Towards Effective Modeling of the Traffic Dynamics Yang Bo (A*STAR, - - PowerPoint PPT Presentation

Towards Effective Modeling of the Traffic Dynamics

Yang Bo (A*STAR, IHPC) yangbo@ihpc.a-star.edu.sg www.a-star.edu.sg/ihpc NTU Complexity Community Sharing

Motivations

• Understanding Traffic is of huge practical

significance

• USD 100 Billion in USA, 1% of GDP in EU
• Traffic dynamics is theoretically very

interesting
 


Boris Kerner, 2002, 2009 Dirk Helbing, 2009

Traffic Theories

• empirical observations


Kerner et.al. 2002

Traffic Theories

• empirical observations


Kerner et.al. 1998, 2002

Traffic Theories

• theoretical modeling (microscopic models)
• no symmetry
• non-identical components
• stochasticity and time dependence

Traffic Theories

• theoretical modeling
• two-phase models

∆vn = vn+1 − vn A One-Dimensional Driven System

n n+1 n-1

{ {

nearest neighbor, anisotropic non-linear interactions in a dissipative media

hn−1 hn

Traffic Theories

• theoretical modeling
• two-phase models

Traffic Theories

• theoretical modeling
• two-phase models

an = a0 (V (hn) − vn + g (∆vn))

g (∆vn) =    λΘ (∆vn) ∆vn λ∆vn λ1Θ (∆vn) ∆vn + λ2Θ (−∆vn) ∆vn

Bando et.al 1997 Helbing et.al 2000

Traffic Theories

• theoretical modeling
• two-phase models

100 200 300 15 20 25

Car index Headway hn

100 200 300 10 20 30

Car index Headway hn

20 30

Headway hn

hmax

2 4

dhn dt

→ n0 ←

Traffic Theories

• theoretical modeling
• Three-phase models

Kerner et.al 2001

Traffic Theories

• theoretical modeling
• Three-phase models

Traffic Theories

• theoretical modeling
• How do we properly characterize the differences

between two traffic models?

• Is there a standard way of extending an existing

traffic model or construction of a new traffic model?

• Is there a standard way in selecting the best

traffic model based on the experimental data?

Traffic Theories

• theoretical modeling
• master model from empirical

data and renormalization

ensemble average identical drivers, time independent, homogeneous traffic lanes

simplest possible approximation of ¯

f

stochasticity, inhomogeneity, time dependence, vehicle/ driver diversity

Traffic Theories

• theoretical modeling
• a universal mathematical structure

f0 (hn, 0, vn) = 0

the “ground state” of the traffic dynamics

an = f0 (hn, ∆vn, vn) f0 (hn, 0, Vop) = 0

Traffic Theories

• theoretical modeling
• a universal mathematical structure

an = X

p,q

κp,q (hn) (vn − Vop (hn))p ∆vq

n

κp,q (hn) = ∂p+qf ∂pvn∂q∆vn

• vn=Vop(hn)

∆vn=0

Traffic Theories

• theoretical modeling
• a universal mathematical structure

an = a 1 − ✓vn v0 ◆δ − ✓h∗ (vn, ∆vn) hn ◆2!

20 40 60 80 100

• 1.2
• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0 Headway h (m) Model Parameters

λ10 λ20 λ30 λ40 λ01 λ02 λ11 λ12 λ21 λ22

an =

p=4,q=2

X

p=1,q=0

λp,q (vn − Vop (hn))p ∆vq

n

an = λ10 (hn) (vn − Vop) + λ01 (hn) ∆vn

Yang Bo et.al arXiv. 1504.02186

Traffic Theories

• theoretical modeling
• a universal mathematical structure

aΔv=0,h

a) v

aΔv=0,h

b) v

aΔv=0,h

c) v

aΔv=0,h

d) v

Traffic Theories

• theoretical modeling
• a universal mathematical structure
• All microscopic traffic models are defined by the
• ptimal velocity (OV) and a set of expansion

coefficients (EC).

• the two-phase and three-phase traffic models can

be unified by a “common language”.

• The simplification of OV and ECs can be

experimentally verified.

Traffic Theories

• theoretical modeling
• Tuning of a simple model

The best model should be as simple as possible (but not simpler) an = X

p,q

κp,q (hn) (vn − Vop)p ∆vq

n

Traffic Theories

• theoretical modeling
• Tuning of a simple model

Traffic Theories

• theoretical modeling
• Tuning of a simple model

an = κ (Vop (hn) − vn) + g (∆vn)

g (∆vn) = λ1∆vn + λ2|∆vn|

hmax, hmin, n0

emergent quantities from non-linear interactions

Yang Bo et.al arXiv. 1504.01256

Traffic Theories

• theoretical modeling
• Numerical simulations
• 27.5

28.5 29.5 30.5 5 10 15 20 25 30 35 Average headway (m) ∆h (m)

• Single perturbation

Random perturbation

Traffic Theories

• theoretical modeling
• Numerical simulations

Yang Bo et.al arXiv. 1504.01256

Traffic Theories

• theoretical modeling
• Numerical simulations

Traffic Theories

• theoretical modeling
• Numerical simulations

Traffic Theories

• Practical applications
• A good model for human drivers
• An optimized model for driverless car
• r adaptive cruise control

Traffic Theories

• Practical applications
• short term
• Understanding the conditions for the
• nset of traffic congestions
• recommendation of traffic routing,

designing of highway systems (speed limit, number of lanes, on-ramp/off- ramp)

Traffic Theories

• Practical applications
• medium term
• optimizing mixed traffics
• ptimized

driving behavior normal (un-

• ptimized)

driving behavior 10% 20%

Traffic Theories

• Practical applications
• medium term
• optimizing mixed traffics
• ptimized

driving behavior normal (un-

• ptimized)

driving behavior 10% 20%

Traffic Theories

• Practical applications
• medium term
• optimizing mixed traffics
• ptimized

driving behavior normal (un-

• ptimized)

driving behavior 10% 20%

Traffic Theories

• Practical applications
• medium term
• optimizing mixed traffics
• ptimized

driving behavior normal (un-

• ptimized)

driving behavior 10% 20%

Traffic Theories

• Practical applications
• medium term
• optimizing mixed traffics
• ptimized

driving behavior normal (un-

• ptimized)

driving behavior 10% 20%

Traffic Theories

• Practical applications
• medium term
• un-signalized intersection traffic control

deceleration zone synchronization zone caution zone

Thank you very much for your attention

Collaborators: Yoon Jiwei, John Pang, Christopher Monterola (IHPC) Xihua Xu (NUS)