TRANSPORTATION ENGINEERING

AND PLANNING
(110401367)
SPRING 2019-2020

Lecture. No. 8
Trip Distribution

Dr. Hamza Alkuime

1

Topic 2 : Transportation planning

References
■ Nicholas Garber and Lester Hoel ,Traffic & Highway
Engineering, 5th Edition.. Cengage Learning, 2015
 Chapter 12 : Forecasting Travel Demand
 Section 11.4
■ Daniel J Findley, Christopher Cunningham, Bastian J.
Schroeder, Thomas H. Brown, Highway Engineering:
Planning, Design, and Operations, 2016, Elsevier
 Chapter 2.2: Planning concepts and Four-step process overview
2

2
 Topic 2 : Transportation planning
References
■ Nicholas Garber and Lester Hoel ,Principles of Highway
engineering and traffic analysis, 5th Edition, 2012
 Chapter 8 : Travel Demand and traffic forecasting
■ Partha chakroborty and Animesh Das, Principles of
transportation engineering, 2012,
 Chapter 9: Transportation demand analysis
■ Dušan Teodorović and Milan Janić,Transportation
engineering theory, practice and modeling , 2017,
 Chapter 8: Transportation demand analysis
3

Example

Study area
4

4
 Example
5
1

4
3

Zoning
5

Example
Attracted trips 5
1

The land use within

Zone 1 are 2

 120 office space

4
3
500 factory
50 educational seats
100 shopping center

6
 Example
How many trips are attracted (Ta) and produced to a zone 1?
Attracted (Ta) trips
Land use ( By Number of units Trip rates
(column 2 X column
survey) ( By survey) (manual)
3)

office space 120 1.18 472

factory 500 0.43 64.5

educational
50 1.2 108
seats

shopping center 100 2.1 630

Total attracted trips (Ta) 626

7

Example
Balanced Trip 5

Productions and 1

Attractions Ta= 620

6 Ta= 650

Tp= 250 Ta= 1200 Tp= 550

Balanced trips
Zone ID Tp= 800
Production Attraction 2

1 250 403 Ta= 560

2 320 364 Tp= 400
3 150 228 4
3
4 400 273 Tp= 320
5 550 423 Ta= 420
Ta= 350
6 800 780
Tp= 150
Total trips 2470 2470

8
 Review
Travel Forecasting Process
■ Four-step process”
 Trip generation
 How many trips
 Trip distribution
 From where to where
 Modal choice
 On what mode
 Traffic assignment
 On what route
9

Trip distribution

■ is a process by which the trips generated in one

zone are allocated to other zones in the study
area.
■ These trips may be
 Internal-internal
 within the study area
Internal-external
 between the study area and areas outside the study area
10

10
 Trip distribution

■ Goal
Where the trips are traveling
What affect the destination
 Time, distance, speed
■ Inputs
Trip generated within the study area and zones
■ Output
Origin- destination matrix
11

11

Trip distribution
Origin- destination matrix

12

12
 Example
Tp= 250
5

4
3

Trip distribution
13

13

Example
5

Ta= 620
1

4
3

Trip distribution
14

14
 Trip distribution
Methods
■ Gravity model
Preferred to be used because
 Simple and accurate
 Uses the attributes of the transportation system and land-use
characteristics
 Has been calibrated extensively for many urban areas

■ Growth factor models

■ Intervening opportunities
15

15

Gravity Model
Definition

■The number of trips between two zones is

directly proportional to the number of trip
attractions generated by the zone of destination
inversely proportional to a function of time of travel
between the two zones

16

16
 Gravity Model
Mathematically i is origin zone number
j is destination zone
n is total number of zones

■ Tij = number of trips that are produced in zone i and attracted to

zone j
■ Pi = total number of trips produced in zone i
■ Aj = number of trips attracted to zone j
The sum of Pi for all zones must equal the sum of Aj for all zone
■ Fij = a value which is an inverse function of travel time
■ Kij = socioeconomic adjustment factor for interchange ij
17

17

Gravity Model
Mathematically i is origin zone number
j is destination zone
n is total number of zones

■ Tij = number of trips that are produced in zone i and attracted to zone
j
Determined from trip generation step
■ Pi = total number of trips produced in zone i
■ Aj = number of trips attracted to zone j
The sum of Pi for all zones must equal the sum of Aj for all zone
■ Fij = a value which is an inverse function of travel time
■ Kij = socioeconomic adjustment factor for interchange ij
18

