Transport: Modelling [PDF]

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Transport Modelling A brief note for urban Transport Course, Universiti Kebangsaan Malaysia

By Riza Atiq Rahmat 2013

Transport modelling Trip Generation

Trip Distribution

Modal Split

Trip Assignment

High density developments generate more trips than low density developments

1

Origin

Destination

Production and attraction

Destination 1

Origin

Destination 2

Destination 2

Trip Distribution

Mode 1

Origin

Modal Split

Origin

Mode 2

Destination

Mode 3

Destination

Trip Assignment

2

Trip Generation Model Home-based

Trips

Non-home-based

To work To go home To school To shopping centre

Business-trip

Percentage of Home-based Trips

City

Percentage

Year

Baghdad

85.8

1980

Johannesburg

84.1

1980

Kuala Lumpur

80.5

1985

High plot ratio zones generate more trips than low plot ratio

3

Percentage of Trip Purposes City

Trip Purposes Work

School

Business

Private

Others

Chicago

37.5

4.0

9.7

41.7

7.1

Detroit

41.6

6.3

8.6

34.0

9.5

Baghdad

34.8

13.0

6.2

38.0

8.0

Johannesburg (Blacks) Johannesburg (Whites) Washington, D.C. Kuala Lumpur

51.3

35.6

2.4

8.2

2.5

30.7

20.4

7.0

35.0

6.9

43.1

9.4

9.6

26.7

11.2

29.2

21.2

6.3

26.5

16.8

Work Trip

4

f (Trip Production) = Household income, household size, Car ownership, number of working person in the household ………….

Socio-economic

f (Trip Attraction) = Land-use characteristic

Ti = 880 + 0.115Aoffice + 0.145Ashoppingc + 0.0367Amanufacturing

Linear Regression Model 5

Y D7 D1

D5 D1

D2

D4

D6 D1

D1

D1

D1

D3 D1

X

The best line – the line that minimise D1 + D2 + D3 + ... + D7

R2 = 1 - maximum correlation between Y and X R2 = 0 - no correlation

t-statistic Regression parameter t = Standard error of the parameter

6

Model development 1. Observe any relationship between parameters Non-linear relationship could be linearised Y = aX

→

log Y = log a + b log X

30 25 Log Y

Y

20

Y = abX

15 10 5 0 0

5

10

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4

15

Log Y = Log a + X Log b 0

5

X

log (Y)

80 Y

Y = aXb

40 20 0 0

5

15

X

100

60

10

10

2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5

15

Log Y = Log a + b Log X

0

0.2

0.4

X

0.6

0.8

1

1.2

log (X)

2

5 4

Y = 1 / (a + bX)

1.5

Y

1/Y

3

1

2 0.5

1 0

1/Y = a + bX

0

0

2

4

6 X

8

10

12

0

5

10

15

X

7

2. Produce Correlation matrix Car ownership Car ownership Household income Number of houses Number of worker Production

Household Number Number of Production income of houses worker

1 0.995135

1

-0.80885

-0.81603

-0.30011

-0.30901 0.240331

-0.81724

-0.82478

1 1

0.98193 0.409236

1

3. Compute each of the parameters of the potential regression equations. 4. Check the following criteria: (a) The model R2. (b) Sign convention (- / +) (c) Reasonable intercept (d) Are the regression parameters statistically significant?

8

Example zo Car ne ownership 1 1.1

Household Number of income houses 3555 2350

Number of workers 235

Daily production 6655

2

1.2

4303

2587

358

7415

3

1.5

7101

2605

417

7598

4

1.7

9111

2498

512

7412

5

1.8

9502

2788

419

8112

6

1.5

7105

2358

235

6625

7

1.8

10052

1988

265

5730

8

2.1

12513

1058

158

3089

9

2.3

14217

1187

254

3588

10

2.7

19221

825

487

2950

11

1.2

4339

2687

987

8655

12

0.8

1305

2350

857

7546

13

0.7

1198

2879

125

7901

14

1.5

7211

1987

847

6612

15

2.1

12589

897

254

2798

16

0.8

1121

2987

748

9731

17

1.8

9083

1578

547

5012

18

1.9

11041

1278

389

4021

19

1.6

8151

1380

587

4525

20

1.9

11051

1089

457

3605

9

Correlation matrix Car ownership Car ownership Household income Number of houses Number of worker Production

