3 trip generation-distribution ( Transportation and Traffic Engineering Dr. Sheriff El-Badawy )

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المنصورة-قسم الهندسة المدنية –معهد مصر العالي للهندسة والتكنولوجيا

Dr. Sherif El-Badawy

3rd Year Civil

Transportation and Traffic

Engineering

Trip Generation/Trip Distribution


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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)

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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 WorkWork Shop


Trip Purpose

Work

School

Shopping

Recreational - Social

Personal Business

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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.

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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)

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Zone # HBW No. of DU Area (km2) EmploymentRetail

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


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D

O1 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 DistributionDistribution 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

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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 MethodThe 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

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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

ExampleIf 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

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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


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D

O 1 2 3 Future

Production

1 100 200 6000

2 400 600 4000

3 500 300 3000

Future

Attraction2000 1500 400 2000

Example

Note that this O/D matrix needs correction

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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


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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

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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


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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

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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

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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)

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A limiting value when reached the trip will not made.

• Specific Distance.

• Specific Time.

• Specific Cost.

• Specific Generalized Cost

Cut-off Value


222523 24 26

15

11

1819

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)

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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


222523 24 26

15

11

1819

20 21

16

12

17

1

1314

(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)

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Incident matrix

O\D 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

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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.


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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

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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


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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

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This formula can be expressed as follows


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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

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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


Solution1000A

2250B

1750C

3200D

YXZones

2015A

1015B

1010C

2015D

Production

Time

Total Attractions:

3700 jobs in X

4500 jobs in Y

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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 productionYX

1000396604A

22501646604B

1750960790C

320012201980D

Total Attractions:

3700 jobs in X , 4500 jobs in Y


Ti-j for origin zones, A, B,

C, D, total productionYX

1000396604A

22501646604B

1750960790C

320012201980D

Total Attractions:

3700 jobs in X , 4500 jobs in Y

820045003700Total predicted

attraction Ai

820042223978Total calculated

Attraction, Ci

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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

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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 productionYX

1000440560A

22501710540B

17501020730C

320014101790D

820045803620Total calculated

Attraction, Ci

820045003700Total predicted

attraction Ai