Urban Network Gridlock: Theory, Characteristics, and Dynamics

Hani Mahmassani, Meead Saberi, Ali ZockaieThe 20th International Symposium on Transportation and Traffic TheoryNoordwijk, the Netherlands

July 17, 2013

Research Question

2

Exploration of the physics of traffic flow in urban networks under highly congested conditions

Focus on:

1. Inhomogeneous spatial distribution of congestion2. Modeling NFD with hysteresis and gridlock3. Characterizing gridlock phenomena

Outline

3

BackgroundTheory

• Non-hysteretic NFD• Hysteretic NFD• Two-Dimensional NFD

Findings from Simulation Results• NFD for the entire network and CBD sub-

network• Gridlock properties• Effects of demand management• Effects of adaptive driving

Conclusion

Background

4

5

Network Fundamental DiagramLink-based definitions of network traffic flow

variables

Source: Geroliminis and Daganzo (2008)

Background

M

ii

M

iii

l

qlQ

1

1

M

ii

M

iii

l

klK

1

1

Source: Mahmassani, Williams and Herman (1984)

Theory

6

Equilibrium (Non-Hysteretic) NFD

Source: Daganzo (2007)

g = G(n)

Such function is intended as an idealized description of the equilibrium (steady-state) behavior that would be expected to hold only when the inputs change slowly in time and traffic is distributed homogenously in space.

Exit rate

Number of vehs in network

7

Proposed Non-equilibrium (Hysteretic) NFD

g = G(n) + Hg = G(n) + H(n,σ)

Theory

H represents the deviation from steady-state conditions due to the hysteretic behavior of the network traffic flow.

TheoryNetwork Flow, Density and Stdv of Density

Relations For the same value of network density, there is a negative correlation between the network average flow and the standard deviation of the network density.

Source: Mazloumian et al. (2010) & Knoop et al. (2011)

0

200

400

600

800

1000

0 20 40 60 80

Net

wor

k A

vera

ge F

low

(vp

h)

Standard Deviation of Network Density

Density = 5 veh/mile

Density = 10 veh/mile

Density = 15 veh/mile

Density = 20 veh/mile

Density = 25 veh/mile

Density = 30 veh/mile

Density = 35 veh/mile

Density = 40 veh/mile

Downtown Chicago sub-network

Network Simulation

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Chicago Metropolitan Network Large Scale Network with ~40,000

links and ~13,000 nodes ~2,000 traffic zones ~4 millions simulated vehicles

Loading profile

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TheoryProposed Two-Dimensional NFD and Calibration

Q = f(K).σK + h(K)

Calibrated Relationship

for Downtown Chicago sub-

network

slope Y-intercept

For a given network density, a linear relationship between Q and σK is assumed.

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Calibration for downtown Chicago

-α=f(K) Β=h(K)

Q = f(K).σK + h(K)

Two-Dimensional NFD

slope Y-intercept

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Calibration for downtown ChicagoProducing hysteresis loop using two-dimensional NFD

relation

Two-Dimensional NFD

The simulated NFD is network average flow versus network average density which are directly obtained from simulation

In the modeled NFD density and its standard deviation are obtained from simulation. The calibrated relationship is used to estimate network average flow.

Network Simulation Results

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Network-wide Relation (entire network) and Gridlock

Loading and unloading phases are shown.

After a certain time the network outflow is close to zero and there are a number of “trapped” vehicles in the network (gridlock).

Network Simulation Results

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Gridlock in the CBD sub-network

The long-lasting invariant large densities with very small flows suggest formation of a gridlock.

Gridlock

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Gridlock evolution in the CBD sub-network (number of lane-mile jammed links)

• Gridlock propagation speed is much larger than gridlock dissipation speed.

• At the end of the simulation, more than 40% of the links are empty while the rest are jammed (significant inhomogeneity of congestion distribution)

Gridlock

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Characteristics

Size (# vehicles or lane-miles)Configuration (spatial form)Formation TimeFormation LocationDissipation TimePropagation DurationRecovery DurationPropagation SpeedRecovery Speed

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Demand ManagementEffects of Demand Management of NFD of CBD Sub-

network

Gridlock configuration at CBD at the end of simulation

100% demand 85% demand 75% demand

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Demand ManagementTemporal Effects of Demand Level on Gridlock Evolution

19Average Network Density

Aver

age

Net

wor

k Fl

owAdaptive Driving

Effects of Adaptive Driving on NFD of CBD Sub-network

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Adaptive DrivingEffects of Adaptive Driving on Gridlock Size &

Configuration

Conclusion

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1. Study of a large-scale urban network consisting of both freeways and arterials with exit flow, under highly congested conditions.

2. The existing theory of equilibrium NFD is extended to non-equilibrium conditions in order to reproduce hysteresis and gridlock phenomena.

3. Networks tend to jam at a range of densities that are considerably smaller than the theoretical average network jam density due to inhomogeneous distribution of congestion.

4. Parameters for characterizing gridlock phenomenon in urban networks are introduced; opens new direction for investigation and application to better traffic management

5. Effects of demand management and adaptive driving on gridlock and hysteresis phenomena and NDF are also studied.

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Thank you!

Meead Saberimeead@u.northwestern.edu

Questions?

Hani Mahmassanimasmah@northwestern.edu

Ali Zockaieali-zockaie@u.northwestern.edu