市區幹道混合車流公車微觀模擬模式之研究

Department of Civil Engineering College of Engineering National Taiwan University

Master Thesis

A Study of Bus Microscopic Simulation Models for Mixed Traffic Flow on Urban Arterial

Huang, Jyun-Ping

Advisor: Hsu, Tien-Pen Ph.D.

102

June 2013

I

2013.7.

II

VISSIM CORSIM

Excel VBA

RMSE 0.4 MAPE 10%

75%

III

:

IV

Abstract

Microscopic traffic simulation has been used to evaluate traffic improvement measure for several years. Even though there are many simulation models around the world, it still can’t simulate mixed flow very well. In development countries, there are a lot of cars, motorcycles and buses on urban arterials. The mixed flow influences speed, delay and road capacity etc. Bus is the largest and heaviest vehicle on road. It influences traffic flow a lot because of its running speed, occupancy and bus stop effect. However, most of microscopic traffic simulation software didn’t take care of these parts. To improve the reality of mixed flow microscopic simulation in Taiwan, this research tries to analyze the bus behavior in mixed flow, and build the bus microscopic simulation models.

This research use digital video and coordinate transformation techniques to get microscopic vehicle data. According to these data, this research analyzes bus following behavior and the process of bus entering and leaving bus stop. The bus following model is according to Wiedemann psycho-physical threshold model’s structure to build and calibrate the model. After model verification and validation, the result of RMSE is about 0.4m per time step, and the MAPE value is smaller than 10%. It proves that this model can simulate real bus following behavior.

Therefore, the behavior model of bus entering and leaving bus stop is built. With the flow chart of bus behavior process, this research uses binary choice model to decide when the bus turning to the bus stop. After the model calibration and validation, the hit rate of the choice model is greater than 75%, and the distribution also fits the real condition, demonstrating good model performance.

To sum up, this research builds bus microscopic behavior models on urban arterial.

For the development of local microscopic traffic model, it can be used to evaluate bus

V

stop effect and make the simulation become more reality and reliability, helping traffic engineer evaluate the traffic flow condition.

Key Words: Microscopic Traffic Simulation, Mixed Flow, Psycho-Physical Threshold Model, Bus Following Model, Bus Microscopic Behavior, Binary Choice Model.

VI

... I ... II Abstract ... IV ... IX ... XIII

... 1

1.1 ... 1

1.2 ... 2

1.3 ... 3

... 5

2.1 ... 5

2.2 ... 18

2.3 ... 27

... 28

3.1 ... 28

3.2 ... 28

3.3 ... 33

... 35

4.1 ... 35

4.2 ... 35

4.3 ... 37

4.3.1 ... 37

4.3.2 ... 39

VII

4.4 VISSIM ... 46

... 49

5.1 ... 49

5.2 ... 50

5.2.1 ... 51

5.2.2 ... 55

5.3 ... 59

5.3.1 ... 59

5.3.2 ... 65

5.3.3 ... 65

5.3.4 ... 66

... 70

6.1 ... 70

6.2 ... 70

6.2.1 ... 70

6.2.2 ... 77

6.3 ... 79

6.4 ... 80

... 83

7.1 ... 83

7.2 ... 85

7.2.1 ... 85

7.2.2 ... 90

7.3 ... 92

7.3.1 ... 92

VIII

7.3.2 ... 93

7.4 ... 94

... 96

8.1 ... 96

8.2 ... 97

... 98

IX

1.1 ... 2

1.2 ... 2

1.3 ... 3

2.1 ... 6

2.2NEWELL ... 9

2.3NEWELL ... 10

2.4NEWELL ... 10

2.5NEWELL Q-K ... 11

2.6WIEDEMANN ... 13

2.7MISSION ... 14

2.8MISSION ... 15

2.9FRITZSCHE ... 16

2.10MITSIM ... 20

2.11MISSION ... 21

2.12MISSION ... 21

2.13MISSION ... 22

2.14AHMED ... 23

2.15 ... 24

3.1 ... 28

3.2 ... 29

3.3 ... 30

3.4 ... 30

X

3.5 ... 31

3.6 ... 31

3.7 ... 32

3.8 ... 32

3.9 ... 33

3.10 ... 33

4.1 ... 35

4.2 ... 36

4.3 ... 36

4.4 ... 37

4.5 ... 38

4.6 ... 38

4.7 ... 41

4.8 ... 41

4.9 ... 42

4.10 ... 42

4.11 ... 43

4.12 ... 43

4.13 ... 44

4.14 ... 44

4.15 ... 45

4.16 ... 45

4.17VISSIM ... 46

4.18VISSIM X-V X-Y ... 47

4.19 X-V ... 47

XI

4.20 X-Y ... 48

5.1 ... 49

5.2 ... 50

5.3 ... 50

5.4 ... 51

5.5 ... 55

5.6 ... 57

5.7 ... 58

5.8 ... 60

5.9 ... 60

5.10 ... 61

5.11 ... 62

5.12 ... 63

5.13 ... 63

5.14 ... 66

5.15 ... 67

5.16 ... 69

6.1 ... 71

6.2 (V=0~5 M/S) ... 72

6.3 (V=5~9 M/S) ... 72

6.4 (V=9~13 M/S) ... 72

6.5 ABX SDX ... 73

6.6 ... 74

6.7 ... 75

6.8 ... 76

XII

6.9 DV-DX ... 77

6.10 ... 79

6.11 ... 80

6.12 ... 80

7.1 ... 84

7.2 ... 84

7.3 DV-DX ... 86

7.4 T-V ... 86

7.5 T-DX ... 86

7.6 DV-DX ... 87

7.7 T-V ... 87

7.8 T-DX ... 87

7.9 DV-DX ... 88

7.10 T-V ... 88

7.11 T-DX ... 88

7.12 RMSE ... 89

7.13 ... 92

7.14 ... 93

7.15 ... 94

XIII

2.1 ... 17

2.2 ... 18

3.1 ... 33

3.2 ... 34

5.1 ... 59

6.1 ABX SDX ... 73

6.2 ... 77

6.3 ... 78

6.4 ... 81

7.1 ... 83

7.2 ... 90

7.3MAPE ... 90

7.4 ... 91

1

1.1

(Intelligent Transportation

System ITS)

VISSIM

VISSIM

2

1.2

1.1

1.2

3

1.3

確立研究 內容與範圍

文獻回顧

跟車模式 變換車道模式

車流錄影調查

車流資料 收集與分析

模式構建

參數校估與驗證

結論與建議

1.3 1.