Household Number Number of Production income of houses worker

1 0.995135

1

-0.80885

-0.81603

-0.30011

-0.30901 0.240331

-0.81724

-0.82478

1 1

0.98193 0.409236

1

Commercial area attract trips in the morning and produce trip in the afternoon

10

Output Regression Regression Statistics Multiple R

0.99801829

R Square

0.996040507

Adjusted R Square Standard Error

0.995574685 141.4405503

Observations

20

ANOVA Df Regression

SS 2

MS

85552805.7 42776403

Residual

17 340092.2977 20005.43

Total

19

Coefficients

F

Significance F 2138.24 3.80133E-21

85892898

Standard Error 101.229828

t Stat

P-value

Lower 95% Upper 95%

-1.0056

0.328709 -315.3730381 111.78009

Intercept

-101.796472

X Variable 1

2.719828956 0.045600893

59.6442

3.45E-21 2.623619347 2.8160386

X Variable 2

1.594915849 0.136378382 11.69478

1.49E-09 1.307182213 1.8826495

R2 = 0.9956 → The model is very good

t-test Number for Houses is 59.64, Number of workers is 11.69 and the intercept is -1.0056 at 95% confident limit. t-test at degree of freedom 20 – 2 = 18 is 2.10 → the intercept is not significant. 11

t-Distribution

12

Regression Statistics Multiple R 0.997900286 R Square 0.995804981 Adjusted R 0.940016369 Square Standard 141.4846514 Error Observations 20 ANOVA df Regression Residual Total

SS

MS

F

Significance F 2 85532575.68 42766288 2136.40 3.82911E-21 2 18 360322.3185 20017.91 20 85892898

Coefficients

Intercept X Variable 1 X Variable 2

Standard t Stat P-value Lower 95% Upper 95% Error 0 #N/A #N/A #N/A #N/A #N/A 2.685964254 0.030756216 87.33078 4.13E- 2.621347791 2.7505807 25 1.539715572 0.124882111 12.32935 3.26E- 1.277347791 1.8020834 10

Trip Production = 2.6859 HH + 1.5397 Number of workers

Residential area produces trips in the morning and attracts trips in the afternoon

13

Category analysis Categorising land-use Type of land-use

Daily production

Link house

Morning peak production / hr 1.26

Semi-detached

1.46

16.37

Apartment

1.03

4.87

Low cost house

1.48

7.35

8.16

Source: Kementerian Kerja Raya

14

Trip Distribution Model Tij

Destination O R I G I N

j

1

2

3

n

1 2 3

T11 T21 T31

T12 T22 T32

T13 T23 T33

n

Tn1

Tn2

Tn3

Tnn

Pn

Tij

A1

A2

A3

An

W

i

Tij = Pi j

Tij = Aj i

 W = T = Pi = Aj i

j

i

j

15

( T11 + T12 + T13 + T14 + -- + T1n ) + ( T21 + T22 + T23 + T24 + -- + T2n ) + ( T31 + T32 + T33 + T34 + -- + T3n ) + …. + ( Tn1 + Tn2 + Tn3 + Tn4 + -- + Tnn ) = W

or P1 + P2 + P3 + P4 + P5 + ……. + Pn = W or A1 + A2 + A3 +A4 + A5 + ……….+ An = W

16

Matrix Balancing Production Attraction 560 1250 750 530 1105 430 545 540 450 1200 1040 500 4450 4450

1 2 3 4 5 6

1 2 3 4 157 67 54 68 211 89 72 91 310 132 107 134 153 65 53 66 126 54 43 55 292 124 100 126 1250 530 430 540