18
 Gravity Model
Mathematically i is origin zone number
j is destination zone
n is total number of zones

■ Pi = total number of trips produced in zone i

Determined from trip generation step
■ Aj = number of trips attracted to zone j
Determined from trip generation step
■ The sum of Pi for all zones must equal the sum of Aj for all zone
■ Fij = a value which is an inverse function of travel time
Determined by a calibrating process
19

19

Gravity Model
Mathematically

■ Fij = a value which is an inverse function of travel time

Determined by a calibrating process
■ Kij = socioeconomic adjustment factor for interchange ij
Determined by a calibrating process

20

20
 Gravity Model
Calibrating process
■ After each distribution process is completed,
 The percentage of trips in each trip length category produced by
the gravity model is compared with the percentage of trips
recorded in the O-D survey.
If the percentages do not agree, then
 The Fij factors that were used in the distribution process are
adjusted
 Another gravity model trip distribution is performed.
 The calibration process is continued until the trip length
percentages are in agreement

21

21

Trip distribution
F values for calibration

22

22
 Trip distribution
F values for calibration

23

23

Trip distribution
Example -1 (Example 12.4)
■ a study area consisting of three zone
■ Trip Productions and Attractions for a Three-Zone Study Area
 Determined from trip generation step ) are provided in Table 12.9
■ Average travel times between each zone
 Determined ( Table 12.10)

■Determine the number of zone-to-zone trips

through two iterations.
24

24
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -1: Trip Productions and Attractions for a Three-Zone
Study Area
Zone Balanced Trip
Production(Pi) Attraction (Aj)
1 140 300
2 330 270
3 280 180
Total 750 750
25

25

Example -1 (Example 12.4)

Use of Calibrated F Values and Iteration
■Step -2: Average travel times between each zone
Average travel time
Zone
Zone
1 2 3
1 5 2 3
2 2 6 6
3 3 6 5
Orange cells are internal-internal green cell are internal-external
26

26
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -3: Determination of F factors based on travel
time (Calibration process

Note that the book use another chart to

determine the f factors for the example

27

27

Example -1 (Example 12.4)

Use of Calibrated F Values and Iteration
■ Step -3: Determination of F factors based on travel
time (Calibration process
Travel
time 1 2 3 4 5 6 7 8
(Min)

f factor 82 52 50 41 39 26 20 13

Note that the book use another chart to determine the f factors for
the example 28

28
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -4: Determine f factor between zones
Travel time
1 2 3 4 5 6 7 8
(Min)
f factor 82 52 50 41 39 26 20 13

Average travel time F factor (Fij)

Zone Zone
Zone Zone
1 2 3 1 2 3
1 5 2 3 1 39 52 50
2 2 6 6 2 52 26 26
3 3 6 5 3 50 26 39
29

29

F factor (Fij) Balanced Trip

Zone (j) Zone
Zone (i) Production(Pi) Attraction (Aj)
1 2 3
1 140 300
1 39 52 50
2 330 270
2 52 26 26
3 280 180
3 50 26 39
Total 750 750

Kij =1 for all zones

Zone
Zone
1 2 3
1 1 1 1
2 1 1 1
i is origin zone number
3 1 1 1
j is destination zone number
n is total number of zones 30

30
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -5: Solve

31

31

Example -1 (Example 12.4)

Use of Calibrated F Values and Iteration
■ Step -5: Solve

32

32
 33

33

Example -1 (Example 12.4)

Use of Calibrated F Values and Iteration
■ Step -5: Solve

34

34
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -6: Adjusted attraction trip factors

35

35

Example -1 (Example 12.4)

Use of Calibrated F Values and Iteration
■ Step -6: Adjusted attraction trip factors

36

36
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -5: Adjusted attraction trip factors

37

37

Example -1 (Example 12.4)

Use of Calibrated F Values and Iteration
■ Step -5: Use the adjusted factors (iteration No.2)

38

38
 Example -1 (Example 12.4)
Use of Calibrated F Values and Iteration
■ Step -5: Use the adjusted factors (iteration No.2)

39

39

Example -2 (Example 12.5)

Selecting Singly or Doubly Constrained Gravity Model Results

40

40
 Example -2 (Example 12.5)
Selecting Singly or Doubly Constrained Gravity Model Results
■A three-zone system with 900 home-based
shopping productions
Zones 1 and 2 each generate 400 productions, while zone 3
generates 100 productions
■Each zone contains a shopping mall with 300
attractions

41

41

Example -2 (Example 12.5)

Selecting Singly or Doubly Constrained Gravity Model Results
■ F factors

The shopping mall in zone 1 can be easily reached due to the parking
availability and transit service.
 Thus, F11, F21, and F31 = 1.0
Parking costs at the shopping mall in zone 2 are moderate with some
transit service.
 Thus, F12, F22, and F32 = 0.5
Parking costs at the mall in zone 3 is high and transit service is
unavailable.
 Thus, F13, F23, and F33 = 0.2

