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

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

Traffic congestion is everywhere from Los Angeles

to Beijing

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

Phase transitions

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

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

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

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

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

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

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

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

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

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

The Model Link flow Diverge flow Merge flow

The Mechanism

Numerical Results

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

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