trip distribution (1)

8/16/2019 Trip Distribution (1)

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GEOG 111/211A Transportation Planning

Trip Distribution

• Additional suggested reading: Chapter 5 of Ortuar! "illu#sen$ third edition

%o&e#ber 2''(


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Trip Distribution Ob)e*ti&es• +epli*ate spatial pattern of trip #a,ing

• A**ount for spatial separation a#ong origins and destinations -pro.i#it in ter#s of ti#e$ *ost$ ! other fa*tors0

• A**ount for attra*ti&eness a#ong TAs

• +efle*t hu#an beha&ior


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Trip Distribution

• Con&ert Produ*tion and Attra*tion Tables into Origin

Destination -O D0 3atri*es

Destinations

1

2

4

(

5

6u#

Origins 1 2 4 ( 5 6u#

T11 T12 T14 T1( T15 T1 O1

T21 T22 T24 T2( T25 T2 O2

T41 T42 T44 T4( T45 T4 O4

T(1 T(2 T(4 T(( T(5 T( O(

T51 T52 T54 T5( T55 T5 O5

T1 T2 T4 T( T5 T O

D1 D2 D4 D( D5 D

TA P15

14

2

17

714

84

A22

5

52

2

84

1

2

4

(

5

6u#


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Crude appro.i#ation for 9"

Crude OD

Produ*tion Attra*tion Cal*ulation

one ;D P A O5

4 2 5 15>5

( 17 52 455 7 2 5

14 8>5

Total 84 84 84


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Trip Distribution$ 3ethodolog

• General E?uation:

@ Ti) < Ti P-T )0

• Ti) < *al*ulated trips fro# one i to one )

• Ti < total trips originating at one i• P-T )0 < probabilit #easure that trips ill be attra*ted

to one )

• Constraints:

• 6ingl Constrained

@ 6u#i Ti) < D ) O+ 6u# ) Ti) < Oi

• Doubl Constrained @ 6u#i Ti) < D ) A%D 6u# ) Ti) < Oi


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Trip Distribution 3odels

• Groth Ba*tor / Bratar 3odel

@ Ti) < Ti -T ) / T0

• Ti) < present trips fro# one i to one )

• Ti < total trips originating at one i• T ) < total trips ending at one )

• T < total trips in the entire stud

@ Ti) < Ti) -Bi B )0 / B

•B

i

< Ti

/ Ti

• B ) < T ) / T )

• B < T / T

• < esti#ated future trips


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• Gra&it 3odel

@ Ti) < Ti

• Ti) < trips fro# one i to one )

• Ti < total trips originating at one i

• A ) < attra*tion fa*tor at )

• A. < attra*tion fa*tor at an one .

• Ci) < tra&el fri*tion fro# i to ) e.pressed as a generalied *ost

fun*tion

• Ci. < tra&el fri*tion fro# i to an one . e.pressed as a

generalied *ost fun*tion

• a < fri*tion e.ponent or restraining influen*e

6u# -A. / Ci.0a

A ) / Ci)a

ou *an *onsider this as the

probabilit spatial distribution

P-T)0


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• ;nter&ening Opportunities 3odel

@ Ti) < Ti -e e 0

• Ti) < trips fro# one i to one )• T < trip destination opportunities *loser in ti#e to one

i than those in one )

• Ti < trip end opportunities in one i

• T ) < trip end opportunities in one )

• < probabilit that an destination opportunit ill be

*hosen

T T-T = T )0


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3odel Co#parison

Groth Ba*tor

Gra&it

;nter&ening

Opportunities

6i#ple

Eas to balan*e origin and

destination trips at an

one6pe*ifi* a**ount of fri*tion

and intera*tion beteen

ones

Does not re?uire origin

destination dataClai#ed to bear a better

Ffit to a*tual traffi*

Does not refle*t *hanges in the

fri*tions beteen ones

Does not refle*t *hanges in the

netor, +e?uires e.tensi&e *alibration

ong iterati&e pro*ess

A**ounts for onl relati&e

*hanges in ti#e distan*e relationship beteen ones

Arbitrar *hoi*e of

probabilit fa*tor

3odel Ad&antages Disad&antages

%e: Destination *hoi*e #odels build on inter&ening opportunities


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Gra&it 3odel Pro*ess

1> Create 6hortest Path 3atri.

3ini#ie in, Cost beteen Centroids

2> Esti#ate Bri*tion Ba*tor Para#eters

Bun*tion of Trip ength Chara*teristi*s b Trip Purpose4> Cal*ulate Bri*tion Ba*tor 3atri.

(> Con&ert Produ*tions and Attra*tions to Origins and

Destinations

5> Cal*ulate Origin Destination 3atri.

> Enfor*e Constraints on O D 3atri.

;terate eteen Enfor*ing Total Origins and Destinations


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6hortest Path 3atri.

