Slides for urban transport course: http://www.eng.ukm.my/riza/UrbanTransport/UrbanTransport.htm

1. Urban Transport
Transport Modelling
Riza Atiq bin O.K. Rahmat

2. Four Steps Transport Model
Trip Generation
Trip Distribution
Modal Split
Trip Assignment

4. Trip Generation Model

5. Percentage of Home-based Trips
City Percentage Year
Baghdad 85.8 1980
Johannesburg 84.1 1980
Kuala Lumpur 80.5 1985

6. Kuala Lumpur Trip Purposes

7. Work Trips
Congestion in the morning

8. 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

9. Trip Generation
Ti = 880 + 0.115Aoffice + 0.145Ashopping +
0.0367Amanufacturing

10. Trip Generation:
Linear Regression Model
The best line – the line that minimise D1 + D2 + D3 + ... + D7

11. 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

12. Trip Generation: Model development
1. Observe any relationship between parameters
Non-linear relationship could be linearised

13. Trip Generation: Model development
2. Produce Correlation matrix – Observe
correlation between independent variables
Car ownership Household Number Number Production
income of of worker
houses
Car ownership 1
Household 0.995135 1
income
Number of -0.80885 -0.81603 1
houses
Number of -0.30011 -0.30901 0.240331 1
worker
Production -0.81724 -0.82478 0.98193 0.409236 1

14. 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?

15. Trip Generation: Example
zone Car Household Number of Number of Daily
ownership income houses workers production
1 1.1 3555 2350 235 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

16. Trip Generation: Correlation Matrix
Car ownership Household Number Number of Production
income of houses worker
Car ownership 1
Household 0.995135 1
income
Number of -0.80885 -0.81603 1
houses
Number of -0.30011 -0.30901 0.240331 1
worker
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.

17. Trip Generation: Regression Analysis
Regression Statistics
Multiple R 0.99801829
R Square 0.996040507
Adjusted R 0.995574685
Square
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

18. Trip Generation: Regression Analysis
Regression Statistics
Multiple R 0.997900286
R Square 0.995804981
Adjusted R 0.940016369
Square
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/A
X Variable 1 2.685964254 0.030756216 87.33078 4.13E-25 2.621347791 2.7505807
X 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

19. Trip Generation: Category analysis
• Categorising land-use
Type of land-use Morning peak Daily production
production / hr
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)

20. Trip Distribution Model
Destination ΣTij
1 2 3 n j
1 T11 T12 T13
2 T21 T22 T23
O 3 T31 T32 T33
R
I
G
I
N
n Tn1 Tn2 Tn3 Tnn Pn
ΣTij A1 A2 A3 An W
i
Σ jTij = Pi
Σ i Σ jTij = W = Σ i Pi = Σ j A j
Σ iTij = A j

21. 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

22. Matrix Balancing
Production Attraction
560 1250
750 530
1105 430
545 540
450 1200
1040 500
4450 4450
Must be equal

23. 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 1105
4 153 65 53 66 147 61 545 Production
5 126 54 43 55 121 51 450
6 292 124 100 126 280 117 1040
1250 530 430 540 1200 500 4450
Attraction
1250 x 1040 /4450 = 292
1250 x 450 / 4450 = 126

24. Gravity Model
m1m2
F =G 2
D
Pi A j
Tij = K
f ( Rij )
Pi = Production of zone i
Aj = Attraction of zone j

25. Gravity Model:
Production Constrain
Pi A j
Tij = K Pi ∑ A j
f ( Rij )
∑ Tij = K
j
j
f ( Rij )
∑T j
ij = Pi
1
K=
A j / f ( Rij ) ∑ Aj / f ( Rij )
Tij = Pi j
∑A
j
j / f ( Rij )

26. Gravity Model:
Attraction Constrain
1
K=
∑ Pi / f ( Rij )
i
Pi / f ( Rij )
Tij = A j
∑ Pi / f ( R )
i
ij

27. Gravity Model:
Double Constrain
Pi A j
Tij = K i K j
f ( Rij )
1 To calculate Ki, give value to Kj as 1.0.
Ki =
∑ K j Aj / f ( Rij )
Use the calculated value Ki to calculate Kj.
Calculate Ki using the new calculated
j
value of Kj. Repeat the calculation until
1 value of Ki and Kj converge to a solution
Kj =
∑ K i Pi / f ( Rij )
i

28. Separation Function
f(Rij) = separation function between zone I and zone j
f ( Rij ) = TravelCost α α is a parameter to be calibrated
α
f ( Rij ) = Traveltime
f ( Rij ) = eα *TravelCost
f ( Rij ) = eα *TravelTime

29. Desire Line
• A visual presentation of OD matrix
Source: JICA, 1981
Klang Valley when NKVE, Shah Alam Highway, SKVE and MRR2 were planned

30. Modal Split Model
Decision Structure All Trips
Choice
Non-motorised Motorised trip
Choice
Public Private
Choice Choice
Bus Rail based M / Cycle Car

31. To choose: Walking or ride a vehicle
Distance (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

32. Plot of Share of Trips by Walking
1
0.9
0.8
Share of trips by walking
0.7
0.6
0.5
0.4
0.3
0.2 Walking or boarding the
0.1 bus?
0
0 200 400 600 800 1000
Distance (m)

33. Modelling the choice
1
P=
1 + Deα *Dis tan ce
Calibration
1− P
= D * eα *Dis tan ce
P
1− P
ln( ) = ln D + α * Dis tan ce
P
Y = C +mX (a linear regression problem)

34. Regression analysis

35. 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

36. 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, 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%

37. ln((1-P)/P) Fare differences Reduction of travel time
X1 X2
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

38. Regression analysis
1
P=
1 + De (αCost + βTime )
α = 0.145515 , β = -0.04766
and D = exp(1.741845) = 5.707863

39. Travel Time Value
• Willingness to pay to safe travel time
1
P=
1 + De (αCost + βTime )
• Cost and time are two different dimensions
• β/α is considered a Transformation Factor to convert time
into monitory value.
1
P= ( 0.145515*Cost + 0.04766*Time ) Value of time
1 + De = 0.04766 / 0.145515 RM/min
= RM 19.65 / hr

40. Trip Assignment
Zone 1 Zone 2
Zone 3
Zone 5
Zone 4
Zone 1 Zone 2 Zone 3 Zone 4 Zone 5
Zone 1 200 150 300 350
Zone 2 250 50 120
Zone 3 550 600 180 220
Zone 4 290 310 420 70
Zone 5 370 410 530 610

41. 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.

42. Trip assignment from Zone 1
Volume =
Volume = 200+150+300+350= 1000
200+150+300=
350
Zon Zone 2
1 Volume =
200
Volume = 150+300
Volume = = 450
350
Zone 3
Zone 5
Volume =
300
Volume =
Zone 4 150