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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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
Trip Distribution 3odels
• 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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GEOG 111/211A Transportation Planning
Trip Distribution 3odels
• ;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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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
GEOG 111/211A T t ti Pl i
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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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GEOG 111/211A Transportation Planning
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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GEOG 111/211A Transportation Planning
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
GEOG 111/211A Transportation Planning
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GEOG 111/211A Transportation Planning
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