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Urban Network Gridlock: Theory, Characteristics, and Dynamics. Hani Mahmassani, Meead Saberi, Ali Zockaie The 20th International Symposium on Transportation and Traffic Theory Noordwijk , the Netherlands July 17, 2013. Research Question. - PowerPoint PPT Presentation
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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
9
Chicago Metropolitan Network Large Scale Network with ~40,000
links and ~13,000 nodes ~2,000 traffic zones ~4 millions simulated vehicles
Loading profile
10
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.
11
Calibration for downtown Chicago
-α=f(K) Β=h(K)
Q = f(K).σK + h(K)
Two-Dimensional NFD
slope Y-intercept
12
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
13
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
14
Gridlock in the CBD sub-network
The long-lasting invariant large densities with very small flows suggest formation of a gridlock.
Gridlock
15
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
16
Characteristics
Size (# vehicles or lane-miles)Configuration (spatial form)Formation TimeFormation LocationDissipation TimePropagation DurationRecovery DurationPropagation SpeedRecovery Speed
17
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
18
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
20
Adaptive DrivingEffects of Adaptive Driving on Gridlock Size &
Configuration
Conclusion
21
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.