4

2.

3.

4.

5.

6.

7.

5

2.1

(Stimulus-response)

18 (GM model) General Motors 1950

𝑅𝑒𝑠𝑝𝑜𝑛𝑠𝑒 = 𝑓(𝑆𝑡𝑖𝑚𝑢𝑙𝑢𝑠, 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦)

(headway)

𝑎_𝑛(𝑡 + 𝑇) = 𝑐𝑣_𝑛^𝑚(𝑡 + 𝑇) 𝑣_𝑛−1(𝑡) − 𝑣_𝑛(𝑡) [𝑥_𝑛−1(𝑡) − 𝑥_𝑛(𝑡)]^𝑙

𝑥_𝑛 , 𝑥_𝑛−1 : 𝑣_𝑛 , 𝑣_𝑛−1 : 𝑎_𝑛 :

𝑇 : 𝑐 , 𝑚 , 𝑙 :

6

(Safety distance) (Collision avoidance)

1. 24

Lewis Michael(1963)

𝑆 ≥ 𝑃 + 𝑉 + 1

2𝐷(𝑉 − 𝑉 ) (𝑄) { 𝑄 = 1 𝑤ℎ𝑒𝑛 𝑉 ₋₁> 𝑉′ 𝑄 = 0 𝑤ℎ𝑒𝑛 𝑉 ₋₁≤ 𝑉′

𝑆:

𝑃:

D:

𝑉: t 𝑉′: t

(1) (Spacing Restriction)

Z t-1 t ZS

2.1 24

𝑍 =1

2(𝑉 ₋₁− 𝑉) 𝑍𝑆 = 𝑋 − 𝑋 ₋₁− 𝑆

7

𝑉 ₋₁> 𝑉’ 𝑍𝑆 =1

2𝑉 ₋₁+1

2𝑉 −3𝐷̅

4 + [9𝐷̅ 16 −𝐷̅

4𝑉 ₋₁−3𝐷̅

4 𝑉 +𝐷̅

2(𝑋 − 𝑋 ₋₁− 𝑃)]

𝑉 ₋₁≤ 𝑉’

𝑍𝑆 =1

3[𝑋 − 𝑋 ₋₁− 𝑃 + 𝑉 ₋₁] (2) (Acceleration Restriction)

A̅

(maximum permissible velocity) V̅ ZA

𝑍𝐴 =1

2[𝑉 ₋₁+ (𝑉 ₋₁+ 𝐴̅)]

(𝑉 ₋₁+ 𝐴̅) ≤ 𝑉̅

(3) (Stopping Restriction)

(stop sign)

x ZD

𝑍𝐷 = 1

2𝑉 ₋₁−𝐷 4+ [𝐷

16−𝐷

4𝑉 ₋₁+𝐷 2𝑥]

(4) (Turning Restriction)

(turn point)

x 𝑉_𝑚 ZT

𝑍𝑇 =1

2𝑉 ₋₁−𝐷̅ 4 + [𝐷̅

16+𝑣 4 −𝐷̅

4𝑉 ₋₁+𝐷̅ 2𝑥]

𝑉_𝑚 = [𝑉 ₋₁+ 2𝐴̅𝑥]

8

2. Gipps 27

Gipps(1981) GM (desired braking)

(acceleration rates)

(safe stop) (desire speed)

Gipps

𝑣 ≤ 𝑣_𝑛(𝑡) + 2 5𝑎_𝑛𝜏(1 −𝑣_𝑛(𝑡)

𝑉_𝑛 )(0 025 +𝑣_𝑛(𝑡) 𝑉_𝑛 )

𝑏̂

𝑣 ≤ 𝑏_𝑛𝜏 + √(𝑏_𝑛𝜏 − 𝑏_𝑛(2[𝑥_𝑛−1(𝑡) − 𝑠_𝑛−1− 𝑥_𝑛(𝑡)] − 𝑣_𝑛(𝑡)𝜏 −𝑣_𝑛−1(𝑡) 𝑏̂ ))

𝑣_𝑛(𝑡 + 𝜏) = min {𝑣 , 𝑣 }

3. PITT 38

PITT

INTRAS FRESIM INTRAS

NETSIM CORSIM

(space headway)

h(t) = L + k𝑉_𝑓+ 10 + bk(𝑉_𝑙− 𝑉_𝑓)

L:

k:

b = {0 1 𝑓𝑜𝑟 (𝑉_𝑙− 𝑉_𝑓) ≤ 10 0 𝑓𝑜𝑟 (𝑉_𝑙− 𝑉_𝑓) > 10

9

𝑎_𝑓 = 2[𝑋_𝑙− 𝑋_𝑓^𝑖 − L − 10 − 𝑉_𝑓^𝑖(𝑘 + 𝑇) − 𝑏𝑘(𝑉_𝑙− 𝑉_𝑓^𝑖) ] (𝑇⁄ + 2𝑘𝑇)

𝑋_𝑓^𝑖 𝑉_𝑓^𝑖 T

c

𝑉_𝑓= 𝑉_𝑓^𝑖 + 𝑎_𝑓(𝑇 − 𝑐) 𝑋_𝑓 = 𝑋_𝑓^𝑖 + 𝑉_𝑓^𝑖𝑇 +𝑎_𝑓(𝑇 − 𝑐)

2

4. Newell 21

Newell (homogenous)

n n-1

2.2 Newell 21

𝜏_𝑛

10

2.3 Newell 21

2.4 Newell 21

𝜏_𝑛:

11

𝑑_𝑛: 𝑠_𝑛 , 𝑠_𝑛:

𝑑_𝑛 + 𝑣𝜏_𝑛 = 𝑠_𝑛 𝑑_𝑛+ 𝑣′𝜏_𝑛 = 𝑠′_𝑛 𝑥_𝑛(𝑡 + 𝜏_𝑛) = 𝑥_𝑛−1(𝑡) − 𝑑_𝑛

:

𝑥_𝑛(𝑡 + 𝜏_𝑛+ 𝜏_𝑛−1+ 𝜏_𝑛− + ⋯ + 𝜏₁) = 𝑥 (𝑡) − 𝑑_𝑛 − 𝑑_𝑛−1− ⋯ − 𝑑₁

𝜏_𝑛 𝑑_𝑛 :

𝜏̅ =_𝑛¹∑^𝑛_𝑘=1𝜏_𝑘 𝑑̅ = ¹_𝑛∑^𝑛_𝑘=1𝑑_𝑘

𝑑̅/𝜏̅ (stationary flow) k = 1/𝑠̅

v = q/k

q =1 𝜏̅−𝑑̅

𝜏̅𝑘

q k

2.5 Newell q-k 21

12

(Psycho-physical) (action point)

1. 35 36

Wiedemann(1974)

MISSION MISSION

 (AX): RND1(I)

AX = L + (AXadd + RND1(I) × AXmult)

 (ABX):

ABX = AX + BX

BX = (BXadd + BXmult × RND1(I)) × √𝑉

 (SDV):

SDV RND2(I)

SDV = (𝐷𝑋 − 𝐴𝑋

𝐶𝑋 )

CX = CXconst × (CXadd + CXmult × (RND1(I) + RND2(I))

 (SDX):

NRND

SDX = AX + EX × BX

EX = EXadd + EXmult × (NRND − RND2(I))

 (CLDV):

13

CLDV = SDV × EX

 (OPDV):

CLDV 1 3

OPDV = CLDV × (−OPDVadd − OPDVmult × NRND)

2.6 Wiedemann 36

14

 (Un-influenced Driving):

BMAX = BMAXmult × (V_𝑀𝐴𝑋− 𝑉 × 𝐹𝑎𝑐𝑡𝑜𝑟𝑉)

FactorV = 𝑉_𝑀

𝑉_𝐷𝐸𝑆+ 𝐹𝑎𝑐𝑡𝑜𝑟𝑉𝑚𝑢𝑙𝑡 × (𝑉_𝑀𝐴𝑋− 𝑉_𝐷𝐸𝑆)

2.7 MISSION 36

 (Closing Process):

B(I) = 1

2∙ 𝐷𝑉

𝐴𝐵𝑋 − 𝐷𝑋+ 𝐵(𝐼 − 1)

 (Following Process):

MISSION

BNULL 0.2m/s²

BNULL = 𝐵𝑁𝑈𝐿𝐿_𝑚𝑢𝑙 ∙ (𝑅𝑁𝐷4(𝐼) + 𝑁𝑅𝑁𝐷)

 (Emergency Braking):

B(I) =1

2∙ 𝐷𝑉

𝐴𝑋 − 𝐷𝑋+ 𝐵(𝐼 − 1) + 𝐵𝑀𝐼𝑁 ∙𝐴𝐵𝑋 − 𝐷𝑋 𝐵𝑋

15

2.8 MISSION 36

2. Fritzsche 23

Fritzsche(1994) (space

headway) :

(1)

 (PTP) (PTN)

PTP = 𝑘_𝑃𝑇𝑃(∆𝑥 − 𝑠_𝑛−1) + 𝑓 PTN = −𝑘_𝑃𝑇𝑁(∆𝑥 − 𝑠_𝑛−1) − 𝑓

(2) (space headway)

 (Desired distance AD):

AD = 𝑆_𝑛−1+ 𝑇_𝐷𝑣_𝑛

 (Risky distance AR): (gap)

AR = 𝑆_𝑛−1+ 𝑇_𝑟𝑣_𝑛−1

 (Safe distance AS):

(headway)

AS = 𝑆_𝑛−1+ 𝑇_𝑠𝑣_𝑛

16

 (Braking distance AB):

AB = AR + ∆𝑣

∆𝑏_𝑚

∆𝑏_𝑚 = |𝑏_𝑚𝑖𝑛| + 𝑎_𝑛−1⁻

2.9 Fritzsche 23

 (Danger)

AR 𝑏_𝑚𝑖𝑛

 (Closing in)

PTN AB AD

AR 𝑎_𝑛 = (𝑣_𝑛−1− 𝑣_𝑛)

2𝑑_𝑐

d_c = 𝑥_𝑛−1− 𝑥_𝑛− 𝐴𝑅 + 𝑣_𝑛−1∆𝑡

∆𝑡:

17

 (Following I)

PTN PTP AR AD

PTP AS AR

±𝑏_{𝑛𝑢𝑙𝑙}

 (Following II)

PTN AB AD

 (Free driving)

PTN AD PTP AS

𝑎_𝑛⁺

±𝑏_{𝑛𝑢𝑙𝑙}

2.1

․

․

․

․

․

․

․

․

․ ․

:

18

2.2

MITSIM

Gazis Herman Rothery AIMSUN

Gipps TSIS-CORSIM

PITT PARAMICS

Fritzsche

VISSIM -

Wiedemann :

Gipps

2.2

(Mandatory Lane Changing MLC) (Discretionary Lane Changing DLC)

19

Gipps 28 (1984)











 ?

 ?

 ?

