Urban Transport

Transport ModellingRiza Atiq bin O.K. Rahmat

Four Steps Transport ModelTrip Generation

Trip Distribution

Modal Split

Trip Assignment

Trip Generation Model

Percentage of Home-based Trips

City Percentage Year

Baghdad 85.8 1980

Johannesburg 84.1 1980

Kuala Lumpur 80.5 1985

Kuala Lumpur Trip Purposes

Work Trips

Congestion in the morning

Trip Generation

f (Trip Production) =

Household income, household size, Car ownership, number of working person in the household

Socio-economic f (Trip Attraction) =

Land-use characteristic

Trip Generation

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

Trip Generation:Linear Regression Model

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

Linear Regression Model (cont ….)

•R2 = 1 - maximum correlation between Y and X •R2 = 0 - no correlation •t-statistic Regression parameter t = Standard error of the parameter

Trip Generation: Model development1. Observe any relationship between parameters

Non-linear relationship could be linearised

Trip Generation: Model development

2. Produce Correlation matrix – Observe correlation between independent variables

Car ownership Household income

Number of

houses

Number of worker

Production

Car ownership

1

Household income

0.995135 1

Number of houses

-0.80885 -0.81603 1

Number of worker

-0.30011 -0.30901 0.240331 1

Production

-0.81724 -0.82478 0.98193 0.409236 1

Trip Generation: Model development

• 3. Compute each of the parameters of the potential regression equations.

• 4. Check the following criteria:

– The model R2. – Sign convention (- / +) – Reasonable intercept – Are the regression parameters statistically

significant?

Trip Generation: Examplezone Car

ownershipHousehold

incomeNumber of

housesNumber of

workersDaily

production1 1.1 3555 2350 235 66552 1.2 4303 2587 358 74153 1.5 7101 2605 417 75984 1.7 9111 2498 512 74125 1.8 9502 2788 419 81126 1.5 7105 2358 235 66257 1.8 10052 1988 265 57308 2.1 12513 1058 158 30899 2.3 14217 1187 254 3588

10 2.7 19221 825 487 295011 1.2 4339 2687 987 865512 0.8 1305 2350 857 754613 0.7 1198 2879 125 790114 1.5 7211 1987 847 661215 2.1 12589 897 254 279816 0.8 1121 2987 748 973117 1.8 9083 1578 547 501218 1.9 11041 1278 389 402119 1.6 8151 1380 587 452520 1.9 11051 1089 457 3605

Trip Generation: Correlation Matrix Car ownership Household

incomeNumber

of housesNumber of

workerProduction

Car ownership

1

Household income

0.995135 1

Number of houses

-0.80885 -0.81603 1

Number of worker

-0.30011 -0.30901 0.240331 1

Production

-0.81724 -0.82478 0.98193 0.409236 1

Correlations between Production with Car Ownership and Household Income are negative which are illogical in real life situation. Therefore the two variable can be omitted from the model.

Trip Generation: Regression AnalysisRegression Statistics

Multiple R 0.99801829

R Square 0.996040507

Adjusted R Square

0.995574685

Standard Error 141.4405503

Observations 20

ANOVA

Df SS MS F Significance F

Regression 2 85552805.7 42776403 2138.24 3.80133E-21

Residual 17 340092.2977 20005.43

Total 19 85892898

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept -101.796472 101.229828 -1.0056 0.328709 -315.3730381 111.78009

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

t-test for the intercept is -1.0056 at 95% confident limit -> not significant > should be omitted

Trip Generation: Regression AnalysisRegression Statistics

Multiple R 0.997900286 R Square 0.995804981 Adjusted R Square

0.940016369

Standard Error 141.4846514 Observations 20

ANOVA

Df SS MS F Significance F Regression 2 85532575.68 42766288 2136.402 3.82911E-21 Residual 18 360322.3185 20017.91 Total 20 85892898

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 0 #N/A #N/A #N/A #N/A #N/AX Variable 1 2.685964254 0.030756216 87.33078 4.13E-25 2.621347791 2.7505807X Variable 2 1.539715572 0.124882111 12.32935 3.26E-10 1.277347791 1.8020834

The final model: Trip Production = 2.6859 HH + 1.5397 Number of workers

Trip Generation: Category analysis

• Categorising land-useType of land-use Morning peak

production / hrDaily production

Link house 1.26 8.16

Semi-detached 1.46 16.37

Apartment 1.03 4.87

Low cost house 1.48 7.35

(Source: Kemeterian Kerjaraya Malaysia)

Trip Distribution Model Destination Tij

j 1 2 3 n

ORIGIN

1 T11 T12 T13 2 T21 T22 T23 3 T31 T32 T33 n Tn1 Tn2 Tn3 Tnn Pn

Tij

i

A1 A2 A3 An W

iijj PT

jiji AT jjiiijji APWT

Trip Distribution Model • ( 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

Matrix Balancing

Production Attraction560 1250750 530

1105 430545 540450 1200

1040 5004450 4450

Must be equal

Matrix Balancing 1 2 3 4 5 6

1 157 67 54 68 151 63 560

2 211 89 72 91 202 84 750

3 310 132 107 134 298 124 11054 153 65 53 66 147 61 5455 126 54 43 55 121 51 4506 292 124 100 126 280 117 1040

