Trip Distribution[1]

8/8/2019 Trip Distribution[1]

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CE 7630

Trip Distribution

John K. Abraham, Ph.D., P.E.

CE 7630 Trip DistributionTrip DistributionTrip DistributionTrip DistributionWhere will they travel?

Daily Person Trips

Home-base Work

Home-based Other

Non-home-based

College

School

Commercial Vehicles

Inter-zonal Accessibilities

(Time and Cost)

Zonal PersonTrip Tables

Home-base Work

Home-based Other

Non-home-based

College

School

Commercial Vehicles


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CE 7630 Trip Distribution Models

l used to distribute generated trips amongst destination

zones.

l Trip distribution is also defined as the interchange

between zones and deals with the spatial interaction

between them

l Linking productions to attractions

l How people decide on possible destinations

l Function of:

Type and extent of transportation facilities

Pattern (location and intensity) of land use

Socio economic characteristics of population

CE 7630 Trip Distribution

Attractions

Production

1 2 3 4 n

1

2

3

4

n


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CE 7630 Trip Distribution Models

l 2 types of models: Growth factor methods and

Theoretically based methods

Growth: Uniform, Average Factor, Fratar,Detroit, . ..

Theoretical: Gravity, Intervening Opportunities,Wilson's Entropy, Logit, ...

l Models must be "calibrated" for the "base

year" by an origin-destination study (OD

study)

CE 7630 Growth Factor Methods

l Future trips can be found by proportioning the

relative growth (trip ends) in those zones

l Iterative in nature

Start with existing

New proportions established

Until we reach stable numbers


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CE 7630

Growth Factor ModelsA B

C D

12

10

1814

6

14

A B C D

A - 12 10 18 40

B 12 - 14 6 32

C 10 14 - 14 38

D 18 6 14 - 38

40 32 38 38 148

80

40

*

0

=

=

A

A

T

T

38

38

*

0

=

=

D

D

T

T

48

32

*

0

=

=

B

B

T

T

114

38

*

0

=

=

c

c

T

T

CE 7630

Uniform Growth Factor Method

T* =Design Year Trips (from trip Generation)

T0=Base year Trips (total)

F = Apply factor to all zonal tripsT*

T0

A B C D

A - 23 19 34 76

B 23 - 26 11 60

C 19 26 - 26 72

D 34 11 26 - 72

76 60 72 72 280

280

148F = = 1.89

12*1.89=23

A B C D

A - 12 10 18 40

B 12 - 14 6 32C 10 14 - 14 38

D 18 6 14 - 38

40 32 38 38 148


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CE 7630 Average Growth Factor Method

