traffic signal design-i · 2019-01-02 · greenshield's model • example –calibrate...
TRANSCRIPT
![Page 1: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/1.jpg)
Traffic stream models
Tom Mathew
![Page 2: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/2.jpg)
2
Traffic stream models
• Macroscopic
– Expression of the average behavior of the
vehicles at the specific location and time
• Mesoscopic
– Small group of traffic entities with activities
and interactions
• Microscopic
– Space-time behavior of the systems’ entities
(i.e. vehicle and drivers)
![Page 3: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/3.jpg)
3
Traffic stream models
![Page 4: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/4.jpg)
4
Traffic stream models
![Page 5: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/5.jpg)
5
Traffic stream models
![Page 6: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/6.jpg)
6
Traffic stream models
• Macroscopic Stream Models
– Greenshield's linear
– Greenberg's logarithmic
– Underwood's exponential
– Pipe's generalized
– Multi regime models
• Two and Three regime
![Page 7: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/7.jpg)
7
Greenshield's model
• Linear speed-density relationship
Relation between speed and density
![Page 8: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/8.jpg)
8
Greenshield's model
• Description
– v = mean speed
– k = density
– 𝒗𝒇 = free flow speed
– 𝒌𝒋= jam density
– When density becomes zero, speed
approaches free flow speed
Two parameter model
𝒗 = 𝑣𝑓 −𝑣𝑓
𝑘𝑗𝒌
0
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250
Sp
ee
d (
v)
Density (k)
vf=80, kj=200
![Page 9: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/9.jpg)
9
Greenshield's model
• Relation between flow and density
𝒗 = 𝑣𝑓 −𝑣𝑓
𝑘𝑗𝒌
𝒒 = 𝒌 𝒗
𝒒 = 𝒌 𝑣𝑓 −𝑣𝑓
𝑘𝑗𝒌
𝒒 = 𝑣𝑓𝒌 −𝑣𝑓
𝑘𝑗𝒌2
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150 200
Flo
w (
q)
Density (k)
vf=80, kj=200
![Page 10: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/10.jpg)
10
Greenshield's model
• Boundary conditions
– Maximum flow qmax
– Density corresponding to max. flow ko
– Speed corresponding to max. flow vo
• Model parameters
– Jam density kj
– Free flow speed vf
![Page 11: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/11.jpg)
11
Greenshield's model
• Derivation of ko
– We have
– Differentiating
𝒒 = 𝑣𝑓𝒌 −𝑣𝑓
𝑘𝑗𝒌2
![Page 12: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/12.jpg)
12
Greenshield's model
• Derivation of qmax
• Derivation of vo
![Page 13: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/13.jpg)
13
Greenshield's model
• Relation between speed and flow
𝒗 = 𝑣𝑓 −𝑣𝑓
𝑘𝑗𝒌
𝒒 = 𝒌 𝒗
𝒌 = 𝑘𝑗 −𝑘𝑗
𝑣𝑓𝒗
𝒒 = 𝑘𝑗𝒗 −𝑘𝑗
𝑣𝑓𝒗2
0
10
20
30
40
50
60
70
80
90
0 1000 2000 3000 4000 5000
Speed (v
)
Flow (q)
vf=80, kj=200
![Page 14: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/14.jpg)
14
Greenshield's model
• Calibration
– Determination of model parameters
– Free flow speed (vf)
– Jam density (kj)
where x is density and y denotes speed
![Page 15: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/15.jpg)
15
Greenshield's model
• Calibration
– Using linear regression method
OR
a is
![Page 16: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/16.jpg)
16
Greenshield's model
• Example
– Calibrate Greenshields model
using the data give in the
table
– Find the maximum flow
– Find the density
corresponding to a speed of
30 km/hr
No K v
1 171 5
2 129 15
3 20 40
4 70 25
![Page 17: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/17.jpg)
17
Greenshield's model
![Page 18: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/18.jpg)
18
Model Comparison
![Page 19: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/19.jpg)
19
Model Comparison
![Page 20: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/20.jpg)
20
Greenberg's model
• Logarithmic relation
– Advantage
• Analytical derivation
• Good at congestion
– Drawbacks
• Infinite speed
• Poor at low densities
𝒗 = 𝑣𝑜𝑙𝑛𝑘𝑗
𝒌
![Page 21: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/21.jpg)
21
Underwood's model
• Exponential Model
– Advantage
• Good at low speed
– Drawbacks
• Speed is zero only at