(gap acceptance)

𝑏_𝑛 = [2 − (𝐷_𝑛 − 𝑥_𝑛(𝑡))/10𝑉_𝑛]𝑏_𝑛^∗

MITSIM 37 (1996) Gipps

20

𝑓_𝑛 = { [−(𝑥_𝑛− 𝑥 )

𝑛 ] 𝑥_𝑛 > 𝑥 1 𝑥_𝑛 ≤ 𝑥

𝑛 = 𝛼 (1 + 𝛼₁𝑚_𝑛+ 𝛼 𝐾)

𝑓_𝑛: n 𝑥_𝑛:

𝑥 : _𝑛:

MITSIM

(impatience factor) (speed

indifference factor)

(Lead gap)

(Lag gap)

2.10 MITSIM 37

Willmann Sparmann 36 (1978) SDXP

SDVP MISSION

SDXP = AX + FX ∙ BX SDVP = FV ∙ SDV

21

2.11 MISSION 36

FX FV

MISSION



(1) FREE :

(2) LEAD :

(3) LAG :

(4) GAP :

LEAD LAG

2.12 MISSION 36

22



(1) FREE :

(2) ACCEL :

2.13 MISSION 【36】

TR (headway)

LR: (distance)

GAP (s)

LEAD (s)

LAG (s)

TB (s)

Ahmed 19 (1999)

23

2.14 Ahmed 19

Ahmed

MLC DCNS

𝑃(𝑀𝐿𝐶|𝑣_𝑛) = 1

1 + (−𝑋_𝑛^𝑀 (𝑡) ^𝑀 − 𝛼^𝑀 𝑣_𝑛)

𝑃(𝐷𝐶𝑁𝑆|𝑣_𝑛) = 1

1 + (−𝑋_𝑛^{𝐷 𝑁𝑆}(𝑡) ^{𝐷 𝑁𝑆}− 𝛼^{𝐷 𝑁𝑆}𝑣_𝑛)

𝑋_𝑛^𝑀 , 𝑋_𝑛^{𝐷 𝑁𝑆}: ^𝑀 , ^{𝐷 𝑁𝑆}: 𝑣_𝑛:

24

𝛼^𝑀 , 𝛼^{𝐷 𝑁𝑆}:

𝑛𝑐𝑟, (𝑡) = (𝑋_𝑛(𝑡) + 𝛼 𝑣_𝑛+ _𝑛(𝑡))

g ∈ {𝑙𝑒𝑎𝑑, 𝑙𝑎𝑔}

_𝑛(𝑡):

𝑃(𝑔𝑎𝑝𝐴𝑐𝑐|𝑣_𝑛)

= 𝑃(𝑙𝑒𝑎𝑑 𝑔𝑎𝑝 𝑎𝑐𝑐𝑒𝑝𝑡𝑎𝑏𝑙𝑒|𝑣_𝑛)𝑃(𝑙𝑎𝑔 𝑔𝑎𝑝 𝑎𝑐𝑐𝑒𝑝𝑡𝑎𝑏𝑙𝑒|𝑣_𝑛)

= P( _𝑛^𝑙 (𝑡) > _𝑛^{𝑐𝑟,𝑙} (𝑡)|𝑣_𝑛)P( _𝑛^𝑙 (𝑡) > _𝑛^{𝑐𝑟,𝑙} (𝑡)|𝑣_𝑛)

= P(ln ( _𝑛^𝑙 (𝑡)) > ln ( _𝑛^{𝑐𝑟,𝑙} (𝑡))|𝑣_𝑛)P(ln ( _𝑛^𝑙 (𝑡)) > ln ( _𝑛^{𝑐𝑟,𝑙} (𝑡))|𝑣_𝑛)

Tzu-Chang Lee 33 (2007)

2.15 33

25

{

𝑉_𝑙 = −2 93 + 0 14𝑠𝑝𝑒𝑒𝑑_𝑙+ 0 42𝑐𝑙𝑒𝑎𝑟_𝑙− 0 46𝑓𝑜𝑟𝑐𝑒𝑅_𝑙+ 3 27𝑙𝑎𝑠𝑡_𝑙 𝑉_𝑐 = 0 05𝑠𝑝𝑒𝑒𝑑_𝑐 − 0 06𝑠𝑖𝑧𝑒_𝑐 𝑉_𝑟 = −3 66 + 0 14𝑠𝑝𝑒𝑒𝑑_𝑟+ 0 42𝑐𝑙𝑒𝑎𝑟_𝑟− 0 46𝑓𝑜𝑟𝑐𝑒𝑅_𝑟+ 3 27𝑙𝑎𝑠𝑡_𝑟

13

2.27 0.40

33

:

1. 30

2. 5m/s

3. 3m/s

4.

R = 𝑉

𝑔(𝑓 + 𝑒)= 𝑉

127(𝑓 + 𝑒)

R (m)

g (9.8 m/s²)

26

V (m/s) f

e

5

LC = −0 76 𝐴𝑃 + 0 999𝑉_𝑖𝑛 + 0 357 𝐴𝑃_{𝑛 𝑛} − 0 012𝐷_𝑖

Gipps

1.

2.

3.

(lead and lag)

27

2.3

1.

2.

3.

4.

28

3.1

3.2

3.1

 1.

29

2.

3.

3.2

30

 1.

KMPlayer

3.3 2.

0.5

3.4

31

 1.

3.5 2.

( )

X Y

3.6 3.

32

3.7



Microsoft Excel

dv dx

3.8

33

3.3

: 3.1

2011/08/15 7:30~9:30

2011/09/02 8:30~9:30

2012/03/28 8:00~12:00

2012/08/14 15:30~18:30

3.9

3.10

34

3.2

(m) (m)

1

( )

3.0

( )

3.0

2 3.0

( )

3.0

3 3.0 3.0

4 4.5 5.2

( : 1 4)

1.

dv dx

2.

35

4.1

60%

4.1

4.2

40 50

36

111

4.2

4.3

37

4.3

4.3.1

(bottleneck)

Reebu Zachariah Koshy

V. Thamizh Arasan 29

4.4 29

38

4.5 29

:

1. :

2. :

3. :

近端站位 街廓中間站位 遠端站位

4.6

39

4

1000

0.03 40 0.5

90 15

10

Transit Co-operative Research Program

(TCRP) 29 1996

1. 250

2. 40mph

3. 10

4. 20 40

5. 30

4.3.2

40

1.

33 13

25kph 5.2 5.1 15

(gap) (space)

2.