Pi*

PiFi =

Pj*

PjFj =

A B C D Pi*

A - 12 10 18 40 80

B 12 - 14 6 32 48

C 10 14 - 14 38 114

D 18 6 14 - 38 38

40 32 38 38 148 280

Fj 2 1.5 3 1

Fi

2

1.5

3

1

( ) 20001jiijij FFTT +=

( )2

111 +=

K

j

K

i

K

ij

K

ij FFTT

CE 7630

First Iteration

A B C D

A - 21.0 25.0 27.0 73.0

B 21.0 - 31.5 7.5 60.0

C 25.0 31.5 - 28.0 84.5

D 27.0 7.5 28.0 - 62.5

73.0 32 38 38 280.0

Pi*

80

48

114

38

280

Fi

1.095

0.800

1.350

0.608

Fj 1.095 0.800 1.350 0.608

(12)*(2+1.5)/2


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CE 7630 9th Iteration

A B C D Pi* FiA - 15 52 14 81 80 0.995

B 15 - 34 2 51 48 0.954

C 52 34 - 24 110 114 1.043

D 14 2 24 - 40 38 0.95

40 32 38 38 Fj 0.995 0.954 1.043 0.95

Criterion 0.95 < F < 1.05

CE 7630 Fratar Modell # of trips from i to j is

proportional to

Present trips from i

Modified by a growth

factor of the zone TO

which trips are attracted

l Trips from i to j

l Trips from j to i

2

00

0001 ji

jiijij

LL

FFTT

+

=

2

11

111

+

=

k

j

k

ik

j

k

i

k

ij

k

ij

LLFFTTIterations


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CE 7630

Continuing Example..with Fratar ModelA B C D Fi

A - 12 10 18 40 2B 12 - 14 6 32 1.5

C 10 14 - 14 38 3

D 18 6 14 - 38 1

40 32 38 38 148

Fj 2 1.5 3 1

j

ijT

j

ijT

66

40

)18*110*312*5.1(

40=

++

=iL

72

32

)6*114*312*2(

32=

++

=jL

A B C D Fi

A - 18.9 38.9 18.4 76.2 2

B 18.9 - 35.8 40 94.7 1.5

C 38.9 35.8 - 23.2 97.9 3

D 18.4 4 23.2 - 45.6 1

40 32 38 38 148

j

ijT

jijT

Pi*

80

48

114

38

280

2

00

0001 ji

jiijijLLFFTT

+=

D

3855,

4066

C

32/72,

40/66

B

40/66,

32/72

A

DCBA

2

72

32

66

40

*5.1*2*129.18

+

=

CE 7630 Detroit Model

l Attempt to make the Fratar model

computationally simpler

l Replaces the Li term is simplified to be

proportional to the growth factors of both zones

i and j divided by the overall growth factor

0

00

01

F

FFTT

ji

ijij =

1

11

1

=k

k

j

k

ik

ij

k

ijF

FFTTIterationkth


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CE 7630

Continuing Example..with Detroit Model

A B C D Pi*

A - 12 10 18 40 80

B 12 - 14 6 32 48

C 10 14 - 14 38 114

D 18 6 14 - 38 38

40 32 38 38 148 280

j

ijT

j

ijT

Fj 2 1.5 3 1

Fi

2

1.5

3

1

A B C D Pi*

A - 19 31.8 19 69.8 80

B 19 - 33.4 4.8 57.2 48

C 31.8 33.4 - 22.2 87.4 114

D 19 4.8 22.2 - 46 3840 32 38 38 148 280

j

ijT

ijT

F1

i

1.48

0.84

1.31

0.83

0

0001

F

FFTTji

ijij =

89.1148280

0

*0===

TTF

89.1

2*5.1*1219 =

CE 7630 Continuing Example..with Detroit Model4th Iteration

A B C D Pi* F5

i

A - 14 53 14 81 80 0.99

B 14 - 34 2 50 48 0.96

C 53 34 - 23 110 114 1.036

D 14 2 23 - 39 38 0.974

81 50 110 39 148 280

j

ijT

ijT


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CE 7630

l Simple process Where travel time matrix is not available

l Assumes no effect of transportation system on trip

distribution (will remain stable..)

l No measure of travel impedance

l Based on growth factors.. Zones without trips on base

my not have any in the forecast year

l Somewhat arbitrary rounding errors rapidly become

large as iterations proceed

l Single number growth factors are assumed, may be very

difficult to obtain

l Uniform and Average Methods are no more used, Fratar

and Detroit are still being used particularly for external

trips or where comprehensive data is not available

Comments on GF Models

CE 7630 Gravity Model

l Loose analogy to Newtons law of gravity

the attractive force between any two bodies isthe attractive force between any two bodies isthe attractive force between any two bodies isthe attractive force between any two bodies isdirectly related to the masses ofdirectly related to the masses ofdirectly related to the masses ofdirectly related to the masses ofthe bodies andinversely related to the distance between them

G= gravitational constant

2

12

21

d

MMGF=


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CE 7630

Gravity Model..

l the number of trips between two areas is directlythe number of trips between two areas is directlythe number of trips between two areas is directlythe number of trips between two areas is directlyrelated to activities in the area represented by triprelated to activities in the area represented by triprelated to activities in the area represented by triprelated to activities in the area represented by trip

generation and inversely related to the separationgeneration and inversely related to the separationgeneration and inversely related to the separationgeneration and inversely related to the separation

between thebetween thebetween thebetween the areas represented as a function of

travel time

i Tij=50j

Centroid

CentroidVector

i jMovement

CE 7630

l The number of trips between 2 zones is directly

proportional to the number of trip attractions at the

destination zone and inversely proportional a function

of the travel time"

Tij

= Trips produced in zone i and attracted to zone j

Pi= Trips produced in zone i

Aj

= Trips attracted in zone j

Fij = Friction factor for impedance (usually travel time)between zones i and j

Kij

= Socioeconomic adjustment factor for trips

produced in i and attracted to j


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CE 7630

How do we determine values for the variables?How do we determine values for the variables?How do we determine values for the variables?How do we determine values for the variables?

- Recall Ps and As come from trip generation- The sum of productions has to equal the sum ofattractions

- Ks are used to force estimates to agree with observedtrip interchanges (careful! do not use too many of these!Have a good reason for using them!)- Fs are determined by a calibration process (by purpose),and depend upon the willingness of folks to make trips ofcertain lengths for certain purposes

recall... trip purposes

HBW - home based work

HBO - home based other NHB - non-home based

HBS - home based school

CE 7630 Gravity Model Example


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CE 7630

Gravity Model Example

CE 7630


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CE 7630

CE 7630 Decay of F factors with Travel Time


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CE 7630 Intervening Opportunities Model

VKP=

1ln CVKP +=

V=total # of opportunities with radius R from origin

P=Number of migrants who find destinations within radius R from

their starting point

This model served as the basis for establishing the intervening

opportunities model in tr ip distribution

CE 7630


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CE 7630

( )njj

LV

LVLV

iij

e

eePT

=

+

1

1

i= origin zone

j= jth destination in order of increasing travel time

Aj=number of destination opportunities

Vj=number of opportunities passed up to the jth zone

CE 7630 Intervening Opportunities Model Example


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CE 7630

CE 7630

Trip Distribution[1]

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