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On The Generation Mechanisms of Stop-Start Waves in Traffic Flow

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

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On The Generation Mechanisms of Stop-Start Waves in Traffic Flow

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  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

  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 • 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

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

  15. 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

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

  17. The Model Link flow Diverge flow Merge flow

  18. The Mechanism

  19. Numerical Results

  20. 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

  21. 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

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