infinity density
• Poor at high densities
𝒗 = 𝑣𝑓𝒆−𝒌𝑘𝑜
![Page 22: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/22.jpg)
22
Pipes' model
• Generalized Model
– When n is 1 Pipe’s model resembles
Greenshield’s model
𝒗 = 𝒗𝒇 1 −𝒌
𝒌𝒋
𝒏
![Page 23: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/23.jpg)
23
Comparison of Models
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250
Sp
eed
V(k
mp
h)
Density k (veh/km)
k = 200, vf = 90, ko = 100, v0 = 45
Liner n = 1
![Page 24: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/24.jpg)
24
Comparison of Models
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250
Sp
eed
V(k
mp
h)
Density k (veh/km)
k = 200, vf = 90, ko = 100, v0 = 45
Liner n = 1
Log
![Page 25: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/25.jpg)
25
Comparison of Models
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250
Sp
eed
V(k
mp
h)
Density k (veh/km)
k = 200, vf = 90, ko = 100, v0 = 45Liner n = 1
Log
Exp
![Page 26: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/26.jpg)
26
Comparison of Models
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250
Sp
eed
V(k
mp
h)
Density k (veh/km)
k = 200, vf = 90, ko = 100, v0 = 45 Gen n = 0.5
Liner n = 1
Gen n = 2
Log
Exp
![Page 27: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/27.jpg)
27
Model Comparison
![Page 28: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/28.jpg)
28
Model Comparison
![Page 29: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/29.jpg)
Model Comparison
• Limitations
– Assumes uniform behaviour
– Poor predictability
– Generalization
• Need for multi-regime models
– Traffic states divided into various regimes
– Behaviour depends on the regime
– Separate models for each regime
30
![Page 30: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/30.jpg)
31
Multiregime model
• Eddie’s Two Regime Model
– Based on field data (Chicago)
Regime 1:
Exponential
Regime 2:
Logarithmic
![Page 31: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/31.jpg)
32
Multiregime model
• Eddie’s Two Regime Model
– Based on field data (Chicago)
![Page 32: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/32.jpg)
33
Multiregime model
• Eddie’s Two Regime Model
Greenshields
Model
![Page 33: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/33.jpg)
34
Multiregime model
• Three Regime Model
– Free flow
– Normal
– Congested
![Page 34: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/34.jpg)
35
Multiregime model
Free flow
CongestedNormal
![Page 35: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/35.jpg)
36
Multiregime model
![Page 36: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/36.jpg)
38
Multi-regime models
![Page 37: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/37.jpg)
39
Speed –Flow: Effect of location
• Simultaneous treatment of q k v
![Page 38: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/38.jpg)
45
Conclusion
• Concerns
– The current status of mathematical models for speed-
flow concentration relationships is in a state of flux
– The models that dominated for nearly 30 years are
incompatible with the data currently being obtained
– but no replacement models have yet been developed
Lieu 1999, Traffic-Flow Theory
US DOT, Federal Highway Administration
http://www.tfhrc.gov/pubrds/janfeb99/traffic.htm
![Page 39: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/39.jpg)
46
Conclusion
• Trends
– Despite those words of caution, it is important
to note that there have been significant
advances in understanding traffic stream
behavior since 1980’s leading to a better
understanding of traffic operation
– Efforts to implement ITS will provide
challenges for applying this improvement
– Equally important, ITS will likely provide the
opportunity for acquiring more and better data
to advance understanding of traffic operations
![Page 40: Traffic signal design-I · 2019-01-02 · Greenshield's model • Example –Calibrate Greenshields model using the data give in the table –Find the maximum flow –Find the density](https://reader033.vdocuments.mx/reader033/viewer/2022042116/5e946a814dea0259102ba381/html5/thumbnails/40.jpg)
Thank You
Questions?