• 3atri. of 3ini#u# Generalied Cost fro# an

one i to an one ) -see O" p> 1540

@ Distan*e$ Ti#e$ 3onetar Cost$ "aiting Ti#e$ Transfer

Ti#e$ et*>> #a be used in Generalied Cost @ Ti#e or Distan*e Often Hsed

@ 3atri. %ot %e*essaril

6##etri* -Effe*t of

One "a 6treets0

TA ;D

12

4

(

5

TA

;D 1 2 4 ( 5

C11 C12 C14 C1( C15 C1 C21 C22 C24 C2( C25 C2

C41 C42 C44 C4( C45 C4

C(1 C(2 C(4 C(( C(5 C(

C51 C52 C54 C5( C55 C5

C1 C2 C4 C( C5 C


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E.a#ple: tra&el ti#e #atri. for TAs

Tra&el ti#e table -#inutes0

one ;D 1 2 4 ( 5 6

1 1 2 4 ( 5 62 2 1 1>5 2 4 4

4 4 4 2 2 2 3

( ( ( 4 1 2 3

5 5 5 ( 4 1 2

5 ( ( 1


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Bri*tion Ba*tor 3odels

• E.ponential:

@ f-*i)0 < e * I '

• ;n&erse Poer:

@ f-*i)0 < *i) b I '

• Ga##a:

@ f-*i)0 < a *i) e a I '$ b I '$ * I ' * -*i)0

* -*i)0

b

b

Trip Purpose a b *9" 275'J '>'2' '>124

9P 1481J4 1>275 '>'8(

%9 218114 1>442 '>'1'ref> %C9+P 45 / TransCAD HTP6 3anual pg> 7'


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E.a#ple fri*tion fa*tors using

tra&el ti#es alone

Zone ID 1 2 3 4 5 6

1 1.349859 1.822119 2.459603 3.320117 4.481689 6.049647

2 1.822119 1.349859 1.568312 1.822119 2.459603 3.320117

3 2.459603 2.459603 1.822119 1.822119 1.822119 2.459603

4 3.320117 3.320117 2.459603 1.349859 1.822119 2.459603

5 4.481689 4.481689 3.320117 2.459603 1.349859 1.822119

6 6.049647 6.049647 4.481689 3.320117 3.320117 1.349859

Bri*tion i) < 1/e.p-'>'4 Ti#ei)0

/ i l i


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Bri*tion Ba*tor 3atri*es• 3atri. of Bri*tion fro# an one i to an one )$ b Trip Purpose

@ Ea*h Cell of a Bri*tion Ba*tor 3atri. is a Bun*tion of the Corresponding Cell of the 6hortest Path 3atri.

@ Ea*h Trip Purpose has a separate Bri*tion Ba*tor 3atri.

e*ause Trip 3a,ing

eha&ior Changes for

Ea*h Trip Purpose

TA ;D

12

4

(

5

TA

;D 1 2 4 ( 5

B11 B12 B14 B1( B15 B1

B21 B22 B24 B2( B25 B2

B41 B42 B44 B4( B45 B4

B(1 B(2 B(4 B(( B(5 B(

B51 B52 B54 B5( B55 B5

B1 B2 B4 B( B5 B

GEOG 111/211A T i Pl i


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Trip Con&ersion-Appro.i#ate0

• 9o#e ased Trips: %on 9o#e ased Trips: @ Oi < -Pi = Ai0 / 2 Oi < Pi

@ Di < -Pi = Ai0 / 2 Di < Ai

• Oi < origins in one i -b trip purpose0• Di < destinations in one i -b trip purpose0

• Pi < produ*tions in one i -b trip purpose0

• Ai < attra*tions in one i -b trip purpose0

• Note: This Only Works for a 24 Hour Time Period

• If our models are for one period in a day we prefer to

work directly with Origins!estinations

GEOG 111/211A T i Pl i


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O D 3atri. Cal*ulation

• Cal*ulate ;nitial 3atri. Gra&it E?uation$ b Trip

Purpose

@ Ea*h Cell has a Different Bri*tion$ Bound in the

Corresponding Cell of the Bri*tion Ba*tor 3atri.• Enfor*e Constraints in ;terati&e Pro*ess

@ 6u# of Trips in +o i 3ust E?ual Origins of TA i

• ;f %ot E?ual$ Trips are Ad)usted Proportionall

@ 6u# of Trips in Colu#n ) 3ust E?ual Destinations of TA )

• ;f %ot E?ual$ Trips are Ad)usted Proportionall

@ ;terate Hntil %o Ad)ust#ents +e?uired

GEOG 111/211A T t ti Pl i


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O D 3atri. E.a#ple:

Destinations

1

24

(

5

6u#

Origins 1 2 4 ( 5 6u#

T11 T12 T14 T1( T15 T1 O1

T21 T22 T24 T2( T25 T2 O2T41 T42 T44 T4( T45 T4 O4

T(1 T(2 T(4 T(( T(5 T( O(

T51 T52 T54 T5( T55 T5 O5

T1 T2 T4 T( T5 T O

D1 D2 D4 D( D5 D



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Attra*tion/fri*tion #atri.

