Source: NHI course on Travel Demand Forecasting, Ch. 6 (152054A)

Trip Distribution

Objectives

• Describe inputs and outputs to gravity model

• Explain concept of friction factors• Explain how friction factors are

obtained• Apply gravity model to sample

data set

Terminology

• Friction factor• Gravity model• K-factors• Trip Distribution

Key concepts

• Trip distribution is a method to determine where trips are going from and to

• Trip interchange, or OD• “match up” the

productions and attractions• Calibrate to reflect current

travel patterns• Apply (aka evaluate) to

forecast future travel patterns

Calculating TAZ “Attractiveness”

Gravity Model

K-Factors

• K-factors account for socioeconomic linkages not accounted for by the gravity model

• Common application is for blue-collar workers living near white collar jobs (can you think of another way to do it?)

• K-factors are i-j TAZ specific (but could use a lookup table – how?)

• If i-j pair has too many trips, use K-factor less than 1.0 (& visa-versa)

• Once calibrated, keep constant? for forecast (any problems here???)

• Use dumb K-factors sparingly• Can you design a “smart” k factor? (TTYP)

Example Problem

Input data

How do models compute this? See next pages…

Does this table need to be

symmetrical? Is it usually?

Convert Travel Times into Friction Factors

Yes, but how

did we get

these?

1 2 3 4

5 6 7 8

9 10 11 12

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631

232

334

444

132 1

132 1

242 1

Find the shortest path from node to all other nodes (from Garber and Hoel)1

Yellow numbers represent link travel times in minutes3

Here’s how

…

1 2 3 4

5 6 7 8

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14 15 1613

631

232

334

444

132 1

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242 1

STEP 11

2

1 2 3 4

5 6 7 8

9 10 11 12

14 15 1613

631

232

334

444

132 1

132 1

242 1

STEP 21

2

4

5

1 2 3 4

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631

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STEP 31

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5

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4

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631

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STEP 41

2

4

4

Eliminate

5 >= 4

4

5

1 2 3 4

5 6 7 8

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631

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334

444

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242 1

STEP 51

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4

4 10

6

1 2 3 4

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132 1

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STEP 61

2

4

4

4 10

6

7Eliminate

7 >= 6

7

6

1 2 3 4

5 6 7 8

9 10 11 12

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631

232

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132 1

132 1

242 1

STEP 71

2

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4

4 10

6

Eliminate8 >= 7

8

7

7

8

6

1 2 3 4

5 6 7 8

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631

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334

444

132 1

132 1

242 1

STEP 81

2

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4

4 10

7

6

10

7

8

6

1 2 3 4

5 6 7 8

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132 1

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STEP 91

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4

4 10

7

6

10

7

8

6

1 2 3 4

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14 15 1613

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132 1

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STEP 101

2

4

4

4 10

7

6

10Eliminate

10 >= 7

10

Eliminate

10 >= 10

7

8

6

1 2 3 4

5 6 7 8

9 10 11 12

14 15 1613

631

232

334

444

132 1

132 1

242 1

STEP 111

2

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4

4 10

7

6

10

10

8

7

8

6

1 2 3 4

5 6 7 8

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132 1

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STEP 121

2

4

4

4 10

7

6

10

8

9

910

Eliminate 10 > 9

Eliminate

10 >= 9

7

8

6

1 2 3 4

5 6 7 8

9 10 11 12

14 15 1613

631

232

334

444

132 1

132 1

242 1

STEP 131

2

4

4

4

7

6

10

8

9

9

12 12

Eliminate

12 >= 10

7

8

6

1 2 3 4

5 6 7 8

9 10 11 12

14 15 1613

631

232

334

444

132 1

132 1

242 1

STEP 141

2

4

4

4

7

6

10

8

9

9

12 10

Eliminate

12 >= 10

7

8

6

1 2 3 4

5 6 7 8

9 10 11 12

14 15 1613

FINAL1

2

4

4

4

7

6

10

8

9

9

10

Calculate the Attractiveness of Each Zone

Calculate the Relative Attractiveness of Each

Zone

Make sense

?

Distribute Productions to TAZs

First Iteration Distribution

Comparing and Adjusting Zonal Attractions

• Balanced attractions from trip generation = 76

• The gravity model estimated more attractions to TAZ 3 than estimated by the trip generation model.

• What can we do? (see homework)

Forecasting for Future Year Assignments

• After successful base year calibration and validation (review … how?)

• Use forecast land use, socioeconomic data, system changes

• Forecasted production and attractions, and future year travel time skims

• Apply gravity model to forecast year• Friction factors remain constant over

time (what to you think?)

In-class exercise