Features of oscillations when propagating through a homogenous highway segment Danjue Chen

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Outline • • • • • •

Introduction Literature review L-L Model Measurement Application Further research

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Introduction (1) What’s oscillation? • Stop-and-go driving motions • Deceleration and acceleration cycles Vehicle Trajectories

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Source: NGSIM (2006)

Source: NGSIM

Introduction (2) • A Common phenomena: oscillations occur in congested traffic. • Problems they cause: severe congestion, reduced fuel efficiency, more emission, safety risk, etc. • Existing models do not capture oscillation accurately.

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Literature Review Three types of models:
Car-following models Period predicted does not match observations. CF models: a few seconds Observations: vary from 2~15min (Kerner & Rehborn, 1996, Mauch & Cassidy, 2002, Ahn & Cassidy, 2007, etc.)
Fully Stochastic Models Oscillations are due to a break probability (Barlovic et al., 1998, 2002) Require a large number of non-physical parameters, hard to implement (Helbing and Treiber, 1998, Shvetsov & Helbing, 1999, etc).


Human-error models Oscillations might be caused by human error (Yeo and Skabardonis, 2009). L-L car-following model (Laval & Leclercq, 2010) 5 5

Source: NGSIM (2006)

Source: NGSIM

L-L Model Basis: Newell’s model (2002) -w vb -w


Drivers try to follow their leaders’ speed. dn vb

va Sn va


Changes of speed spread upstream with distance dn and time
To switch to a new speed, a driver changes his speed upon reaching the spacing he prefers for the new speed. : the time needed to get to the preferred spacing for a new speed. Independent of speed.

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L-L Model L-L Model: Newell’s CF model-Exact KWT solution L-L Car-following Model

<1

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L-L Model L-L model: Key problems: measurement of ηi (t)
Initial value?
How will it change?

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Source: NGSIM (2006)

Source: NGSIM

Measurement Definitions Xi(t) τi+1 (t)

ηi (t)=τi (t) / τ0= Si (t) /S0

w

τ ηi (t)~ ratio of actual spacing to equilibrium spacing 9

Xi+1(t)

where τ0 is the theoretical τ, i.e., τ0=1/(Kjw)-1 τ0 is set to be 1~2.1sec

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Measurement Definitions Xi(t)

ηi (t)=τi (t) / τ0

τi+1 (t)

w

τ ηi (t)~ ratio of actual spacing to equilibrium spacing 10

Xi+1(t)

where τ0 is the theoretical τ, i.e., τ0=1/(Kjw)-1 τ0 is set to be 1~2.1sec

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Measurement Definitions Xi(t)

ηi (t)=τi (t) / τ0

τi+1 (t)

w τ0

i

τ

ηi (t)~ ratio of actual spacing to equilibrium spacing 11

Xi+1(t)

where τ0 is the theoretical τ, i.e., τ0=1/(Kjw)-1 τ0 is set to be 1~2.1sec η0i =τ0 i / τ0 τ0 =mean(τ0 i ) 11

Measurement Example (1) :

R: τ0 =1sec Y: τ0 =1.5sec G: τ0 =2.1sec

R: leader G: follower

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Measurement Example (1) : Characteristics of ηi (t) :
Remains stable under stationary state- η0i.

η 0i

R: τ0 =1sec Y: τ0 =1.5sec G: τ0 =2.1sec

R: leader G: follower

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Measurement Example (1) : Characteristics of ηi (t) :

η 0i

R: τ0 =1sec Y: τ0 =1.5sec G: τ0 =2.1sec

R: leader G: follower

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Remains stable under stationary state- η0i.
Tends to decrease/increase when oscillation wave starts.
Tends to be stable again after oscillation passes.

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Measurement Example (2) : Characteristics of ηi (t) :
ηi (t) may go up-down or

ID:232 W=16km/h

down-up, or remain constant.

η 0i

R: τ0 =1sec Y: τ0 =1.5sec G: τ0 =2.1sec

R: leader G: follower 15


η0i varies from 0.4~2.5

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Measurement Example (3) :

η 0i

R: τ0 =1sec Y: τ0 =1.5sec G: τ0 =2.1sec

R: leader G: follower 16

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Measurement Statistics Results If set: τ0 ~1.5sec
η0i mean: 0.97, variance:0.28 Distribution of η

0

1.

η< 1

2.

η=1

3.