166 KS

4.7 4.8

41

: = 166 ( ), = -3.3 (m), = 10.1 (m)

4.7

: = 166 ( ), = 2.7 (m), = 0.8 (m)

4.8

: 45 3

0%

5%

10%

15%

20%

25%

30%

35%

40%

-40 -30 -20 -10 0 10 20 30 40

Probability Density

縱向位置 (m)

公車停靠縱向位置分佈

0%

5%

10%

15%

20%

25%

30%

35%

40%

0 1 2 3 4 5 6 7

Probability Density

側向位置 (m)

公車停靠側向位置分佈

42

4.9

公 車 停 靠 區 本車

服務中公車 本車目標停靠位置

安全淨間距

4.9

( )

1

182 KS

11.3 7.1

4.10

0%

5%

10%

15%

20%

25%

30%

35%

40%

0 5 10 15 20 25 30 35 40 45

Probability Density

停站時間(s)

公車停站時間分佈

43

3.

4.11 4.12

公 車 停 靠 區 跟車離站 直行離站

彎入主線離站

4.11

4.12

dX

44

dY_pass 4.13

𝜃 = tan⁻¹𝑑𝑌 _𝑠𝑠 𝑑𝑋

公 車 停 靠 區

dX 影響前車 dY_pass θ

4.13

53

25

4.14

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 5 10 15 20 25 30 35 40

轉向角 (度)

公車出站轉向角度累積機率圖

45

s

s = 𝑑𝑌 _𝑠𝑠 − 𝑑𝑌 − 0 5(𝑊 + 𝑊_𝑙)

s : (m)

𝑑𝑌 _𝑠𝑠 : (m)

𝑑𝑌 : (m)

𝑊, 𝑊_𝑙 : (m)

4.15

: = 53 ( ), =0.82 (m), =0.38 (m)

4.16

0%

10%

20%

30%

40%

50%

60%

0 0.4 0.8 1.2 1.6 2

Probability Density

側向淨間距 (m) 公車出站轉向超車側向淨間距分佈

46

0.8

KS

4.4 VISSIM

VISSIM VISSIM

Wiedemann(1974)

VISSIM

VISSIM

4.17 VISSIM

VISSIM

VISSIM

VISSIM

VISSIM

47

4.18 VISSIM

X- V X- Y

4.18 VISSIM X-V X-Y

X-V X-Y

4.19 4.20 VISSIM

25 kph/10m VISSIM 16 kph/10m

30 50

VISSIM 150

VISSIM

4.19 X-V

48

4.20 X-Y

VISSIM

49

5.1

公車模擬 公車車種

車道種類

路段位置

公車行為 行駛路線

停靠車站

路口紓解 減速煞停 路段推進

班次密集度

公車專用道 混合車道

進出站行為 變換車道

跟車

公車性能 加減速性能

轉彎半徑 快車道

5.1

50

公車進出站模式 路段跟車模式 判斷是否進入

公車站影響範圍 判斷是否

Yes 進站服務 Yes

No No

5.2

5.2

5

本車

影響前車 傳統定義之前車

5.3

51

5.2.1

Wiedemann 1974

dx

SDV

CLDV

SDX

ABX CLDV

OPDV

ABX

5.4

52

1.

:

 (AX):

AX = L + S × RND1(I)

L: (m)

S: (m)

RND1(I):

 (ABX):

ABX = AX + BX

BX: (m)

 (SDX):

SDX = AX + EX × BX

EX:

 (SDV):

SDV

SDV = (𝐷𝑋 − 𝐴𝑋

𝐶𝑋 )

CX:

53

 (CLDV):

4 CLDV = SDV × EX

EX:

 (OPDV):

CLDV

OPDV = CLDV × NRND

NRND:

2.

 (Un-influenced Driving):

(Desire speed)

𝑎_𝑓𝑟 = 𝑎_𝑚 − 𝑎_𝑚 × ( 𝑉 𝑉 _𝑠𝑖𝑟 )

𝑎_𝑓𝑟 : (m/s²)

𝑎_𝑚 : (m/s)

𝑉: (m/s)

𝑉 _𝑠𝑖𝑟 : (m/s)

54

 (Closing Process):

SDV

CLDV

ABX

𝑏_{𝑐𝑙 𝑠𝑖𝑛} =1 2

𝑑𝑣

𝐴𝐵𝑋 − 𝑑𝑥+ 𝑏 ₋₁

𝑏_{𝑐𝑙 𝑠𝑖𝑛} : (m/s²)

𝑑𝑣: (m/s)

𝑑𝑥: (m)

𝑏 ₋₁: (m/s²)

 (Following Process):

ABX SDX

MISSION 𝑏_{𝑛𝑢𝑙𝑙}

0.2m/s²

𝑎_{𝑓 𝑙𝑙 𝑖𝑛}

 (Emergency Braking):

ABX

𝑏 _{𝑟 𝑘𝑖𝑛} =1 2

𝑑𝑣

𝐴𝑋 − 𝑑𝑥+ 𝑏 ₋₁+ 𝑏_𝑚𝑖𝑛∙𝐴𝐵𝑋 − 𝑑𝑥 𝐵𝑋

𝑏 _{𝑟 𝑘𝑖𝑛} : (m/s²)

55

𝑏_𝑚𝑖𝑛: (m/s²)

𝐵𝑋: ABX AX (m)

5.2.2

5.5

(headway) (spacing)

56

V dx dv

𝑎_{𝑓 𝑙𝑙 𝑖𝑛} = 𝛼 + 𝛼₁𝑑𝑣 + 𝛼 𝑑𝑥 + 𝛼₃𝑉 + 𝛼₄𝑙𝑒𝑎𝑑 _𝑦 + Rnd _{𝑟𝑖𝑣 𝑟}

𝑎_{𝑓 𝑙𝑙 𝑖𝑛} : (m/s²)

dv: (m/s)

d : (m)

V: (m/s) l ad_type:

𝑅𝑛𝑑 _{𝑟𝑖𝑣 𝑟}: 𝛼_𝑖:

Excel VBA

57

公車跟車模式模擬流程

定義跟車參數 Definition

判斷是否已達 模擬時間 計算本車模擬時間

Simulation time

讀取初始跟車參數 Initialization

計算各行為區間速度值 Speed value

以行為區間決策模組 決定本時階車輛速度

Desision 輸出本時階結果 更新時階跟車參數

Renew data

結束模擬 End

Yes

No, Next time step

5.6

ABX

58

ABX SDX

CLDV OPDV

CLDV

SDV

公車跟車 行為區間決策模組

dx≦ABX

dx≦SDX No

Yes

dv≧CLDV

dv≧SDV

dv≧OPDV Yes

Yes

No Yes No

No Yes

No

緊急煞車

接近程序

自由駕駛 跟車過程

5.7

59

5.1

(Un-influenced Driving) 𝑎_𝑓𝑟 = 𝑎_𝑚 − 𝑎_𝑚 × ( 𝑉

𝑉 _𝑠𝑖𝑟 )

(Closing Process) 𝑏_{𝑐𝑙 𝑠𝑖𝑛} =1

2 𝑑𝑣

𝐴𝐵𝑋 − 𝑑𝑥+ 𝑏 ₋₁

(Following Process)

𝑎_{𝑓 𝑙𝑙 𝑖𝑛} = 𝛼 + 𝛼₁𝑑𝑣 + 𝛼 𝑑𝑥 + 𝛼₃𝑉 + 𝛼₄𝑙𝑒𝑎𝑑 _𝑦 + Rnd _{𝑟𝑖𝑣 𝑟}

(Emergency Braking) 𝑏 _{𝑟 𝑘𝑖𝑛} =1 2

𝑑𝑣

𝐴𝑋 − 𝑑𝑥+ 𝑏 ₋₁+ 𝑏_𝑚𝑖𝑛∙𝐴𝐵𝑋 − 𝑑𝑥 𝐵𝑋

5.3

5.3.1

60

5.8

127 Xdists

5.9

20 50

33.7 15.9 KS

100 100

61

(critical gap)

(gap)

5.10

( )

( )

0.22(m/s) 0.13(m/s)

62

5.11

(Binary choice model)

(Discrete choice model) Ben-Akiva Lerman

20

𝑈 = 𝑉_𝑖𝑛+ 𝜀_𝑖𝑛

𝑈: n i

𝑉_𝑖: n i

𝜀_𝑖:

Gumbel

n i

63

P_𝑖𝑛 = 𝑒^𝑉𝑖𝑛

∑_{𝑗∈ 𝑛}𝑒^𝑉𝑗𝑛

0.5 2

12m

2.5m dx

2.0m 淨空影響區

5.12

12m

2.5m

2m

淨空影響區

dx

dXrf dXrb

dYr

公 車 停 靠 區

Xdists

影響 前車

Ydists

5.13

 (Xdists):

64

 (Ydists):

 (dYr):

 (dXrf):

(gap)

 (dXrb):

(gap)

 (dVrb): (dXrb)

(logistic regression)

(Maximum Likelihood Method)

log(𝑃⁄1 − 𝑃) = + ∑ 𝑋_𝑖

𝑛

𝑖=1

P_t: Xi: β_i:

1

: {𝑃 + 𝑅𝑎𝑛𝑑 ≥ 1 𝑃 + 𝑅𝑎𝑛𝑑 1

𝑃:

Rand: ~uniform(0, 1)

65

5.3.2

Xdists_𝑠 ∈ N( , ) dists _{t p}∈ Log N( _𝑦, _𝑦)

ST

𝑆𝑇 ∈ 𝐷𝑖𝑠𝑡 (𝑆𝑇_{𝑖 𝑖} , _𝑖) 𝑖 ∈

5.3.3

θ

66 判斷是否小於最大偏向角

(θ≦θmax?)

彎入主線離站 Yes

等候 (next time step) No

判斷前方是否有服務公車

直行離站 No

判斷前車是否啟動

跟車離站

公車出站邏輯

產生本車可接受 轉向超車側向間距值s

計算dY_pass與θ Yes

判斷是否可彎入主線 (Gap Acceptance)

Yes Yes

No No

5.14

5.3.4

67

公車進出站模式

判斷進站轉向決策 Binary logit model

維持路段 跟車模式

判斷 Xdists、Ydists 是否超過門檻值

依據分佈產生 Xdists停站位置

停站服務 計算縱向與側向速度

減速轉向進站 公車停靠區 是否有服務中公車

等候停靠區內公車 完成服務

判斷是否 完成服務

以公車出站邏輯 離開車站

Yes

維持跟車 No

Next Time Step

轉向進站

No

Next Time Step No 以服務中公車車尾

後一靜態間距為 暫時Xdists停站位置

依據分佈產生 Ydists停站位置

判斷車站容量 是否足夠

Yes Yes

產生停站時間ST Yes

No

Next Time Step 判斷是否進入

公車站影響範圍 Yes 判斷本車是否進站

Yes

No

No

判斷本車是否處於 外側兩車道

Yes

以側向偏移速度進行偏移 Next Time Step

No

5.15

68

1.