5 6 151 63 560 202 84 750 298 124 1105 147 61 545 121 51 450 280 117 1040 1200 500 4450

Production

Attraction

1250 x 1040 / 4450 = 292

1250 x 450 / 4450 = 126 17

Gravity Model m1 m2 F=G

D2

Pi Aj Tij = K f(Rij)

Traffic from one origin is distributed to all possible destinations

18

Gravity Model: Production Constrain

Tij = K j

Pi  Aj j

f(Rij)

Tij = Pi 1 Ki =  Aj / f(Rij) j

Aj / f(Rij) Tij = Pi  Aj / f(Rij) j

19

Gravity Model: Attraction Constrain

1 Kj =

 Pi / f(Rij) i

Pi / f(Rij) Tij = Aj

 Pi / f(Rij) i

Trips in on attraction are coming from all possible origins

20

Gravity Model : Double Constrain Pi Aj Tij = Ki Kj f(Rij) 1 Ki =

 Kj Aj / f(Rij) j

1 Kj =

 Ki Pi / f(Rij) i

21

Example Input : Trip Generation Zone Production Attraction 1 2 3 4 5 6 7

1100000 650000 542000 498000 510000 250000 325000 3875000

2600000 250000 210000 320000 210000 135000 150000 3875000

Output 1 : O-D Matrix Destination 1 1 2 3

Origin

738065 436129 363665

2

70968 41935 34968

3

59613 35226 29373

334142 32129 26988 5 342194 32903 27639 6 167742 16129 13548 7 218065 20968 17613 2600000 250000 210000 4

4

90839 53677 44759

5

59613 35226 29373

6

38323 22645 18883

7

42581 1100000 25161 650000 20981 542000

41125 26988 17350 19277 498000 42116 27639 17768 19742 510000 20645 13548 8710 9677 250000 26839 17613 11323 12581 325000 320000 210000 135000 150000 3875000

22

Output 2: Desire Line

Desire lines indicate future transport demand. The lines’ thickness are scaled to the trip interchanges between O-D pairs. The lines are very important to show visually where to propose future transport facilities.

23

Modal Split Model Decision Structure

All Trips Choice

Non-motorised

Motorised trip Choice

Public

Private Choice

Choice

Bus

Rail based

M / Cycle

Car

Use public transport or private car 24

To choose: Walking or ride a vehicle Distance (m) 100 150 200 250 300 350 400 450 500 600 700 800 900 1000

Share of trips by walking 0.95 0.92 0.88 0.83 0.77 0.7 0.61 0.5 0.39 0.27 0.17 0.09 0.06 0.04

Walking or bus 25

1

Share of trips by walking

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

200

400

600

800

1000

Distance (m)

Walking or boarding the bus?

26

1 P = 1+De

( Distance)

Calibration: ( 1 – P)/P = D e( Distance) ln [ (1-P)/P ] = ln D +  Distance

Y = mX + C

Linear regression analysis

27

Regression Statistics Multiple R 0.989694148 R Square 0.979494507 Adjusted R 0.977785716 Square Standard 0.292947102 Error Observations 14 ANOVA df Regression Residual Total

SS MS 1 49.1916 49.1916 12 1.02981 0.08582 13 50.2215

Coefficients Intercept X Variable 1

Standar t Stat d Error 2.920840037 0.14545 20.0808 -5.722665616 0.23902 -23.9418 4

ln D = 2.920840037 D = 18.5569

F 573.2091

P-value 1.33E-10 1.69E-11

Significance F 1.69E-11

Lower 95%

Upper 95% 2.603922 3.237758 -6.24345 -5.20188

 = -5.72266562

1 P =

1 + 18.5569 e(-5.72266562 Distance)

28

Stated preference Survey Methods for measuring non-market benefits Recall revealed preference

Guide line       

Minimize non-response Personal interviews Pretest for interviewer effects etc. Referendum format Provide adequate background info. Remind of substitute commodities Include & explain non-response option

