04 transport modelling

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

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04 transport modelling

  1. 1. Urban TransportTransport Modelling Riza Atiq bin O.K. Rahmat
  2. 2. Four Steps Transport Model Trip Generation Trip Distribution Modal Split Trip Assignment
  3. 3. Trip Generation Model
  4. 4. Percentage of Home-based Trips City Percentage Year Baghdad 85.8 1980 Johannesburg 84.1 1980 Kuala Lumpur 80.5 1985
  5. 5. Kuala Lumpur Trip Purposes
  6. 6. Work TripsCongestion in the morning
  7. 7. Trip Generationf (Trip Production) = Household income, household size, Car ownership, number of working person in the household Socio-economicf (Trip Attraction) = Land-use characteristic
  8. 8. Trip GenerationTi = 880 + 0.115Aoffice + 0.145Ashopping +0.0367Amanufacturing
  9. 9. Trip Generation: Linear Regression ModelThe best line – the line that minimise D1 + D2 + D3 + ... + D7
  10. 10. 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
  11. 11. Trip Generation: Model development1. Observe any relationship between parameters Non-linear relationship could be linearised
  12. 12. Trip Generation: Model development2. Produce Correlation matrix – Observecorrelation 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
  13. 13. 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?
  14. 14. Trip Generation: Examplezone Car Household Number of Number of Daily ownership income houses workers 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 358810 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
  15. 15. Trip Generation: Correlation Matrix Car ownership Household Number Number of Production income of houses workerCar 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.
  16. 16. 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 1.8826495t-test for the intercept is -1.0056 at 95% confident limit -> not significant > should be omitted
  17. 17. Trip Generation: Regression Analysis Regression StatisticsMultiple R 0.997900286R Square 0.995804981Adjusted R 0.940016369SquareStandard Error 141.4846514Observations 20ANOVA Df SS MS F Significance FRegression 2 85532575.68 42766288 2136.402 3.82911E-21Residual 18 360322.3185 20017.91Total 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
  18. 18. 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)
  19. 19. Trip Distribution Model Destination ΣTij 1 2 3 n j 1 T11 T12 T13 2 T21 T22 T23O 3 T31 T32 T33RIGIN n Tn1 Tn2 Tn3 Tnn Pn ΣTij A1 A2 A3 An W iΣ jTij = Pi Σ i Σ jTij = W = Σ i Pi = Σ j A jΣ iTij = A j
  20. 20. 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
  21. 21. Matrix BalancingProduction Attraction 560 1250 750 530 1105 430 545 540 450 1200 1040 500 4450 4450 Must be equal
  22. 22. Matrix Balancing 1 2 3 4 5 61 157 67 54 68 151 63 5602 211 89 72 91 202 84 7503 310 132 107 134 298 124 11054 153 65 53 66 147 61 545 Production5 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
  23. 23. Gravity Model m1m2 F =G 2 D Pi A j Tij = K f ( Rij ) Pi = Production of zone i Aj = Attraction of zone j
  24. 24. Gravity Model: Production Constrain Pi A jTij = 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 )
  25. 25. Gravity Model: Attraction Constrain 1 K= ∑ Pi / f ( Rij ) i Pi / f ( Rij )Tij = A j ∑ Pi / f ( R ) i ij
  26. 26. Gravity Model: Double Constrain Pi A jTij = 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
  27. 27. Separation Function f(Rij) = separation function between zone I and zone jf ( Rij ) = TravelCost α α is a parameter to be calibrated αf ( Rij ) = Traveltimef ( Rij ) = eα *TravelCostf ( Rij ) = eα *TravelTime
  28. 28. Desire Line• A visual presentation of OD matrix Source: JICA, 1981 Klang Valley when NKVE, Shah Alam Highway, SKVE and MRR2 were planned
  29. 29. Modal Split ModelDecision Structure All Trips Choice Non-motorised Motorised trip Choice Public Private Choice Choice Bus Rail based M / Cycle Car
  30. 30. 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
  31. 31. Plot of Share of Trips by Walking 1 0.9 0.8Share 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)
  32. 32. Modelling the choice 1 P= 1 + Deα *Dis tan ceCalibration 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)
  33. 33. Regression analysis
  34. 34. 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
  35. 35. Travel Between Bangi and Putrajaya If there is an LRT service between Bangi and PutrajayaIf 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%
  36. 36. ln((1-P)/P) Fare differences Reduction of travel time X1 X21 1.94591 1.30 02 1.695912 1.30 53 1.45001 1.30 104 1.208311 1.30 155 0.994623 1.30 206 0.753772 1.30 257 0.489548 1.30 308 0.040005 1.30 401 0.84254 0.40 202 0.88569 0.65 203 0.909999 0.90 204 0.944462 1.15 205 0.989555 1.40 206 1.020141 1.65 207 1.06162 1.90 208 1.098612 2.15 20
  37. 37. Regression analysis 1 P= 1 + De (αCost + βTime )α = 0.145515 , β = -0.04766and D = exp(1.741845) = 5.707863
  38. 38. 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
  39. 39. Trip Assignment Zone 1 Zone 2 Zone 3Zone 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
  40. 40. Minimum path tree for zone 1 Zone 1 Zone 2 Zone 3Zone 5 Zone 4 Minimum path tree from zone 1 to all other zones.
  41. 41. Trip assignment from Zone 1 Volume = Volume = 200+150+300+350= 1000 200+150+300= 350 Zon Zone 2 1 Volume = 200 Volume = 150+300Volume = = 450350 Zone 3 Zone 5 Volume = 300 Volume = Zone 4 150

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