Aj/friction factor Table

Zone ID 1 2 3 4 5 6 Total

1 16.298 3.293 2.033 15.662 0.446 0.992 38.724

2 12.074 4.445 3.188 28.538 0.813 1.807 50.8653 8.945 2.439 2.744 28.538 1.098 2.439 46.203

4 6.626 1.807 2.033 38.523 1.098 2.439 52.526

5 4.909 1.339 1.506 21.142 1.482 3.293 33.670

6 3.637 0.992 1.116 15.662 0.602 4.445 26.453



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Gra&it #odel probabilitGrait! "o#el $robabilit!Zone ID 1 2 3 4 5 6 Total

1 0.421 0.085 0.052 0.404 0.012 0.026 1

2 0.237 0.087 0.063 0.561 0.016 0.036 1

3 0.194 0.053 0.059 0.618 0.024 0.053 1

4 0.126 0.034 0.039 0.733 0.021 0.046 15 0.146 0.040 0.045 0.628 0.044 0.098 1

6 0.137 0.037 0.042 0.592 0.023 0.168 1

6u# -A. / fri*tioni.0

A ) / fri*tioni)



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Trip ;nter*hange iteration 1

T;K iteration 1 Target

one ;D 1 2 4 ( 5 Total Oi

1 J>7 1> 1>' J>5 '>2 '>5 17>5 17>5

2 2>4 '>7 '> 5>4 '>2 '>4 8>5 8>5

4 4>' '>7 '>8 8> '>( '>7 15>5 15>5( (>( 1>2 1>( 25>J '>J 1> 45 45

5 '>J '>2 '>2 4>1 '>2 '>5 5 5

1>4 '>( '>( 5> '>2 1> 8>5 8>5

Total 18>5 5>' (>5 5>7 1>8 5>4 84

D) 17>5 8>5 15>5 45 5 8>5

+atio '>8(8'88 1>8'J411 4>(J'( '>1587 2>4'1(7 1>JJ777

Bor ea*h *ell &alue e appl the gra&it e?uation on*e in this iteration

after this e use the ratio to ad)ust the &alues in the *ells until ro and

*olu#n targets are satisfied see also O" *hapter 5



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Trip inter*hange iteration 2

T;K iteration 2

one ;D 1 2 4 ( 5 Total Oi +atio

1 J>( 4>' 4>( (> '> '>7 18>7 17>5 '>8455772 2>1 1> 2>1 4>4 '>( '> 1'>1 8>5 '>8(4'8

4 2>7 1> 4>2 5>8 1>' 1>5 15>8 15>5 '>8J4284

( (>2 2>4 (>J 15>7 1>8 2>8 41>7 45 1>1'''82

5 '>J '>( '>7 1>8 '> '>8 5>2 5 '>85'J5

1>2 '>J 1>( 4>5 '> 2>7 1'>2 8>5 '>8428

Total 17>5 8>5 15>5 45 5 8>5 84

Hsing the ratios fro# before e su**eed in getting the targets for the su#s

of *ells for ea*h *olu#n loo, at the other ratios



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Trip inter*hange iteration 4

T;K iteration 4

one ;D 1 2 4 ( 5 Total

1 >8 2>7 4>2 (>4 '>5 '>7 17>5

2 2>' 1>5 1>8 4>1 '>( '> 8>5

4 2>7 1>5 4>1 5>J '>8 1>( 15>5( (> 2>5 5>2 1J>( 2>1 4>2 45

5 '>J '>( '>J 1>7 '> '>7 5

1>2 '> 1>4 4>2 '>5 2> 8>5

Total 17>1 8>4 15>( 45> 5>' 8>( 84

+atio 1>'2'278 1>'17(4 1>''(8J7 '>872(JJ '>88122( 1>''J'(


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3ultiple 3atri*es

• Bor ea*h trip purpose obtain different Origin

Destination Ti) #atri*es

• Hsuall these are 2( hour 3atri*es -nu#ber of trips

fro# one one to another in a 2( hour period0• ;n assign#ent e ill need a #atri. of &ehi*les

#o&ing fro# a one to another during a spe*ifi*

period -pea, usuall0 in a tpi*al da



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Binal O D 3atri. -si#plified0

• Co#bine -Add0 O D 3atri*es for Marious Trip Purposes

• 6*ale 3atri. for Pea, 9our

@ 6*ale b Per*ent of Dail Trips 3ade in the Pea, 9our

@ '>1 Often Hsed -1'N of dail trips0

• 6*ale 3atri. for Mehi*le Trips

@ 6*ale b ;n&erse of +idership +atio to Con&ert Person Trips to

Mehi*le Trips

@ '>85 to 1 Often Hsed

• %ote: 3ode 6plit Pro*ess / 3odels 3ore A**urate$ e ill

e.plore the# in *lass

trip distribution (1)

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