29

Travel between Bangi and Putrajaya If there is an LRT service between Bangi and Putrajaya If LRT ticket is RM 2.90 for the journey and certain reduction in travel time if a traveller shift from bus to the proposed LRT: Bus fare LRT fare Reduction in % of bus travel time passengers shift to LRT 1 1.60 2.90 0 4.3% 2 1.60 2.90 5 6.9% 3 1.60 2.90 10 10.9% 4 1.60 2.90 15 16.7% 5 1.60 2.90 20 24.9% 6 1.60 2.90 25 35.3% 7 1.60 2.90 30 51.0% 8 1.60 2.90 40 75.0% If reduction in travel time is 20 minutes and the proposed LRT fare as follows: Bus fare LRT fare Reduction in % of bus travel time passengers shift to LRT 1 1.60 2.00 20 26.1% 2 1.60 2.25 20 25.9% 3 1.60 2.50 20 25.8% 4 1.60 2.75 20 25.6% 5 1.60 3.00 20 25.4% 6 1.60 3.25 20 25.3% 7 1.60 3.50 20 25.1% 8 1.60 3.75 20 25.0% 1 P =

1 + D e( Cost +  Time) 30

(1-P)/P

ln((1-P)/P) Fare

Reduction of differences travel time 3.09790129 1.30 0

1

22.15

2

13.46 2.599770506

1.30

5

3

8.18 2.101639722

1.30

10

4

4.97 1.603508939

1.30

15

5

3.02 1.105378155

1.30

20

6

1.84 0.607247371

1.30

25

7

0.96 -0.040005335

1.30

30

8

0.33 -1.098612289

1.30

40

1

2.83 1.040989873

0.40

20

2

2.86 1.049455984

0.65

20

3

2.88 1.057922096

0.90

20

4

2.90 1.066388207

1.15

20

5

2.93 1.074854319

1.40

20

6

2.95 1.083320431

1.65

20

7

2.98 1.091786542

1.90

20

8

3.00 1.100252654

2.15

20

X1

X2

31

Regression Statistics Multiple R 0.999739 R Square 0.999479 Adjusted R Square 0.999399 Standard Error 0.010826 Observations 16 ANOVA df Regression Residual Total

Intercept X Variable 1 X Variable 2

2 13 15

SS MS F 2.922473 1.46123629 12468.41 0.001524 0.00011720 2.923996

Standard Coefficients Error 1.741845 0.010741 0.145515 0.006679 -0.04766 0.000305

t Stat 162.17302 21.788274 -156.33184

P-value 7.02E-23 1.29E-11 1.13E-22

Significance F 4.57E-22

Lower 95% 1.718641 0.131087 -0.04832

Upper Lower Upper 95% 95.0% 95.0% 1.765048 1.718641 1.765048 0.159943 0.131087 0.159943 -0.047 -0.04832 -0.047

 = 0.145515 ,  = -0.04766 D = eksp(1.741845) = 5.707863.

1 P =

1 + D e( Cost +  Time)

32

Travel time value

1 P =

1 + D e( Cost +  Time)

Cost and time are two different dimensions

/ is considered a Transformation Factor to convert time into monitory value.

33

Trip Assignment Zone 1

Zone 2

Zone 3 Zone 5

Zone 4

Zone 1 Zone 1

Zone 2

Zone 3

Zone 4

Zone 5

200

150

300

350

250

50

120

180

220

Zone 2

450

Zone 3

550

600

Zone 4

290

310

420

Zone 5

370

410

530

70 610

34

Minimum path tree for zone 1

Zone 1

Zone 2

Zone 3 Zone 5

Zone 4 Minimum path tree from zone 1 to all other zones.

35

Volume = 200+150+300+350= 1000

Zon 1

Zone 2

Volume = 200+150+300= 350 Volume = 200 Volume = 150+300 = 450

Volume = 350

Zone 3

Zone 5 Volume = 300

Zone 4

Volume = 150

36