INTRODUCTION

Trip distribution studies the trips from a number of travel origins to a number of travel destinations

The objective of trip distribution is to predict the flow of trips Tij from zones i to j.

Common MethodsGrowth factor

Uniform factor

Average factor

Fratar method

Detroit method

Synthetic methodGravity method

Electrostatic method

Regression method

Opportunity method

Neural network

Components

of trip details

QUESTIONS???

Trip distribution is

a method to

determine where

trips are going

from and to

Trip interchange,

or OD

Where trip

productions go

TRIP DISTRIBUTION

General form:

Wherethe number of trips produced in zone i by type q

trip makers from zones i to j

the number of trips attracted to zone j by type q trip makers from zone i

the number of trips produced in zone i and attracted to zone j by type q trip makers

j

q

ij

q

i tp i

q

ij

q

j ta

pq

i

aq

j

tq

ij

ORIGIN DESTINATION MATRIX

O D 1 2 3 . n-1 n

1 t11 t12 t13t1n-1 t1n p1

2 t21 t22 t23t2n-1 t2n p2

3 t31 t32 t33t3n-1 t3n p3

. . . . . . . .

n-1 tn-1 tn-2 tn-3 . t(n-1)-(n-1) tn-(n-1) pn-1

n tn tn2 tn3 . T(n-1)-n tnn pn

a1 a2 a3 . an-1 an

METHODS IN TRIP DISTRIBUTION

Growth factor method

Uniform factor

Average factor

Fratar factor

Detroit method

Synthetic method

Gravity model

Electrostatic model

Regression model

Opportunity model

GROWTH FACTOR METHODS

Assumptions: The trip making patterns will remain the same in the future as it is

in the base year

The volume will increase according to the trip growth in the generating and attracting zones

Uniform growth (constant) factor method

Assumes: The growth in all zones will increase in an uniformed manner

The existing traffic pattern will be the same for the future but the volume will change

The growth which is expected to take place in the survey area will have equal factor for all areas

GROWTH FACTOR METHOD

General form

Tij = tijE

Where

Tij future number of trips from i to j

tij existing number of trips from i to j

E growth factor

Uniform Factor

T total number of trips in the future

t total present number of trips

Average Factor

t

TE

tT

Ei

i

i

tT

Ej

j

j

2

EE jiE

FRATAR METHOD (1)

expected future trips from zone i

ti-j, ti-n present trips from zone i to all the other zones j,...,n

Ei, En growth factors of individual zones i,...,n

EtEtEtEtT

Tnnikkijji

jjiGi

ji

...

)(

T Gi )(

APPLICATION OF FRATAR METHOD

A B C D

A - 10 12 18

B 10 - 14 14

C 12 14 - 6

D 18 14 6 -

Total 40 38 32 38

Ti(G) 80 114 48 38

E 2 3 1.5 1

TA-B and TB-A ???

APPLICATION OF FRATAR METHOD

A BT

80 10 3

10 3 12 1 5 18 136 4

( ) ( . ) ( ).

B AT

114 10 2

10 2 14 1 5 14 141 5

( ) ( . ) ( ).

ANOTHER FORM OF FRATAR METHOD

Where

the number of trips from zones i to j in the horizon year

the number of trips from zones i to j in the base year

fi, fj the growth factors for zones i and j

Location factors are considered here as:

ijbt

2

llfftt

ji

ji

b

ij

h

ij

th

ij

p

pf b

i

h

i

i

n

ii

b

ij

b

j

j

ft

al

1

DETROIT METHOD

E growth factor for all the areas as a whole

E

EEtT

ji

jiji

COMMENTS ON GROWTH FACTOR METHOD

Easy to be understood and applied

Less information required

Flexible in terms of purpose

They have been well tested

It is not sensitive with changes of network

Future number of trips is often unknown

Cannot reflect land-use impact on trip makers

DISADVANTAGES

Tends to overestimate the trips between

densely populated zones which probably

have little further development potential

Tends to underestimate the future trips

between underdeveloped zones which

could be extensively populated in the

future

STOCHASTICS TRIP DISTRIBUTION (1)

General form

T=PB

T = nn square matrix of

P + nn diagonal matrix of the zone trip

productions

B = nn square matrix of the probabilities

bij that a trip produced in zone i will be attracted to zone j

The above relationship must satisfy (apart from pi=tij, ai=tij)

A=PB

A = 1n matrix of trip attractions

P = 1n matrix of trip productions

ijjb 0

EXAMPLE OF STOCHASTICS TRIP

DISTRIBUTION

=

P

100

150

50

200

.. .. ..

