1. On The Generation Mechanisms of Stop-Start Waves in Traffic Flow
H. Michael Zhang, Professor
Department of Civil and Environmental Engineering
University of California
Davis, CA 95616
Distinguished Professor
School of Transportation Engineering
Tongji University
Shanghai, China
The Sixth International Conference on Nonlinear Mechanics
August 12-15, 2013, Shanghai, China

2. Outline of Presentation
Features of congested traffic
Conventional wisdom about stop-start waves
An alternative explanation of stop-start waves
Discussions and conclusion

3. Traffic congestion is everywhere
from Los Angeles

4. to Beijing

5. Features of congested traffic
Phase transitions
Nonlinear waves
Stop-and-Go Waves (periodic motion)

6. Phase transitions

7. Nonlinear waves Vehicle platoon traveling through two shock waves
flow-density phase plot

8. Stop-and-Go Waves (Oscillations)
Scatter in the phase diagram is closely related to stop-and-go wave motion
Variability in driver population
e.g., age, gender, driving habits
Variability in vehicle population
e.g., cars, trucks, SUVs
Variability in driving environment
e.g., lane restrictions, sag, tight turn, lane drop, weaving
Nonlinearity and randomness in driving behavior
e.g., over/under reaction, situation dependent aggression, delayed response

9. Conventional Wisdom
Phase transitions: nonlinearity and randomness in driving behavior
Nonlinear waves: nonlinear, anisotropic driving behavior
Stop-and-Go waves: stochasticity +
H1: instability in CF (ODE) or Flow (PDE)
H2: Lane change

10. Models and Evidences Microscopic Macroscopic continuum
Modified Pipes’ model
Newell’ Model
Bando’ model
Macroscopic continuum
LWR model
Payne-Whitham model
Aw-Rascle, Zhang model

11. Illustration: cluster solutions in the Bando model with a non-concave FD
L=6,000 m, l=6m, T=600s, dt=0.1s, rj=167 veh/km,
N=300 veh, average gap=14 m, Avg. occ is 0.3 .
Vehicles randomly placed on circular road with 0 speed

12. Evidence I: cluster solutions in the Bando model with a non-concave FD

13. Evidence II: cluster solutions in PW model with a non-concave FD
L=22.4km, T=0.7 hr
t=5s,
From Kerner 1998

15. Evidence II: cluster solutions in PW model with a non-concave FD
Time=500 t
location

16. Difficulties with CF/Flow Models
Due to instability, cluster solutions are sensitive to initial conditions and the resolution of the difference scheme
Wave magnitudes and periods are hard to predict and often not in the same order of magnitudes with observed values

17. An Alternative Explanation
Main cause: lane changing at merge bottlenecks
Mechanism: “route” and lane-change location choice produces interacting waves
Model: network LWR model

18. The Model
Link flow
Diverge flow
Merge flow

19. The Mechanism

20. Numerical Results

21. Discussions Solutions can be obtained analytically if FD is triangular
Wave periods are controlled by free-flow speed, jam wave speed, and distance between diverge and merge “points”
Only under sufficiently high demands stop-start waves occur
Stop-start waves travel at the speed of jam wave
Stop-start waves do not grow in magnitude

22. Conclusions
Stop-start waves can arise from ‘routing’ and lane change choices
A network LWR model can produce stop-start waves with right periods and magnitudes
But waves do not grow, need to introduce instability/stochastic elements