100

: (1)

𝑎 _{𝑖𝑛,𝑛} = − 𝑉 _,𝑛

2(𝑋𝑑𝑖𝑠𝑡𝑠 _,𝑛− 𝑋𝑑𝑖𝑠𝑡𝑠 𝑠𝑡𝑜𝑝)

𝑎 _{𝑖𝑛,𝑛}: n (m/s²)

𝑉 _,𝑛: n (m/s)

𝑋𝑑𝑖𝑠𝑡𝑠 _,𝑛: n (m)

𝑋𝑑𝑖𝑠𝑡𝑠 𝑠𝑡𝑜𝑝: (m)

n+1 𝑉_{𝑖𝑛 ,𝑛+1}

𝑉 _{𝑖𝑛,𝑛+1} = 𝑉 _,𝑛+𝑎_{𝑥𝑖𝑛,𝑛}𝑇

𝑇: (s)

69

n+1

𝑉 _,𝑛+1= 𝑀𝑖𝑛(𝑉𝑓 𝑙𝑙 𝑖𝑛 ,𝑛+1, 𝑉 _{𝑖𝑛,𝑛+1}) (2)

淨空影響區

Ysafe

公 車 停 靠 區

影響 前車

5.16

𝑉_{𝑦𝑠 𝑓 ,𝑛+1} = 𝑌_{𝑠 𝑓 ,𝑛}/𝑇 𝑉_𝑦,𝑛+1 = 𝑀𝑖𝑛(𝑉_{𝑦𝑠 𝑓 ,𝑛+1}, 𝑉_{𝑦𝑖𝑛,𝑛+1})

𝑉_{𝑦𝑠 𝑓 ,𝑛+1}: n+1 (m/s)

𝑌_{𝑠 𝑓 ,𝑛}: n (m)

𝑉_{𝑦𝑖𝑛,𝑛+1} : n+1 (m/s)

2.

3.

70

6.1

6.2

111 19

74 18 2086

6.2.1

ABX SDX SDV

CLDV OPDV

1. ABX SDX

71

dv- dx

6.1

5 6

0~5 m/s 5~9

m/s 9~13 m/s dx 6.2

6.4 10% 90%

ABX SDX

72

6.2 (V=0~5 m/s)

6.3 (V=5~9 m/s)

6.4 (V=9~13 m/s)

73

ABX SDX (V=0)

AX(1.5 ) ABX SDX

6.1 ABX SDX

V (m/s) ABX (m) SDX (m)

0 1.5 1.5

0~5 3.6 8.3

5~9 5.0 19.2

9~13 9.8 27.1

0.6997V+1.3888 2.3282V+2.0931

R² 0.9358 0.9961

6.5 ABX SDX

2. CLDV OPDV SDV

74

θ₁ W D₁

V_f1 V_l1

θ2 W D2

V_f2 V_l2

6.6

:

W ≈ 𝐷₁𝜃₁ = 𝐷 𝜃

𝐷₁− 𝐷 = [(𝑉_𝑓1− 𝑉_𝑓1) + (𝑉_𝑓 − 𝑉_𝑓 )]/2 ∙ 𝑑𝑡 = 𝑑𝑣 ∙ 𝑑𝑡

dv dx :

𝑑𝜃

𝑑𝑡 = 𝜃 − 𝜃₁

𝑑𝑡 =

𝐷𝑊 −𝑊 𝐷₁

𝑑𝑡 = 𝑊𝐷₁− 𝐷

𝐷₁𝐷 𝑑𝑡 ≈ 𝑑𝑣 𝑑𝑥

dv

dx -

CLDV

OPDV

75

CLDV OPDV

6.7

:

 CLDV: ABX

SDX (dv>0)

(a>0) CLDV

 OPDV: ABX

SDX (dv<0)

(a<0) OPDV

 SDV: SDX

(dv>0) (a>0)

SDV

(

)

76

CLDV

OPDV

SDV

6.8

10

90% 1m/s

Excel VBA 90%

0 5 10 15 20 25 30 35

-4 -3 -2 -1 0 1 2 3 4

dx (m)

dv (m/s)

77

6.2

CLDV 0 007(𝑑𝑥 − 1 5) + 1

OPDV −0 006(𝑑𝑥 − 1 5) − 1

SDV 0 002(𝑑𝑥 − 1 5) + 1

6.9 dv-dx

6.2.2

0 5 10 15 20 25 30 35

-4 -3 -2 -1 0 1 2 3 4

dx (m)

dv (m/s)

SDV

CLDV OPDV

78

dx dv

𝑎_{𝑓 𝑙𝑙 𝑖𝑛} = 𝛼 + 𝛼₁𝑑𝑣 + 𝛼 𝑑𝑥 + 𝛼₃𝑉 + 𝛼₄𝑙𝑒𝑎𝑑 _𝑦

6.3

1192 -0.05 0.92

R² 0.123

t (p-value)

𝜶_𝟏 (𝐝𝐯) -0.255 -11.610 <.000

𝜶_𝟐 (𝐝𝐱) 0.025 3.787 <.000

𝜶_𝟑 (𝐕) -0.044 -3.942 <.000

R²

Excel VBA

79

6.3

0.5m/s

6.10

80

6.11

6.12

6.4

(dYr) (dXrf)

(dXrb) (dVrb) SPSS

(logistic regression) (Maximum Likelihood Method)

81

log(𝑃⁄1 − 𝑃) = + ∑ 𝑋_𝑖

𝑛

𝑖=1

= + ₁𝑋𝑑𝑖𝑠𝑡𝑠 + 𝑌𝑑𝑖𝑠𝑡𝑠 + ₃𝑑𝑌𝑟 + ₄𝑑𝑋𝑟𝑓 + 𝑑𝑋𝑟𝑏 + ₆𝑑𝑉𝑟𝑏

(dVrb)

6.4

174

Cox & Snell R² 0.363

Nagelkerke R² 0.484

Hosmer Lemeshow 0.352

Wald (p-value)

( ) -13.154 22.237 <.000

1 (Xdists) -2.409 2.704 <.100

(Ydists) -4.315 6.948 <.008

3 (dYr) 12.591 23.810 <.000

4 (dXrf) 2.576 8.310 <.004

(dXrb) 2.457 11.622 <.001

82

Cox & Snell R² :

Co & Sn ll 𝑅 = 1 − [𝐿(0) 𝐿(𝐵)] ^/𝑁

𝐿(0): likelihood

𝐿(𝐵): likelihood

𝑁:

Cox & Snell R² 0.363 Nagelkerke R² 0.484 0.15 Hosmer

Lemeshow 0.352 α 0.05

Wald 3.84 Xdists

(dYr)

(dXrf) (dXrb)

Xdists Ydists

83

7.1

22 :

 (Input) (Output) (bug)



Excel VBA

7.1

70

(m) - 60

(m/s) 7 ( ) 9

(m/s²) 0 0

84

70

7.1

7.2

60 40

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70

跟車淨間距

dx (m)

