Some Laws of Urban Traffic Dynamics: Analysis, Physical Evidence and Control Applications

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Some Laws of Urban Traffic Dynamics Analysis,
Physical Evidence and Control Applications
Carlos F. Daganzo U.C. Berkeley Center for Future
Urban Transport www.its.berkeley.edu/volvocenter/
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References

• 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.
• Daganzo, C.F. (2006) On the variational theory
  of traffic flow well-posedness, duality and
  applications Networks and Heterogeneous Media
  1(4) 601-619.
• Daganzo, C.F. (2007) Urban gridlock macroscopic
  modeling and mitigation approaches
  Transportation Research B 41, 49-62 with
  corrigendum Transportation Research Part B 41,
  379.
• Daganzo, C.F. and Geroliminis, N. (2008) An
  analytical approximation for the macroscopic
  fundamental diagram of urban traffic
  Transportation Research Part B, available on
  line.
• Geroliminis N., Daganzo C.F. (2007a) Macroscopic
  modeling of traffic in cities 86th Annual
  Meeting Transportation Research Board, Washington
  D.C.
• 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
  (Transportation Research Part B available on
  line).

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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)
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Link Laws

• (q, k, v) related by FD
• q / f d
• Optimal density (Capacity Max C-rate)

(Daganzo, 2007)
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Composition J Identical Links
(Daganzo, 2007)
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Known Result for Ring Roads

• Assume multiple blocks arbitrary block lengths
  and widths arbitrary signal settings conserved
  vehicles.
• Theorem If traffic behaves according to
  variational theory, the ring road exhibits a
  concave MFD.

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Conjectures
Network of identical links

• Real Networks
• An MFD exists
• Trip completions / Network flow Constant

(Daganzo, 2007)
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San Francisco Simulation No Control
Outflow
Vehicle Accumulation
(Geroliminis Daganzo, 2007a)
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Real World Experiment Site Description

• Fixed sensors
• 500 ultrasonic detectors
• Occupancy and Counts per 5min
• Mobile sensors
• 140 taxis with GPS
• Time and position
• Other relevant data
• (stops, hazard lights, blinkers etc)
• Geometric data
• Road maps
• (detector locations, link lengths, intersection
  control, etc.)

10 km2
(Dec. 2001 data)
(Geroliminis Daganzo, 2007b)
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Real World Experiment The Demand
Occupancy by time-of-day
Flow by time-of-day
(Geroliminis Daganzo, 2007b)
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Real World Experiment The Detectors
qi (dimensionless)
oi ()
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Real World Experiment The Detectors
(Geroliminis Daganzo, 2007b)
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Real World ExperimentTaxis
Conjecture Passenger carrying taxis use the same
parts of the network as cars
Then
(Geroliminis Daganzo, 2007b)
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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 gt 45 sec or
• speed lt 3 km/hr for gt60sec
• A trip is valid if
• trip duration gt 5 min and length gt 1.5 km and
• trip distance lt 2 Euclidean distance

(Geroliminis Daganzo, 2007b)
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Illustration of Filter Results
(Geroliminis Daganzo, 2007b)
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Illustration of Filter Results (Cont.)
(Geroliminis Daganzo, 2007b)
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Real World ExperimentTaxis
Conjecture Passenger carrying taxis use the same
parts of the network as cars
Then
(Geroliminis Daganzo, 2007b)
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Real World Experiment Results
(Geroliminis Daganzo, 2007b)
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Aggregate Dynamics

• Given inflow qin
• Output e G(n)

qin
e G(n)
n
(Daganzo, 2007)
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Finding Effect of Control
No Control
With Control
Trips Ended
Time
Trips Ended
Time
Restrict vehicles from entering
(Geroliminis Daganzo, 2007a)
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Ongoing Work San Francisco
(Daganzo Geroliminis , 2007)