.. .. ..

.. .. ..

.. .. ..

B

. . . .

. . . .

. . . .

. . . .

4 3 2 1

2 4 2 2

1 2 4 3

2 2 2 4

80404040

1520105

30306030

10203040

PBT 20050150100A

4.2.2.2.

3.4.2.1.

2.2.4.2.

1.2.3.4.

115 140 110 135

ELECTROSTATICS FIELD METHOD (WORKER-JOB)

probability of movement from zones i to j

probability of movement from zones j to I

Pi number of workers living in zone I

Qj number of jobs available in zone j

Rij straight line distance from zones i to j

m

j ij

j

i

ij

j

PiQjj

R

Q

PR

Q

V

1

n

i ij

i

jij

i

QjPi

RP

QRP

V

1

V PiQj

V QjPi

MULTIPLE REGRESSION METHOD

General form

Tij=a+bx0+cx1 +dx2 +

Co efficiency R2

Model depends on number of variables and measure of variables

ORIGINAL GRAVITY MODEL

It is a most widely applied method

Pi total number of trips produced in zone i

Ai total number of trips attracted to zone i

Aj total number of trips attracted to zone j

Di-j , Di-n space separation between zones i-j.,.i-n

b empirically determined which expresses the average area wide effect of space separation

)(......

)()(

)(

D

A

D

A

D

A

D

A

P

nib

n

kib

k

jib

j

jib

j

i

GRAVITY MODEL TODAY

Fi-j empirically derived travel-time factor

expressing the average area-wide effect of

space separation

Ki-j special zone to zone adjustment factor

n

jjijij

jijij

iji

KFA

KFAPT

1

Fi-j and Ki-j Factors

Ki-j K-factors account for socioeconomic linkages not

accounted for by the gravity model

Common application is workers living near jobs (can you think of another way to do it?)

K-factors are i-j TAZ specific

If i-j pair has too many trips, use K-factor less than 1.0

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

Fi-j Convert travel times into friction factors for ALL pairs

EXAMPLE (NHB)

The trip

production equals

to trip attraction

1816

Gravity Model

INPUT DATA (travel time in minute)

TAZ 1 2 3 4 5

1 4 12 8 15 21

2 6 3 9 23 14

3 20 7 4 10 25

4 12 18 8 4 17

5 24 19 23 15 8

Travel

time

3 4 7 10 15 20 25

Friction

factor

87 45 29 18 10 6 4

Travel time and Friction factor for TAZ

Attraction TAZ 1 2 3 4 5

Travel time 20 7 4 10 25

Friction factor 6 29 45 18 4

Attractiveness of Zones

Attractiveness of j=Attraction of j x Fi-jKi-j

Attraction

TAZ1

1 2 3 4 5

Attraction

Aj

1080 531 76 47 82

Friction factor

Fi-jKi-j

6 29 45 18 4

Attractiveness

Aj=Fi-jKi-j

6480 15399 3420 846 328

Relative Attractiveness

Relative attractiveness=)( KFA

KFAjijij

jijij

Attraction 1 2 3 4 5 Sum

Attractiveness

Aj=Fi-jKi-j

6480 15399 3420 846 328 26473

Relative

attractiveness

0.244

8

0.5817 0.1292 0.031

9

0.0124 1.000

15399/26473 3420/26473

)( KFAKFA

jijij

jijij

Trip Distribution

n

jjijij

jijij

iji

KFA

KFAPT

1

TAZ P3=602 Relative attractiveness Trip distribution

1 602 0.2448 147

2 602 0.5817 350

3 602 0.1292 78

4 602 0.0319 19

5 602 0.0124 8

Total 1.000 602

Trip Distribution

(first Iteration)Trprrrr

OPPORTUNITY METHOD

Pj probability of trip stopping in zone j

PTT jGiji )(

Neural Network and Training Algorithm

P

Tij

DA

wj-i

wk-j

Input layer

Hidden layer

Output layer

Start

diff

Finish

w, w(n+1)