trip distribution
DESCRIPTION
Teknik Lalu LintasTRANSCRIPT
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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
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Components
of trip details
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QUESTIONS???
Trip distribution is
a method to
determine where
trips are going
from and to
Trip interchange,
or OD
Where trip
productions go
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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
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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
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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
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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
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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
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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 )(
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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 ???
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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
( ) ( . ) ( ).
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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
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DETROIT METHOD
E growth factor for all the areas as a whole
E
EEtT
ji
jiji
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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
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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
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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
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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
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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
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MULTIPLE REGRESSION METHOD
General form
Tij=a+bx0+cx1 +dx2 +
Co efficiency R2
Model depends on number of variables and measure of variables
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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
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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
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EXAMPLE (NHB)
The trip
production equals
to trip attraction
1816
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Gravity Model
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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
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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
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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
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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
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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
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Trip Distribution
(first Iteration)Trprrrr
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OPPORTUNITY METHOD
Pj probability of trip stopping in zone j
PTT jGiji )(
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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)