
-
Upload
rodrigue-pujol -
Category
Documents
-
view
111 -
download
0
Transcript of LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)
![Page 1: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/1.jpg)
LICIT 1
Traffic flow modelling : what do we know?
J.B Lesort (LICIT)
![Page 2: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/2.jpg)
LICIT 2
Introduction
• When traffic engineers meet mathematicians…• What is a useful model ?• Paul Valéry : « Tout ce qui est simple est faux,
tout ce qui est compliqué est inutilisable »• But traffic models can be complex and unusable
altogether…• So What do we know about traffic flow ? What
can models explain? How can we validate it ?
![Page 3: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/3.jpg)
LICIT 3
I What do we know from empirical observation?
• On an homogeneous portion of freeway:Traffic flows from upstream to downstream ! Information may propagate in both directionsNo information can propagate faster than vehicles
(exceptions?)There is some link between flow, speed and density
![Page 4: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/4.jpg)
LICIT 4
• Contd…There are various vehicles behaviours (lorries, faster
and slower cars…)There are complex bidimensionnal phenomenaPhenomenons as breakdowns, wide moving jams are
observedThere is no scale separation between microscopic and
macroscopic behaviours
![Page 5: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/5.jpg)
LICIT 5
• At bottlenecksCapacity drops are observed, but not systematic
• At mergesVarious capacities repartitions do exist, no evident
explanation holds
• At divergesComplex phenomenons may exist due to variations in
traffic composition and are sometimes misunderstood (« spontaneous breakdown »)
![Page 6: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/6.jpg)
LICIT 6
II The basic modelling agreement
• The conservation equation (The only universal equation !)
• The existence of a flow density relationship under steady-state conditions
0
t
K
x
Q
![Page 7: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/7.jpg)
LICIT 7
III What can models explain ?(everybody agrees…)
• The global phenomenon : waves, queue propagation, travel times
• Merges and diverges, to some extent
![Page 8: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/8.jpg)
LICIT 8
IV What do models try to explain
• Capacity drops at bottlenecksBounded accelerationLane changing
• Wide moving jamsSpecific modelsBounded accelerations
• Moving bottlenecksMoving boundary conditions
![Page 9: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/9.jpg)
LICIT 9
• Bidimensionnal phenomena« multipipes » or unique regimesLane changing models
• Mixed flowsSystems of conservation laws« Slugs and rabbits »
• Speeds and accelerationsUnphysical in any basic modelExtensions of bounded accelerations
![Page 10: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/10.jpg)
LICIT 10
V What do models fail to explain or describe
• Priority (queues at roundabouts…)• Micro/macro effects• « spontaneous » breakdowns ?• Networks effects
![Page 11: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/11.jpg)
LICIT 11
VI Comparing models to reality
• Scale problems in measurement• Interpretating empirical observations
Capacity drops ?
• Any model or numerical implementation is easy to calibrate and validate to somme extent…
• Boundary conditions
![Page 12: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/12.jpg)
LICIT 12
Conclusions
• The simpler the better ?
• From Ford to Toyota : toward lean traffic flow models ?
![Page 13: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/13.jpg)
LICIT 13
![Page 14: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/14.jpg)
LICIT 14
II Les modèles
![Page 15: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/15.jpg)
LICIT 15
Une vision microscopique :
Accélération = (distance, vitesse....)
Ex :
21
1
)()()()()(
txtxtxtxTtx
nn
nnn
![Page 16: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/16.jpg)
LICIT 16
Intérêt et Difficultés
Facilité de traitement de véhicules hétérogènesCinématique des véhicules réalisteFacilité d’implantation d’aspects stochastiquesValable pour une voie unique (dépassements…)Difficulté de calibrage et de validation (stabilité…)Réplicabilité
=> Intérêt de modèles plus globaux
![Page 17: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/17.jpg)
LICIT 17
modèles Macroscopiques
• Trois variables Q(x,t), K(x,t), U(x,t)• Relations fondamentales :
L’équation de conservation
Q=KUNécessité d’une troisième équation
0
t
K
x
Q
![Page 18: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/18.jpg)
LICIT 18
•Relation d’équilibre Q = Qe(K) ou U = Ue(k) => modèles du premier ordre (LWR)
q
k
![Page 19: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/19.jpg)
LICIT 19
• Equation de vitesse : modèles dits du 2ème ordre
Ross :
Payne :
Liu et al :
Aw et Rascle :
uuTdt
dux
1
x
k
kuku
Tdt
due
)(
1
ukukTt
ue
)()(
1
0))(())((
xkΡu
ut
kΡu
![Page 20: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/20.jpg)
LICIT 20
Relations entre modèles macroscopiques et microscopiques
• En conditions stationnaires, on peut parfois retrouver une relation d’équilibre :
• Ex :
x
xenn
nnn k
kkvQtxtxtxtxTtx
1)()()()()( 2
1
1
![Page 21: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/21.jpg)
LICIT 21
• En dynamique, c’est plus compliquéLe modèle de Payne est dérivé d’un modèle micro,
mais dérivation très approximativeDiscrétisation particulaire de modèles macroscopiques :
• Information portée par les véhicules
• Les espacements sont une estimation locale de la concentration
• Différence de nature : temps de réaction/temps de propagation
![Page 22: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/22.jpg)
LICIT 22
III Les difficultés
![Page 23: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/23.jpg)
LICIT 23
Vitesse et accélération
• Vitesses négatives (Ex Payne, etc…)• Accélérations non physiques (pas de bornes
explicites)Ex (1er ordre) :
xk
dkdu
kdtdw e
2
![Page 24: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/24.jpg)
LICIT 24
Capacité
• Notion de débit maximum triviale avec les modèles du 1er ordre (solutions entropiques)
• Peut n’exister qu’en situation stationnaire• Problème de la capacité variable
![Page 25: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/25.jpg)
LICIT 25
Discontinuités
• Spatiales (changement du nombre de voies) ou temporelles (incidents)
• Plus généralement, introduction d’un terme en • Problèmes des discontinuités mobiles (bus)
xue
![Page 26: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/26.jpg)
LICIT 26
Avec modèles du premier ordre
• Pb de Riemann facile à résoudre en termes d ’offre/demande
• Discontinuité mobile => résolution en coordonnées mobiles
![Page 27: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/27.jpg)
LICIT 27
Multiclasses - multiflots
• Multiclasses : types de véhicules différents (VL/PL)
• Multiflots : problème de l’écoulement sur un réseau (flots partiels par destination, pb du FIFO)
• Multivoies : problème des interactions entre voies
![Page 28: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/28.jpg)
LICIT 28
Les intersections
• Convergents
• Divergents
![Page 29: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/29.jpg)
LICIT 29
Confrontation modèle/réalité
• Interprétation des mesures expérimentales• Valeur des paramètres physiques (ex temps de
réaction)• Définition des conditions aux limites (Ex 1er
ordre, demande en entrée offre en sortie)
![Page 30: LICIT 1 Traffic flow modelling : what do we know? J.B Lesort (LICIT)](https://reader036.fdocuments.net/reader036/viewer/2022062621/551d9d8d497959293b8c2d9a/html5/thumbnails/30.jpg)
LICIT 30
Conclusion
• LE modèle de trafic n’existe pas• Nécessité d’adapter le modèle à son application :
que veut-on représenter ? Que veut-on évaluer ?