3-Trip Generation-Distribution ( Transportation and Traffic Engineering Dr. Sheriff El-Badawy )

1
‫والتكنولوجيا‬ ‫للهندسة‬ ‫العالي‬ ‫مصر‬ ‫معهد‬–‫المدنية‬ ‫الهندسة‬ ‫قسم‬-‫المنصورة‬
Dr. Sherif El-Badawy
3rd Year Civil
Transportation and Traffic
Engineering
Trip Generation/Trip Distribution

2
Trip Generation
Trip generation: is a model for the calculation of the
number of trips ends in given area .
Objectives:
• Understand the reasons behind the trip making
behavior.
• Produce mathematical relationships to represent trip-
making pattern on the basis of observed trips, land-
use data and household characteristics.
Trip Making
(Fricker, J. D. and Whitfor R. K. 2004)

3
Trips
Home Based
• 80% - 90%
• One end of the trip is
home
None-Home
Based
• 10% - 20%
• Neither end of the trip
is home
Trip ends are classified into Generations and Attractions
No. of Trip Generations = No. of Trip Attractions
Home Work Work Shop
Trip Purpose
Work
School
Shopping
Recreational - Social
Personal Business

4
Factors Govern Trip Generation
• Income
• Car ownership
• Family size and composition
• Land use characteristics
• Distance of the zone from the town center.
• Accessibility to public transport system and its
efficiency
• Employment opportunities
The general form of the equation obtained is:
Yp = a1X1 + a2X2 + a3X3, ...,anXn + U
Yp = number-of trips generated for specified purpose
X1, X2, X3,....... Xn= independent variables, for example,
land-use socio-economic factors etc.
a2 ,a3 ….. a0 = Regression Coefficients obtained by
linear regression analysis
U = Error term
Multiple Linear Regression Analysis
multiple regression analysis is used develop the prediction
equations for the trips generated by various types of
land use.

5
Dohuk City
27 total zones
20 residential zones
Based on Home interview surveys,
Trip attraction purposes were categorized into 5 types:
1) Home-Based Work (HBW)
2) Home-Based Education (HBED)
3) Home-Based Shopping (HBSH(
4) Home-Based Social (HBSO(
5) Home Based Other (HBO)

6
Zone # HBW No. of DU Area (km2
) Employment
Retail
Sales
Distance
to CBD
No. of
Schools
School
Enrollment
1 1289 995 0.155 1031 1221 0.4635 5 2020
2 866 640 0.415 700 1680 0.4697 3 1354
3 2954 1273 1.081 1728 1081 0.9159 9 1437
4 1864 1570 0.738 2179 1560 1.63 5 2123
5 293 262 0.172 108 888 0.64 3 1431
6 955 408 0.412 452 1128 0.42 4 1079
7 347 520 0.424 636 1104 1.27 5 1851
8 843 1200 0.384 746 1344 0.5 4 3243
9 1640 1120 0.251 960 1320 1 3 2653
10 1054 1550 0.33 1116 1416 0.52 5 2723
11 1100 700 0.411 800 1512 0.558 6 2475
12 908 1160 0.496 630 1632 0.7889 5 2023
13 551 583 1.113 331 1872 1.5 10 3121
14 1406 4505 2.553 3604 2136 2.95 13 4523
15 713 884 0.669 598 1896 2.65 4 1821
16 986 1744 0.637 1662 1704 1.75 4 2330
17 1985 1350 1.31 1826 1848 1.34 8 2411
18 2754 1600 1.117 1806 1800 1.63 12 3253
19 1367 550 0.523 523 1464 1.78 5 2056
20 302 1060 0.811 1060 1512 2.37 9 1983
Zone Characteristics
DU=Dwelling Units
W = work, H = home
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.77
R Square 0.59
Adjusted R Square 0.45
Standard Error 547.52
Observations 20
Coefficients
Intercept 740.2329848
X Variable 1 -0.92854194
X Variable 2 267.7267828
X Variable 3 1.429164322
X Variable 4 0.126868013
X Variable 5 -332.6795369

7
D
O
1 2 3 4
1 100 200 120
2 300 170 300
3 250 400 320
4 210 200 220
D
O
1 2 3 4 S P
1
2
3
4
SA
Present O/D Matrix Future O/D Matrix
Trip Distribution
Distribution of Trips between zones.
S P = No. of Trip Generations
S A = No. of Trip Attractions
Methods of Trip Distribution
1. Growth Factors Methods  Old
• Uniform factor method
• Average factor method
• Fratar method
• Furness method
2. Synthetic Methods  More Rational
• Gravity model
• Tanner model
• Intervening opportunities model
• Competing opportunities model

