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
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