luminy, october 2007 traffic flow in networks: scaling conjectures, physical evidence, and control...
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![Page 1: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/1.jpg)
Luminy, October 2007
Traffic Flow in Networks:Scaling Conjectures, Physical Evidence,
and Control Applications
Carlos F. DaganzoU.C. Berkeley Center for Future Urban Transport
www.its.berkeley.edu/volvocenter/
![Page 2: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/2.jpg)
References
1. Daganzo, C.F. (1996) “The nature of freeway gridlock and how to prevent it" in Transportation and Traffic Theory, Proc. 13th Int. Symp. Trans. Traffic Theory (J.B. Lesort, ed) pp. 629 646, Pergamon Elsevier, Tarrytown, N.Y.
2. Daganzo, C.F. (2007) “Urban gridlock: macroscopic modeling and mitigation approaches” Transportation Research B 41, 49-62; “corrigendum” Transportation Research B 41, 379.
3. Daganzo, C.F. and Geroliminis, N. (2007) “How to predict the macroscopic fundamental diagram of urban traffic” Working paper, Volvo Center of Excellence on Future Urban Transport, Univ. of California, Berkeley, CA (submitted).
4. Geroliminis N., Daganzo C.F. (2007a) “Macroscopic modeling of traffic in cities” 86th Annual Meeting Transportation Research Board, Washington D.C.
5. Geroliminis, N. and Daganzo, C.F. (2007b) “Existence of urban-scale macroscopic fundamental diagrams: some experimental findings” Working paper, Volvo Center of Excellence on Future Urban Transport, Univ. of California, Berkeley, CA (submitted).
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T
x L
Definitions
Flow, q = VKT / TL (veh/hr)
Density, k = VHT / TL (veh/km)
Speed, v = VKT / VHT (km/hr)
C-rate, f = Completions / TL (veh/km-hr)
(Daganzo, 1996)
![Page 4: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/4.jpg)
Link Laws
k0
Optimum Density
Density, kfmax
Max completion rate
C-rate, f
Flow, q
qmax, Capacity
d, kms per completion
(Daganzo, 2007)
• (q, k, v) related by FD
• q / f = d
• Optimal density (Capacity; Max C-rate)
![Page 5: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/5.jpg)
Composition: J Identical Links
Lj Lj = L dj = d
kj , qj , vj , fj
f f ; k k
(Daganzo, 2007)
q/Jq)/(TLJ)VKT(qj jj j
![Page 6: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/6.jpg)
Network of identical links: Jensen’s inequality: q ≤ Q(k)
If vi ~ constant:
q ~ Q(k)
f ~ Q(k) / d
Density
q( ki , qi )
d ( ki , qi )k q
f
Flow
C-rate
(Daganzo, 2007)
Conjectures
Real Networks:
• An MFD exists• Trip completions / Network flow ~ Constant
![Page 7: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/7.jpg)
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Ou
tflo
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Vehicle Accumulation
San Francisco Simulation: No Control
(Geroliminis & Daganzo, 2007a)
![Page 8: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/8.jpg)
• Fixed sensors500 ultrasonic detectors
– Occupancy and Counts per 5min
• Mobile sensors140 taxis with GPS
– Time and position– Other relevant data
(stops, hazard lights, blinkers etc)
• Geometric dataRoad maps(detector locations, link lengths, intersection control, etc.)
(Dec. 2001 data)
10 km2
(Geroliminis & Daganzo, 2007b)
Real World Experiment: Site Description
![Page 9: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/9.jpg)
Real World Experiment: The Demand
Occupancy by time-of-day Flow by time-of-day
(Geroliminis & Daganzo, 2007b)
![Page 10: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/10.jpg)
0
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1
0 10 20 30 40 50 60 70o i (%)
q i/m
ax {q
i}
Detector #: 10-003D Detector #: T07-005D
Real World Experiment: The Detectors
oi (%)
q i (
dim
ensi
onle
ss)
![Page 11: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/11.jpg)
Real World Experiment: The Detectors
0
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0 20 40 60 80o u (%)
qu (
vhs/
5min
)
A1B1C1D1A2B2C2D2
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0 20 40 60o u (%)
vu (
km
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B1
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D1
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B2
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D2
(Geroliminis & Daganzo, 2007b)
![Page 12: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/12.jpg)
Real World Experiment:Taxis
Conjecture: Passenger carrying taxis use the same parts of the network as cars
(Geroliminis & Daganzo, 2007b)
Then:
taxi
taxi
u t u t
n t n t t
t t
![Page 13: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/13.jpg)
Filters to determine full vs. empty taxis
A stop is a passenger move, if:• hazard lights are ON or• parking brake is used or• left blinker is ON and taxi stops > 45 sec or • speed < 3 km/hr for >60sec
A trip is valid if:• trip duration > 5 min and length > 1.5 km and • trip distance < 2 × “Euclidean distance”
(Geroliminis & Daganzo, 2007b)
![Page 14: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/14.jpg)
A1
A3 A2
Taxi ID:1087 Date:12/14/2001
Direction:
A1→A2→A3→A4→A5→A6→A7→A8
Time Position Trip17:11.30 A1
17:22.00 A2
17:26.00 A3
17:48.00 A4
19:00.30 A5
19:34.30 A6
19:40.00 A7
19:57.00 A8
A5
A4
A8
A6
A7
1km
SEA
Area of Analysis
FULLEMPTYFULL
EMPTYFULL
EMPTYFULL
Illustration of Filter Results
(Geroliminis & Daganzo, 2007b)
![Page 15: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/15.jpg)
Illustration of Filter Results (Cont.)
0.5
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2
3:35 6:05 8:35 11:05 13:35 16:05 18:35 21:05 23:35
time
outb
ound
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boun
d
detectors
taxis
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![Page 16: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/16.jpg)
Real World Experiment:Taxis
Conjecture: Passenger carrying taxis use the same parts of the network as cars
(Geroliminis & Daganzo, 2007b)
Then:
taxi
taxi
u t u t
n t n t t
t t
![Page 17: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/17.jpg)
Real World Experiment: Results
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v T (k
m/h
r)
12/14/2001,3.30-13.30
12/14/2001,13.30-24.00
^
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%error < 2/√average N' T
^
^
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time
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D
(km
s)^
^
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Aggregate Dynamics
Given : inflow qin
Output: e = G(n)
e = G(n)
qin
n ))t(n(G)t(qdt
)t(dnin
(Daganzo, 2007)
n
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Time
Tri
ps
En
de
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No Control With Control
Time
Tri
ps
En
de
d
Restrict vehicles from entering
Finding: Effect of Control
(Geroliminis & Daganzo, 2007a)
![Page 20: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/20.jpg)
Ring Road Simulation: No Control
(Daganzo, 1996)
![Page 21: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/21.jpg)
Ring Road Simulation: Control
(Daganzo, 1996)
![Page 22: Luminy, October 2007 Traffic Flow in Networks: Scaling Conjectures, Physical Evidence, and Control Applications Carlos F. Daganzo U.C. Berkeley Center](https://reader034.vdocuments.mx/reader034/viewer/2022051619/56649d645503460f94a471d0/html5/thumbnails/22.jpg)
Ongoing Work: San Francisco
(Daganzo & Geroliminis , 2007)
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