η> 1

i

q

20%

1

15%

10%

3

2

5%

k

0% 0.4

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0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Sample size: 185

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Measurement Statistics Results If set: τ0 ~1.5sec
η0i : mean: 0.97, variance:0.28 Distribution of η 0 i

Driver categories:

20% 15% 10% 5% 0% 0.4 0.5 0.6 0.7 0.8 0.9

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1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

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Sample size: 185


Originally aggressive driver: η0i <0.9
Originally timid driver: η0i >1.1
Newell driver: 0.9≤ η0i≤1.1 18

Measurement Statistics Results If set: τ0 ~1.5sec
η0i : mean: 0.97, variance:0.28 Driver categories:
Originally aggressive driver: η0i <0.9
Originally timid driver: η0i >1.1
Newell driver: 0.9≤ η0i≤1.1 19

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Sample size: 185

Measurement Behavior Patterns ( change of ηi (t) ) Aggresive AG Originally

All Drivers

con-con, 10% up-dn, 38%

con-con, 16%

con-up, 10%

up-dn, 57%

con-up, 10%

con-dn, 1% con-dn, 3% dn-up, 27%

up-con, 14%

dn-up, 7%

up-con, 6%

Timid TM Originally

Newell

Originally NW

dn-up, 60%

con-up, 4% 20

up-dn, con-con, 13% 18%

con-con, 22%

up-dn, 34%

con-up, 15%

dn-dn, 2% up-con, 2% up-con, 1%

Dominant patterns:
AG: up-down
TM: down-up
NW: up-dn, dn-up, con-con.
All: up-dn, dn-up, and con-con.

dn-up, 26%

dn-con, 1%

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Measurement Flow-density path (1) Clock-wise oriented: up-down pattern ID:232

η increases 1 2 3

k 21

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Measurement Flow-density path (2) Counter clock-wise oriented: down-up pattern ID:1212

q

η increases 3 2 1

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Measurement Flow-density path (3) Straight line oriented: con-con pattern ID:1129

q

η increases 1 3

2

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Measurement Distribution of the derivative of η

35%

Distribution Distribution of of η’ η’


Normal?

30% 25% 20% 15% 10% 5%

-0 .2 75 -0 .0 25 -0 .2 00 -0 .1 50 -0 .1 25 -0 .1 00 -0 .0 75 -0 .0 50 -0 .0 25 0. 00 0 0. 02 5 0. 05 0 0. 07 5 0. 10 0 0. 12 5 0. 15 0 0. 17 5 0. 20 0 0. 25 0

0%

-1

η'/s

Sample size: 227 24

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Measurement Example (2) : Characteristics of ηi (t) :
ηi (t) may go up-down or

ID:232 W=16km/h

down-up, or remain constant.

η 0i

R: τ0 =1sec Y: τ0 =1.5sec G: τ0 =2.1sec

R: leader G: follower 25


η0i varies from 0.4~2.5

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Application Example: an oscillation sequence

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Application Different steps in an oscillation sequence

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Application Different steps in an oscillation sequence Observation Observation

Simplification Simplification

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Growth 28

Stabilization

Application Simulation ηi (t)

η0i

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Appendix Deceleration and acceleration of vehicles


Each trajectory has a deceleration and acceleration cycle. So the deceleration and acceleration rates of a vehicle are shown by an orange and green dot respectively.
All these trajectories are in one oscillation sequence. 30

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References 1. 2. 3. 4. 5. 6. 11. 12.

Kerner B.S., and H., Rehborn. 1996. Experimental Features and Characteristics of Traffic jams. Physical Review E, Vol. 53, pp. 1297-1300 Mauch, M., and M. J.,Cassidy. 2002. Freeway Traffic Oscillations: Observations and Predictions. Taylor, M. (Ed.), 15th Int. Symp. on Transportation and Traffic Flow Theory. Ahn, S., M., Cassidy. 2007. Freeway Traffic Oscillations and Vehicle Lane-change Manoeuvres. 17th International Symposium on Transportation and Traffic Flow Theory. Barlovic, R., Santen L., Schadschneider A., and M., Schreckenberg. Metastable States in Cellular Automata for Traffic Flow. The European Physical Journal B, Vol. 5, No. 3 pp. 793-800 Barlovic, R., Huisinga T., Schadschneider A., and M., Schreckenberg. Open Boundaries in A Cellular Automation Model for Traffic Flow with Metastable States. Physical Review E, Vol. 66, Issue 4 Helbing, D., Treiber, M., 1998. Gas-kinetic-based traffic model explaining observed hysteresis phase transition. Physical Review Letters 81 (14), 3042-3045 Shvetsov, V., Helbing, D., 1999. Macroscopic dynamics of multilane traffic Physical Review E, 59 (6), 6328-6339. Yeo, H., Skabardonis, A., 2009. Understanding stop-and-go tra±c in view of asymmetric traffic theory. 18th International Symposium of Traffic Theory and Transportation. pp. 99-116.

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Newell, G. F., 1961. Non-linear effects in the dynamics of car following. Opns. Res. 2 (9), 209– 229.

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Laval, A.J., Leclercq, L. 2010. Mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic. Proceedings of the royal society A. 31

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Thank you! Any question?