8
Assume that in the future the trip-making pattern will
remain substantially the same as today but that the volume
of trips will increase according to the growth of the
generating and attracting zones.
Advantages:
• Simpler than Synthetic Methods
• Good for small towns where considerable changes in
land-use and external factors are not expected
Growth Factors Methods
Uniform (Constant) Factor Method
The oldest growth factor method
Assumes that the growth factor (E) for the entire area is
constant.
E = Future number of trips ends / Base Year trip ends
Ti-j = ti-j x E
Ti-j = Future No. of Trips between Zones I, j
ti-j = Base Year No. of Trip between Zones I, j
E = Constant Growth Factor

9
D
O
1 2 3 ti Ti
1 60 100 200 360 360
2 100 20 300 420 1260
3 200 300 20 520 3120
Total 1300 4740
D
O
1 2 3
1 60 100 200
2 100 20 300
3 200 300 20
Example
If you were given that the
future trips generated in
zone 1, 2,3 are expected to
be 360, 1260 and 3120.
It is required to distribute the
future trips among the zones
D
1 2 3 ti Ti
O
1 219 365 729 1313 360
2 365 73 1094 1531 1260
3 729 1094 73 1896 3120
Total 4740 4740
D
O
1 2 3 ti Ti
1 60 100 200 360 360
2 100 20 300 420 1260
3 200 300 20 520 3120
Total 1300 4740

10
20
Average Factor Method
• A growth factor for each zone is calculated based on
the average growth factors calculated for both ends
of the trip.
• The factor represents the average growth associated
both with origin and destination zone.
Pi = future production (generation) of zone i,
pi = present production of zone i,
Aj = future attraction of zone j,
aj = present attraction of zone j.
Where Ei = Pi/pi and Ej = Aj/aj
21
D
O
1 2 3 Future
Production
1 100 200 6000
2 400 600 4000
3 500 300 3000
Future
Attraction 2000 1500 400 2000
Example
Note that this O/D matrix needs correction

11
22
D
O
1 2 3 pi Pi Ei
1 100 200 300 6000 20
2 400 600 1000 4000 4
3 500 300 800 3000 3.75
aj 900 400 800
Aj 2000 1500 400
Ej 2.22 3.75 0.5
Example
Ei = Pi/pi
Ej = Aj/aj
23
D
O
1 2 3 pi Pi Ei
1 1188 2050 3238 6000 1.853
2 1244 1350 2594 4000 1.542
3 1493 1125 2618 3000 1.146
aj 2738 2313 3400
Aj 2000 1500 400
Ej 0.73 0.65 0.12
Iteration one

12
24
D
O
1 2 3 pi Pi Ei
1 1486 2020 3506 6000 1.711
2 1414 1120 2534 4000 1.579
3 1401 1009 2410 3000 1.245
aj 2815 2495 3140
Aj 2000 1500 400
Ej 0.71 0.60 0.13
Iteration Two
25
D
O
1 2 3 pi Pi Ei
1 1718 1857 3575 6000 1.678
2 1618 955.4 2574 4000 1.554
3 1369 931.6 2301 3000 1.304
aj 2988 2649 2813
Aj 2000 1500 400
Ej 0.67 0.57 0.14
Iteration Three

13
26
D
O
1 2 3 pi Pi Ei
1 1928 1691 3618 6000 1.658
2 1799 810.4 2610 4000 1.533
3 1351 871 2222 3000 1.35
aj 3150 2799 2501
Aj 2000 1500 400
Ej 0.63 0.54 0.16
Iteration Four
The process is iterated using successive values of
p’i and a’j until:
• The growth factor approaches unity
• and the successive values of t’ij and tij are within
1 to 5 percent depending upon the accuracy
required in the trip distribution.
Average Factor Method

14
28
Criticism of Growth Factors Methods
• Present trip distribution matrix has to be obtained first.
• The error in the original data collected on specific zone
to zone movements gets magnified.
• None of the methods provide a measure of the
resistance to travel, they neglect the effect of change in
travel pattern by the construction of new facilities and
new network.
• Distance.
• Time.
• Cost.
• Generalized Cost.
Travel Resistance
Determine and Compare:
Short Travel ?????????????? Matrix
(Time-Distance-Cost-Generalized Cost)

15
A limiting value when reached the trip will not made.
• Specific Distance.
• Specific Time.
• Specific Cost.
• Specific Generalized Cost
Cut-off Value
22
2523 24 26
15
11
18
19
20 21
16
12
17
1
13
14
(4)
(4)
(2)
(2)
(2) (2)
(2) (2) (2)
(2)
(2)
(1)
(1)
(1)
(5)
(3)
(3)
(3)
(3)(3)
(5)
(5)
Example:
Least Travel Time from City Centroid
(3)