42

42
 Example -2 (Example 12.5)
Selecting Singly or Doubly Constrained Gravity Model Results

43

43

Example -2 (Example 12.5)

Selecting Singly or Doubly Constrained Gravity Model Results

44

44
 Example -2 (Example 12.5)
Selecting Singly or Doubly Constrained Gravity Model Results

45

45

Example -2 (Example 12.5)

Selecting Singly or Doubly Constrained Gravity Model Results

46

46
 Growth Factor Models

■ This model is used when the available data is only

T he origins and destinations between each zone for the current or base year
The trip generation values for each zone for the future year
■ These models are used primarily to distribute trips between zones
in the study area and zones in cities external to the study area.
■ cannot be used to forecast traffic between zones where no traffic
currently exists.
■ the only measure of travel friction is the amount of current travel.
■ cannot reflect changes in travel time between zones, as does the
gravity mod
47

47

Growth Factor Models

■These models are used primarily to distribute

trips between zones in the study area and zones
in cities external to the study area.
■This model is used when the available data is only
The origins and destinations between each zone for the
current or base year
The trip generation values for each zone for the future year
48

48
 Growth Factor Models

■ Cannot be used to forecast traffic between zones

where no traffic currently exists.
■ The only measure of travel friction is the amount of
current travel.
■ Cannot reflect changes in travel time between
zones, as does the gravity model
■ The most popular growth factor model is the Fratar
method
49

49

Growth Factor Models

Fratar method
■is a mathematical formula that proportions future
trip generation estimates to each zone as a
function of
 The product of the current trips between the two zones Tij
The growth factor of the attracting zone Gj

50

50
 Growth Factor Models
Fratar method

■ Tij = number of trips estimated from zone i to zone j

■ tij = present trip generation in zone i
i is origin zone number
■ Gi = growth factor of zone i j is destination zone number
■ Gj = growth factor of zone j
x are all zones in the study area
■ Gx = growth factor of zone x except the origin zone i
■ Ti = ti Gi = future trip generation in zone i
■ tix = number of trips between zone i and other zones x
■ tij = present trips between zone i and zone j

51

51

Example 12.6
Forecasting Trips Using the Fratar Model

52

52
 Example 12.6
Forecasting Trips Using the Fratar Model
■ A study area consists of four zones (A, B, C, and D).
■ An O-D survey indicates that the number of trips between each zone is
as shown in Table 12.17.
■ Planning estimates for the area indicate that in five years the number
of trips in each zone will increase
by the growth factor shown in Table 12.18 on page 612
■ That trip generation will be increased to the amounts shown in the last
column of the table 12.18
■ Determine the number of trips between each zone for future
conditions.

53

53

Example 12.6
Forecasting Trips Using the Fratar Model
■Present Trips between Zone

54

54
 Example 12.6
Forecasting Trips Using the Fratar Model
■Present Trip Generation and Growth Factors

55

55

Present Trip between zone i and zone j ( tij ) Present Trip Generation and Growth Factors
Zone (j) Zone Present
Zone (i) Trip Trip Generation
A B C D Generation Growth in
(Trips/ day) factor Five Years
A - 400 100 100 ( Ti ) ( Gj ) (= column 2 X
B 400 - 300 - column 3)
C 100 300 - 300 = 1.2*600)
A 600 1.2 720
D 100 - 300 - B 700 1.1 770
Total 600 700 700 400 C 700 1.4 980
D 400 1.3 520

i is origin zone number

j is destination zone number

x are all zones in the study area

except the origin zone i

56

56
 Example 12.6
Forecasting Trips Using the Fratar Model

57

57

58

58
 59

59

60

60
 61

61

62

62
 Example 12.6
Forecasting Trips Using the Fratar Model

63

63

Example 12.6
Forecasting Trips Using the Fratar Model

64

64
 Example
5
1

6 Ta= 650
Ta= 620

Tp= 250 Ta= 1200 Tp= 550

Tp= 800
2

Ta= 560
Distination zone Tp= 400
Origin Compute
Given P 4
zone 1 2 3 4 5 6 3 dp
Tp= 320
1 63 20 20 35 62 50 250 250
Ta= 420
2 41 22 63 50 80 64 Ta= 350
320 320
3 18 22 26 60 14 10 150 150
4 40 70 60 90 60 80 T400
p= 150 400
5 63 80 60 100 137 110 550 550
6 90 80 180 150 140 160 800 800

65