Transportation Planning Asian Institute of Technology Trip Distribution 1 Transportation Planning Asian Institute of Technology

Contents Input and Output for Trip Distribution Model Types of Trip Distribution Model Uniform Growth Factor Model Average Factor Model Detroit Growth Model Fratar Growth Model

Input and Output for Trip Distribution Model Production, Pi Attraction, Aj Trip Costs (Out-of-pocket, distance, convenience) Output Trip Matrix

Types of Trip Distribution Model Growth Factor Method Uniform Growth Average Factor Detroit Model Fratar Model Single Constrain Double Constrain Theory Based Method Gravity Model Intervening Opportunity Model Wilson’s Entropy

Uniform Growth Factor Model Trip growth factor equals to the ratio of the total projected trips to the total existing trips. Trip between any given O-D in the study area uses the same growth factor. Disadvantages Land use in each subarea does not change at the average rate. The actual growth is not constant, but changes with time.

Uniform Growth Factor Model Example 1 1 2 4 3 1 2 3 4 SPi 12 10 18 40 14 6 32 38 SAj 148 SSTij 280

Uniform Growth Factor Model 1 2 3 4 SPi 23 19 34 76 26 11 60 72 SAj 280 1 2 3 4 SPi 12 10 18 40 14 6 32 38 SAj 148

Average Factor Model Trip growth factor equals to the ratio of the total projected trips to the total existing trips. Trips between O-D in the study area use average growth factor between production and attraction. kth iteration Disadvantages Factors do not indicate actual growth. Calculation may need a large number of iterations

Average Factor Model Example 2 1 2 3 4 SPi 12 10 18 40 14 6 32 38 SAj 12 10 18 40 14 6 32 38 SAj 148 SPi 80 48 114 38 280 SAj 80 48 114 38 280

Average Factor Model Iteration 1 1 2 3 4 SPi 12 10 18 40 14 6 32 38 12 10 18 40 14 6 32 38 SAj 148 SPi* 80 48 114 38 280 Fi 2 1.5 3 1 SAj* 80 48 114 38 280 Fj 2 1.5 3 1

Average Factor Model Iteration 2 1 2 3 4 SPi 21 25 27 73 31.5 7.5 60 21 25 27 73 31.5 7.5 60 28 84.5 62.5 SAj 280 SPi* 80 48 114 38 280 Fi 1.096 0.800 1.349 0.608 SAj* 80 48 114 38 280 Fj 1.096 0.800 1.349 0.608

Average Factor Model Iteration 3 1 2 3 4 SPi 19.91 30.56 23.00 73.47 19.91 30.56 23.00 73.47 33.85 5.28 59.04 27.40 91.81 55.68 SAj 280 SPi* 80 48 114 38 280 Fi 1.089 0.813 1.242 0.682 SAj* 80 48 114 38 280 Fj 1.089 0.813 1.242 0.682

Average Factor Model Iteration 25 1 2 3 4 SPi 12 56 80 34 48 24 114 38 12 56 80 34 48 24 114 38 SAj 280 SPi* 80 48 114 38 280 SAj* 80 48 114 38 280

Detroit Growth Model Ensuing development from average growth model Considers both subarea growth and total growth. kth iteration

Detroit Growth Model Example 3 1 2 3 4 SPi 12 10 18 40 14 6 32 38 SAj 12 10 18 40 14 6 32 38 SAj 148 SPi* 80 48 114 38 280 SAj* 80 48 114 38 280

Detroit Growth Model Iteration 1 1 2 3 4 SPi 12 10 18 40 14 6 32 38 12 10 18 40 14 6 32 38 SAj 148 SPi* 80 48 114 38 280 Fi 2 1.5 3 1 SAj* 80 48 114 38 280 F = 1.892 Fj 2 1.5 3 1

Detroit Growth Model Iteration 2 1 2 3 4 SPi 19.03 31.71 69.77 33.30 19.03 31.71 69.77 33.30 4.76 57.09 22.20 87.21 45.99 SAj 260.06 SPi* 80 48 114 38 280 Fi 1.147 0.841 1.307 0.826 SAj* 80 48 114 38 280 F = 1.077 Fj 1.147 0.841 1.307 0.826

Detroit Growth Model Iteration 3 1 2 3 4 SPi 19.91 30.56 23.00 77.93 19.91 30.56 23.00 77.93 33.85 5.28 54.10 27.40 100.41 42.09 SAj 274.53 SPi* 80 48 114 38 280 Fi 1.027 0.887 1.135 0.903 SAj* 80 48 114 38 280 F = 1.020 Fj 1.027 0.887 1.135 0.903

Detroit Growth Model Iteration 11 1 2 3 4 SPi 12 56 80 34 48 24 114 38 12 56 80 34 48 24 114 38 SAj 280 SPi* 80 48 114 38 280 SAj* 80 48 114 38 280

Fratar Growth Model Trips from i to j vary with Trips from i to j Productioin from zone i (Pi) Growth factor of TAZ (F) Location Factor (L) Trips from i to j where Disadvantages Complex calculation Does not tak into account accessibility

Fratar Growth Model Example 4 Find Fi and Fj 1 2 4 3 1 2 3 4 SPi 12 10 12 10 18 40 14 6 32 38 SAj 148 SPi* 80 48 114 38 280 Fi 2 1.5 3 1 SAj* 80 48 114 38 280 Fj 2 1.5 3 1

Fratar Growth Model Iteration 1: Find Li (i = j; Li = Lj) Li/Lj 1 2 3 4 - 0.6061/0.4444 0.6061/0.6909 0.6061/0.4368 0.4444/0.6061 0.4444/0.6909 0.4444/0.4368 0.6909/0.6061 0.6909/0.4444 0.6909/0.4368 0.4368/0.6061 0.4368/0.4444 0.4368/0.6909

Fratar Growth Model 1 2 3 4 SPi 0.00 18.91 38.91 18.77 76.59 35.76 3.97 58.64 23.68 98.35 46.42 SAj 280 SPi* 80 48 114 38 280 Fi 1.0445 0.8186 1.1591 SAj* 80 48 114 38 280 Fj 1.0445 0.8186 1.1591

Fratar Growth Model Iteration 9 1 2 3 4 SPi 12 56 80 34 48 24 114 38 12 56 80 34 48 24 114 38 SAj 280 SPi* 80 48 114 38 280 SAj* 80 48 114 38 280

Assignment #5 District A is divided into 4 TAZs. It is expected that there will be different economic growth by area in the next ten years after a new town plan. This results in production and attraction as shown in the following table: Determine future OD trip matrix using Uniform Growth Factor, Average Growth Factor and Fratar Models. 1 2 3 4 SPi SPi, 2023 20 44 16 80 90 36 14 70 110 100 140 50 60 SAj 300 SAj , 2023 130 120 400

Gravity Model Derived from Newton’s gravity model Trips between i and j Tij = trips from i to j Pi = Production from i Aj = Attraction by j f(cij) = “generalized cost function” or “deterrence function” cij = trip costs (usually in form of distance)

Travel Cost Function Exponential function Power function Combined function

Model Calibration Non-constrained Method Production-constrained Method Attraction-constrained Method Double-constrained Method

Non-constrained Model When total trips are not constrained Tij = trips from i to j

Non-constrained Model Example 5: Observed trips between zones are as follows: and distances bewteen zones are Zone 1 2 3 SPi 150 60 210 130 120 250 70 190 SAi 200 270 180 650 Zone 1 2 3 7 5

Non-constrained Model Average travel distance Distance, ci km. Frequency, fi fici 3 280 840 5 240 1200 7 130 910 Total 650 2950