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

NTU Complexity Community Sharing Towards Effective Modeling of the Traffic Dynamics Yang Bo (A*STAR, IHPC) yangbo@ihpc.a-star.edu.sg www.a-star.edu.sg/ihpc


 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 • A One-Dimensional Driven System n-1 n n+1 { { h n − 1 h n ∆ v n = v n +1 − v n nearest neighbor, anisotropic non-linear interactions in a dissipative media

Traffic Theories theoretical modeling • two-phase models •

Traffic Theories theoretical modeling • two-phase models • Helbing et.al 2000 a n = a 0 ( V ( h n ) − v n + g ( ∆ v n ))  λ Θ ( ∆ v n ) ∆ v n Bando et.al 1997  g ( ∆ v n ) = λ ∆ v n λ 1 Θ ( ∆ v n ) ∆ v n + λ 2 Θ ( − ∆ v n ) ∆ v n 

Traffic Theories theoretical modeling • two-phase models • 30 Headway h n Headway h n 25 20 20 15 10 0 100 200 300 0 100 200 300 Car index Car index h max 30 4 Headway h n 2 dh n d t 20 0 → n 0 ←

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 stochasticity, inhomogeneity, identical drivers, time independent, time dependence, vehicle/ homogeneous traffic lanes driver diversity simplest possible approximation of ¯ f

Traffic Theories theoretical modeling • a universal mathematical structure • f 0 ( h n , 0 , v n ) = 0 a n = f 0 ( h n , ∆ v n , v n ) f 0 ( h n , 0 , V op ) = 0 the “ground state” of the traffic dynamics

Traffic Theories theoretical modeling • a universal mathematical structure • κ p,q ( h n ) ( v n − V op ( h n )) p ∆ v q X a n = n p,q ∂ p + q f � � κ p,q ( h n ) = � ∂ p v n ∂ q ∆ v n � v n = V op ( h n ) ∆ v n =0

Traffic Theories theoretical modeling • a universal mathematical structure • ✓ h ∗ ( v n , ∆ v n ) ◆ 2 ! ◆ δ ✓ v n a n = a 1 − − v 0 h n 0.0 p =4 ,q =2 λ p,q ( v n − V op ( h n )) p ∆ v q -0.2 X a n = λ 10 n Model Parameters -0.4 λ 20 p =1 ,q =0 λ 30 λ 40 -0.6 λ 01 λ 02 -0.8 λ 11 λ 12 a n = λ 10 ( h n ) ( v n − V op ) + λ 01 ( h n ) ∆ v n -1.0 λ 21 λ 22 -1.2 0 20 40 60 80 100 Headway h (m) Yang Bo et.al arXiv. 1504.02186

Traffic Theories theoretical modeling • a universal mathematical structure • b) a) a Δ v=0,h a Δ v=0,h v v 0 0 c) d) a Δ v=0,h a Δ v=0,h v v 0 0

Traffic Theories theoretical modeling • a universal mathematical structure • All microscopic traffic models are defined by the • optimal 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) κ p,q ( h n ) ( v n − V op ) p ∆ v q X a n = n p,q

Traffic Theories theoretical modeling • Tuning of a simple model •

Traffic Theories theoretical modeling • Tuning of a simple model • a n = κ ( V op ( h n ) − v n ) + g ( ∆ v n ) g ( ∆ v n ) = λ 1 ∆ v n + λ 2 | ∆ v n | h max , h min , n 0 emergent quantities from non-linear interactions Yang Bo et.al arXiv. 1504.01256

Traffic Theories theoretical modeling • Numerical simulations • 35 ● ● ● 30 ● ● ● ● 25 ● ● ● 20 ∆ h (m) ● ● ● ● 15 ● ● ● ● ● ● 10 ● ● ● ● ● Single perturbation ● ● ● ● 5 Random perturbation ● ● ● ● ● ● 0 27.5 28.5 29.5 30.5 Average headway (m)

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 or adaptive cruise control

Traffic Theories • Practical applications • short term • Understanding the conditions for the onset 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 normal (un- 10% optimized) driving behavior optimized 20% driving behavior

Traffic Theories • Practical applications • medium term • optimizing mixed traffics normal (un- 10% optimized) driving behavior optimized 20% driving behavior

Traffic Theories • Practical applications • medium term • optimizing mixed traffics normal (un- 10% optimized) driving behavior optimized 20% driving behavior

Traffic Theories • Practical applications • medium term • optimizing mixed traffics normal (un- 10% optimized) driving behavior optimized 20% driving behavior

Traffic Theories • Practical applications • medium term • optimizing mixed traffics normal (un- 10% optimized) driving behavior optimized 20% driving behavior

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)