The Intelligent-Driver Model with Stochasticity:

Transkript

1 The Intelligent-Driver Model with Stochasticity: New Insights into Traffic Flow Oscillations TU Dresden ISTTT 22, Chicago. July

2 Overview Ø Traffic Flow Oscillations: Empirical Facts - Stationary detector data - Trajectory data - Floating-car data - Platoon and ring experiments Ø A General Model Framework - Instability - Noise - Action points Ø Results 2 2

3 I Empirical Facts: Oscillations... from Stationary Detector Data (A9-South near Munich) German A9 South, Oct 29, 1998 TSG OCT Downstream front: Either fixed or moving upstream with velocity c Upstream front: Determined by supply and demand Internal structures: Moving with velocity c as well Amplitude of internal structures grows when moving upstream Frequency grows with severety of bottleneck 3 3

4 from Trajectory Data (NGSIM I=80, reconstructed) I-80, reconstructed 4 4

5 from Floating-Car Data (TomTom, A99 South near Munich) TOMTOM: approx vehicles X 1 data telegram/min =10 9 datasets/day 5 5

6 in Car Platoon Experiments (Tian et al., 2016) Platoon behind a leading car driving at 30 km/h: Speed as a function of time and vehicle number Speed standard deviation once stationary 6 6

7 and in Bicycle Experiments (Jiang et al., 2016) 7 7

8 II. General Framework Time-continuous car-following model relative distance from instability threshold acceleration noise => Mechanisms I (flow instability) and II (noise) Action points: change acceleration only if => Mechanism III: indifference zone 8 8

9 Mechanism II: White Noise Creates Correlated Fluctuations! 9 9

10 Mechanism III: Action Points in Action 10 10

11 Subcritical Noise-Induced Oscillations: Analytics Linearisation of the stochastic equation w/o action points: y_n = gap deviation u_n = speed deviation partial derivatives of the acceleration function at the steady-state point 11 11

12 Fourier Ansatz modal expansion (#modes=#vehicles) resulting stochastic linear 2X2 system modal noise term 12 12

13 Solution: Fluctuation-Dissipation Theorem 13 13

14 Total Fluctuation Intensity modal fluctuation intensity spectral intensity 14 14

15 Total Fluctuation Intensity 15 15

16 Reproducing the Platoon Experiment (Leader's Speed=30 km/h) Mechanism I: Instability, alone speed time series speed standard deviation deterministic followers (IDM, ε=0.6, Q=0, Δa max =0) with noisy leader 16 16

17 Reproducing the Platoon Experiment (Leader's Speed=30 km/h) Mechanism II: noise at marginal stability speed time series speed standard deviation stochastic followers (IDM, ε=0, Q=0.32 m 2 /s 3, Δa max =0), same for the leader 17 17

18 Reproducing the Platoon Experiment (Leader's Speed=30 km/h) Mechanism III: action points at marginal stability speed time series speed standard deviation stochastic followers (IDM, ε=0, Q=0, Δa max =1 m/s 2 ), same for the leader 18 18

19 Applying the Mechanisms to Other Models point 19 19

20 Reproducing the Bicycle Ring Experiment Jiang et al., 2016 subcritical IDM with noise (v0=4 m/s) 20 20

21 Low Desired Speeds: even Subcritical Regime (ε=-0.2) leads to Oscillations 21 21