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# Jam and Fundamental Diagram in Traffic Flow on Sag and Hill - PowerPoint PPT Presentation

Jam and Fundamental Diagram in Traffic Flow on Sag and Hill. K.Komada S.Masukura T.Nagatani Shizuoka Univ. Japan. Purpose of Study. Proposal of traffic model including the gravitational force 　　－ We extend the optimal velocity model to study the

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Presentation Transcript

Shizuoka Univ.Japan

• Proposal of traffic model including the gravitational force

－We extend the optimal velocity model to study the

jamming transition induced by the gravitational force.

• Fundamental diagrams for the traffic flow on sag and hill

－We study the flow, traffic states ,and jamming

transitions induced by sag and hill.

• Jam induced by sag

－We clarify the relationship between densities before and

after the jam from the theoretical current curves.

Equation of motion on uphill

→ 1

for

→ ∞

sensitivity

→ 0

for

→ 0

Extended Optimal

velocity Function

We extend the OV model and obtain the following

①OV function on normal section

② Extended OV function on uphill section

③Extended OV function on downhill section

• Single lane

• The periodic boundary condition

• Forth-order Runge-Kutta method

Values of parameters

• LN1=LD1=LU1=LN2=L/4

• Time interval isΔｔ＝１/１２８

• Vf,max=2.0,xｃ＝4.0

• Number of cars N=200

Fundamental diagram（ Xc=Xdown,b=Xup,b）

Sensitivity:a=3.0>ac=2.0(critical value)

Sensitivity:a=1.5<ac=2.0(critical value)

Traffic jam induced by sag

Velocity profile（ρ=0.17）

Traffic jam induced by sag

＋oscillating jam at low sensitivity

High sensitivity⇒3 traffic states

Low sensitivity ⇒5 traffic states

Velocity profile （ ρ=0.19）

Relationship between headway profile and theoretical current（Xｃ=Xup,b=Xdown,b）

Velocities are Optimal Velocity.

Theoretical current

（ in the case of no jam at high sensitivity）

Fundamental diagram（ Xc=Xdown,b≠Xup,b）

Velocity profile（ρ=0.16）

3 traffic states

(3) of case2 is not consistent with that of case1 but (1) and (2) case 2 agree with those of case1.

(1)Free traffic

(2)Traffic with saturated current

(3) Congested traffic

xc=xup,b≠xdown,b：「the different case」（case1）xc=xup,b=xdown,b ：「the same case」（case2）

Relationship between headway profile and theoretical current （ Xc=Xdown,b≠Xup,b）

In the case of

Xc=Xdown,b≠Xup,b

The length of jam shorten.

Velocity profile(ρ=0.20)

As the gradient is high, the maximum velocity become lower and higher on up- and down-hills respectively.

The region of saturated flow extend.

The maximum current is lower.

The traffic jam occurs

●We have extended the optimal velocity model to take into

account the gravitational force as an external force.

● We have clarified the traffic behavior for traffic flow on a

●We have showed where, when, and how the traffic jams

● We have studied the relationship between densities

before and after the jam from the theoretical analysis.