1250 530 430 540 1200 500 4450

Attraction

1250 x 1040 /4450 = 292

1250 x 450 / 4450 = 126

Production

Gravity Model

221

D

mmGF

)( ij

jiij Rf

APKT

Pi = Production of zone iAj = Attraction of zone j

Gravity Model: Production Constrain

j ij

jji

ij Rf

AP

KT)(

)( ij

jiij Rf

APKT

j

iij PT

jijj RfA

K)(/

1

jijj

ijjiij RfA

RfAPT

)(/

)(/

Gravity Model: Attraction Constrain

iiji RfP

K)(/

1

iij

ijjij RfPi

RfPiAT

)(/

)(/

Gravity Model: Double Constrain

)( ij

jijiij Rf

APKKT

jijjj

i RfAKK

)(/

1

iijii

j RfPKK

)(/

1

To calculate Ki, give value to Kj as 1.0.Use the calculated value Ki to calculate Kj.Calculate Ki using the new calculated value of Kj. Repeat the calculation until value of Ki and Kj converge to a solution

Separation Function

TravelCostRf ij )(

f(Rij) = separation function between zone I and zone j

TraveltimeRf ij )(

TravelCostij eRf *)(

TravelTimeij eRf *)(

α is a parameter to be calibrated

Desire Line

• A visual presentation of OD matrix

Source: JICA, 1981

Klang Valley when NKVE, Shah Alam Highway, SKVE and MRR2 were planned

Modal Split Model

Decision Structure All Trips

Non-motorised Motorised trip

Public Private

Bus Rail based M / Cycle Car

Choice

Choice

Choice Choice

To choose: Walking or ride a vehicleDistance (m) Share of trips by walking

100 0.95

150 0.92

200 0.88

250 0.83

300 0.77

350 0.7

400 0.61

450 0.5

500 0.39

600 0.27

700 0.17

800 0.09

900 0.06

1000 0.04

Plot of Share of Trips by Walking

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Distance (m)

Sh

are

of

trip

s b

y w

alk

ing

Walking or boarding the bus?

Modelling the choice

ceDisDeP

tan*1

1

ceDiseDP

P tan**1

Calibration

ceDisDP

Ptan*ln)

1ln(

Y = C +mX (a linear regression problem)

Regression analysis

Stated preference Survey

• 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

Travel Between Bangi and PutrajayaIf 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, are you going to shift from bus to the proposed LRT?

Bus fare LRT fare Reduction in travel time % of bus passengers shift to LRT

1 1.60 2.90 0 12.5%

2 1.60 2.90 5 15.5%

3 1.60 2.90 10 19.0%

4 1.60 2.90 15 23.0%

5 1.60 2.90 20 27.0%

6 1.60 2.90 25 32.0%

7 1.60 2.90 30 38.0%

8 1.60 2.90 40 49.0%

If reduction in travel time is 20 minutes and the proposed LRT fare as follows:

Bus fare LRT fare Reduction in travel time % of bus passengers shift to LRT

1 1.60 2.00 20 30.1%

2 1.60 2.25 20 29.2%

3 1.60 2.50 20 28.7%

4 1.60 2.75 20 28.0%

5 1.60 3.00 20 27.1%

6 1.60 3.25 20 26.5%

7 1.60 3.50 20 25.7%

8 1.60 3.75 20 25.0%

ln((1-P)/P) Fare differences X1

Reduction of travel timeX2

1 1.94591 1.30 0

2 1.695912 1.30 5

3 1.45001 1.30 10

4 1.208311 1.30 15

5 0.994623 1.30 20

6 0.753772 1.30 25

7 0.489548 1.30 30

8 0.040005 1.30 40

1 0.84254 0.40 20

2 0.88569 0.65 20

3 0.909999 0.90 20

4 0.944462 1.15 20

5 0.989555 1.40 20

6 1.020141 1.65 20

7 1.06162 1.90 20

8 1.098612 2.15 20

Regression analysis

= 0.145515 , = -0.04766 and D = exp(1.741845) = 5.707863

)(1

1TimeCostDe

P

Travel Time Value

• Willingness to pay to safe travel time

• Cost and time are two different dimensions• / is considered a Transformation Factor to convert time

into monitory value.

)(1

1TimeCostDe

P

)*04766.0*145515.0(1

1TimeCostDe

P Value of time

= 0.04766 / 0.145515 RM/min= RM 19.65 / hr

Trip AssignmentZone 1 Zone 2

Zone 3Zone 5

Zone 4Zone 1 Zone 2 Zone 3 Zone 4 Zone 5

Zone 1 200 150 300 350

Zone 2 450 250 50 120

Zone 3 550 600 180 220

Zone 4 290 310 420 70

Zone 5 370 410 530 610

Minimum path tree for zone 1Zone 1 Zone 2

Zone 3Zone 5

Zone 4

Minimum path tree from zone 1 to all other zones.

Trip assignment from Zone 1

Zon 1

Zone 2

Zone 3Zone 5

Zone 4

Volume = 200+150+300+350= 1000Volume = 200+150+300= 350

Volume = 200

Volume = 150+300 = 450

Volume = 150

Volume = 300

Volume = 350