時階

0 1 2 3 4 5 6 7 8 9 10 11 12

0 10 20 30 40 50 60 70

速度

(m/s)

時階

本車 前車

85

7.2

7.2.1

70 776 20

38 12

dv- dx t- v

t- dx

86

7.3 dv-dx

7.4 t-v

7.5 t-dx

87

7.6 dv-dx

7.7 t-v

7.8 t-dx

88

7.9 dv-dx

7.10 t-v

7.11 t-dx

89

RMSE(Root Mean Square Error) EM(Error Metric) MAPE(Mean Absolute Percentage Error)

 𝑅𝑀𝑆𝐸 = √_𝑁¹∑^𝑁_𝑛=1(𝑂_𝑠− 𝑂_𝑟)

 𝐸𝑀 = √∑(𝑙𝑜𝑔_𝑂^𝑂𝑠

𝑟)

 𝑀𝐴𝑃𝐸 =^{∑𝑁𝑖=1|(𝑂𝑟}_𝑁^{−𝑂𝑠)/𝑂𝑟|}× 100%

Os Or N

RMSE EM MAPE

70 RMSE

0.1 0.9 0.4

7.12 RMSE

90

RMSE 0.4 MAPE

10%

7.2

RMSE (m/time step)

EM MAPE

(%)

0.36 0.12 8.28

0.18 0.09 6.28

- : 0.40 - : 0.32 - : 0.40

- : 0.14 - : 0.11 - : 0.13

- : 9.25 - : 7.35 - : 9.46

7.3 MAPE MAPE (%)

< 10 10~20 20~50

> 50

: 25

7.2.2

40 2 80

91

7.4

80

26 5

14 35

(%) = ( )/( ) = (26+35)/80 = 76.3%

76.3%

40

Excel VBA

92

7.13

7.3

7.3.1

70 776

0 1 2 3 4 5 6 7

-20 0 20 40 60 80 100

Ydists (m)

Xdists (m)

公車進站模擬 Xdists - Ydists圖

實際 模擬

93

dx

7.14

12.2

6.4 11.8 6.1

KS

7.3.2

127

0%

5%

10%

15%

20%

25%

30%

35%

0 5 10 15 20 25 30 35

Probability Density

跟車淨間距dx (m)

模擬 實際

94

7.15

35.3

15.7 34.1 14.3

KS

7.4

RMSE 0.4 MAPE 10%

95

96

8.1

1.

2.

3.

4. RMSE

0.36 MAPE 10%

5. 76%

6.

97

8.2

1.

2.

3.

4.

98

[1] 2011

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10] ADVANCE-F

[11]

[12]

99

[13]

[14]

[15]

[16]

[17]

[18] A. D. May. (1990), Traffic Flow Fundamentals, Prentice Hall, Englewood Cliffs, New Jersey, pp.162-171.

[19] Ahmed, K. I. (1999), Modeling drivers' acceleration and lane changing behavior, PhD dissertation, Massachusetts Institute of Technology, USA.

[20] Ben-Akiva & Lerman, S. R. (1985), Discrete choice analysis: theory and application to travel demand, MIT Press, Cambridge, Massachusetts.

[21] G. F. Newell (2002), A simplified car-following theory: a lower order model, Transportation Research Part B 36.

[22] H. Rakha, B. Hellinga, M. Van Aerde, & W. Perez (1996), Systematic Verification, Validation and Calibration of Traffic Simulation Models, Transportation Research Board 75th Annual Meeting.

[23] Johan Janson Olstam (2004), Comparison of Car-following models, VTI meddelande 960A.

[24] Lewis & Michael (1963), Simulation of Traffic Flow to Obtain Volume Warrants for Intersection Control, Highway Research Record 15, pp. 1-43.

100

[25] Lewis (1982), Industrial and Business Forecasting Method, London Butterworth Scientific Publishers.

[26] Mark Brackstone & Mike McDonald (2000), Car-following: a historical review, Transportation Research Part F, Vol. 2, No. 4, pp. 181-196.

[27] P. G. Gipps (1981), A Behavioral Car-Following Model for Computer Simulation, Transportation Research Part B, Vol. 15B, pp105-111.

[28] P. G. Gipps (1986), A model for the structure of Lane-change decisions, Transportation Part B, Vol. 20, No.5, pp. 403-414.

[29] Reebu Zachariah Koshy & V. Thamizh Arasan (2005), Influence of Bus Stops in Flow Characteristics of Mixed Traffic, Journal of transportation engineering ASCE.

[30] Sakda Panwai & Hussein Dia (2005), Comparative Evaluation of Microscopic Car-following Behavior, IEEE Transactions on Intelligent Transportation System, Vol. 6, No. 3.

[31] Sandeep Menneni, Carlos Sun & Peter Vortisch (2008), An Integrated Microscopic and Macroscopic Calibration for Psycho-Physical Car Following Models.

[32] Toledo, T. (2003), Integrated driving behavior modeling, PhD dissertation, Massachusetts Institute of Technology, USA.

[33] Tzu-Chang Lee (2007), An Agent-Based Model to Simulate Motorcycle Behaviour in Mixed Traffic Flow, Department of Civil and Environmental Engineering, Imperial College London, United Kingdom.

[34] VISSIM 5.10 User Manual.

[35] Wiedemann, R. (1974), Simulation de Stranssenverkehrsflusses, Schriftenreihe des Institutsfur Verkehrswesen, Heft 8, Universitat Karlsruhe.

[36] Wiedemann, R. (1992), Microscopic Traffic Simulation the Simulation System

101

MISSION Background and Actual State, Project ICARUS(V1052) Final Report.

[37] Yang, Q., & Koutsopoulos, H. N. (1996), A Microscopic Traffic Simulator Evaluation of Dynamic Traffic Management System. Transportation Research C, Vol. 4, pp. 113 129.

[38] Yan Zhang (2004), Scalability of Car-following and Lane-changing Models in Microscopic Traffic Simulation System.