7. 智慧交通應用-交通三元素
Green shield’s model (1935)(線性模型)
Pipes’ generalized model (冪次模型)
7
模型公式參考來源:
1. T.V. Mathew, “Chapter 3 Traffic Stream Models,” Transportation Systems Engineering, 2014.
2. M. Jabeena, “Comparative Study Of Traffic Flow Models And Data Retrieval Methods From Video Graphs,” Journal of Engineering Research and Applications, vol. 3, no. 6, pp. 1087-1093, 2013.
j
f
k
k
uu 1
n
j
f
k
k
uu 1
Greenberg’s logarithmic model (1959)(對數模型)
Underwood exponential model (1961)(指數模型)
k
k
uu
j
1ln0
0k
k
f euu
uf: free flow speed
kj: jam density
u0: optimum speed
k0: optimum density
8. 智慧交通應用-交通三元素
Green shield’s model (1935)(線性模型)
Pipes’ generalized model (冪次模型)
8
Greenberg’s logarithmic model (1959)(對數模型)
Underwood exponential model (1961)(指數模型)
0
50
100
150
200
250
300
350
400
450
0 10 20 30 40 50 60 70 80
Speed(km/hr)
Density (car/km/lane)
Speed
Estimation
j
f
k
k
uu 1
n
j
f
k
k
uu 1
k
k
uu
j
1ln0
0k
k
f euu
uf
kj
uf: free flow speed
kj: jam density
u0: optimum speed
k0: optimum density
9. 0
20000
40000
60000
80000
100000
120000
140000
160000
0 20 40 60 80 100 120
Flow(car/hr)
Speed (km/hr)
Flow (per hr)
Estimation
智慧交通應用-交通三元素
Green shield’s model (1935)(線性模型)
Pipes’ generalized model (冪次模型)
9
Greenberg’s logarithmic model (1959)(對數模型)
Underwood exponential model (1961)(指數模型)
uf: free flow speed
kj: jam density
u0: optimum speed
k0: optimum density
j
f
k
k
uu 1
n
j
f
k
k
uu 1
k
k
uu
j
1ln0
0k
k
f euu
u0, k0
14. 線性迴歸(最小平方法)
線性迴歸公式證明
14
n
i
ii
n
i
ii
n
i
ii
n
i
ii
n
i
yyxxw
xwyxwy
xwyb
ybxwe
1
2
1
2
1
2
1
2
1
2
運用最小平方法可以證明
n
i
i
n
i
iin
i
ii zzzf
1
2
1
1
2
min
定理
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i
i
n
i
iii
n
i
ii
xx
yyxx
w
yyxxwwf
1
2
1
1
2
min
相關係數
(Correlation Coefficient)
15. 線性迴歸(最小平方法)
線性迴歸公式證明
定理證明
15
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i
n
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iin
i
ii
n
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i
n
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n
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i
n
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iii
n
i
iii
n
i
ii
zz
zz
z
z
f
zzf
1
2
1
11
2
11
2
1
2
1
1
2
00
02
min
2
2
2
2
0
0
02
min
i
ii
iii
iii
iii
iii
ii
z
z
z
z
z
z
g
zzg
對z偏微分,令一階導
函數為0,即為最小值