16
32
Starting from centroid 1 we go to each connecting link and
choose the least travel time
T1-20 = 3 T1-17 = 3
The time is the same , if we begin with the node with lower
number node 17 is noted:
T1-17-19 = 5 T1-17-16 = 5 T1-17-16 = 6
The next closest node to centroid 1 is 20
T1-20-19 = 4 T1-20-25 = 6 T1-20-21 = 7
There are two routes to reach 19 from centroid 1, i.e. 1-17-19
and 1-20-19. the rout 1-20-19 is shorter in time, therefore is
chosen
22
2523 24 26
15
11
18
19
20 21
16
12
17
1
13
14
(4)
(4)
(2)
(2)
(2) (2)
(2) (2) (2)
(2)
(2)
(1)
(1)
(1)
(5)
(3)
(3)
(3)
(3)(3)
(5)
(5)
• The process is repeated until all nodes have been covered by the
shortest path.
• The minimum path tree for this highway network is given in figure.
(3)

17
Incident matrix
OD
A B C D E F G H I Sum
A 1 0 0 0 0 0 0 0 1*
B 1 1 0 0 0 1 0 0 3
C 0 1 1 0 0 1 0 1 4
D 0 0 1 1 0 1 0 0 3
E 0 0 0 1 1 1 0 0 3
F 0 0 0 0 1 1 1 0 3
G 0 1 1 1 1 1 1 0 6*
H 0 0 0 0 0 1 1 1 3
I 0 0 1 0 0 0 0 1 2
Incident Matrix

18
Balancing Productions and Attractions
No. of Trip Generations (Productions) = No. of Trip Attractions
• However, they are often different since trip productions
and attractions are estimated separately.
• There is a greater degree of confidence in the
production models than the attraction models.
• The attractions are scaled to productions.
37
Balancing Attractions and Productions.
Example
Computed Productions and Attractions
Zone Productions Attractions
1 25 1000
2 125 350
3 350 500
4 800 100
5 600 250
Total 1900 2200

19
Balancing Attractions and Productions
solution
Adjusted Productions and
Attractions
1 25 864
2 125 302
3 350 432
4 800 86
5 600 216
Total 1900 1900
Computed Productions and
Attractions
1 25 1000
2 125 350
3 350 500
4 800 100
5 600 250
Total 1900 2200
40
Trip Distribution by Gravity Model
Where:
Ti-j = Trips between zones i and j
Pi = Trips produced in zone i
Aj = Trips attracted to zone j
di-j = Distance or Time or Cost between zones i and j
n = an exponential constant, usually between 1 and 3
K = constant

20
41
This formula can be expressed as follows
42
A small town consists of four areas A, B, C, D and two
industrial estates X and Y. generation equations show that,
for the design year in question, the trips from home to work
generated by each residential area per 24 hour day are as
follows:
There are:
3700 jobs in industrial state X
4500 jobs in industrial state Y.
1000A
2250B
1750C
3200D
Example

21
43
The attraction between zones is inversely proportional
to the square of the journey times between zones.
The journey times in minutes from home to work are:
YXZones
2015A
1015B
1010C
2015D
Calculate and tabulate the
inter-zonal trips for journeys
from home to work
Solution 1000A
2250B
1750C
3200D
YXZones
2015A
1015B
1010C
2015D
Production
Time
Total Attractions:
3700 jobs in X
4500 jobs in Y

22
In the same way we can get:
TB-X = 604, TB-Y = 1646, TC-X = 790, TC-Y = 960, TD-X = 1980
TD-Y = 1220
Ti-j for origin zones, A, B,
C, D, total production
YX
1000396604A
22501646604B
1750960790C
320012201980D
Total Attractions:
3700 jobs in X , 4500 jobs in Y
Ti-j for origin zones, A, B,
C, D, total production
YX
1000396604A
22501646604B
1750960790C
320012201980D
Total Attractions:
3700 jobs in X , 4500 jobs in Y
820045003700Total predicted
attraction Ai
820042223978Total calculated
Attraction, Ci

23
47
The calculated attractions are not balanced with the
predicted attractions so we use the following equation in
an iterative procedure to balance them:
for destination zones X and Y
Where:
Ajm = Adjusted attraction, iteration m
Aj = Desired attraction
Aj(m-1) = Attraction, iteration m-1
Cj(m-1) = Actual attraction, iteration m-1
For the second iteration m= 2
Aj2 for zone X =
Aj2 for zone Y=
Recalculating:
YX
396604A
1646604B
960790C
12201980D
42223978Calc.
Attr., Ci
45003700Pred.
Attr., Ai

24
49
In the same way we can get:
TB-X = 540
TB-Y = 1710
TC-X = 730
TC-Y = 1020
TD-X = 1790
TD-Y = 1410
The results are now closer and with a few more iterations
they can be much more closer to the predicted attractions
Ti-j for origin zones, A,
B, C, D, total production
YX
1000440560A
22501710540B
17501020730C
320014101790D
820045803620Total calculated
Attraction, Ci
820045003700Total predicted
attraction Ai

3-Trip Generation-Distribution ( Transportation and Traffic Engineering Dr. Sheriff El-Badawy )

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