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TRANSCRIPT
Modeling Concept
Model
Tools and media to reflect and simple a measured reality.
Types of Model
Physical Model
Map and Chart Model
Statistics and mathematical Models
MODEL?
What is the final goal of designing model?
What is variables considered?
What is variables that influenced and
arranged by planner?
What is the theory?
How grouping model level?
How the role of time?
What kind of data that available?
How about the calibration and validity?
Objectives
Help to understanding how the system working
Predicted the changes in land use and transport
infrastructure system
The main variables
Land Use
Transportation Infrastructure System
Traffic flow
Parameters that can be set
Land Use RTRW, RDTRK, etc.
Transportation Infrastructure Tatranas,
Tatrawil, Tatralok, etc.
Theory/ Concept
Accessibility
Generated and Attracted Trip
Trip Distribution
Mode choice
Route choice
Dynamic Traffic Flow
Grouping Level
Areas?
Combining and Grouping traffic flow?
Time
Static Model
Dynamic Model
Scope Mathematical, statistical, operational research,
programming
Data Quantity
Quality
Calibration and Validation Calibration : process of assessing the parameter
value of a model with various techniques (numerical analysis, linear algebra, optimization, etc.)
Validation : expected models with calibrated parameters before it produce the same output with reality (data) forecasting future
Modification : Reduction or addition of several variables suit for the applications in the area or another condition.
Determination of the study area
Study area divided into several zones,
numbers and areas depend on level of
accuracy expected
The Outside of study area divided into
several external zones to reflect the
other zones
System activities simplified in the zone
form and considered to represented by
the central zone
Internal Zone the zone that located in
studies area have major contribution to the
movement that occurred
External Zone the zone that located
outside study area have small contribution to
movement occurred
Central Zone virtual point that
representing the center activity zone, the
beginning and the ending of the movement
to another zone
Network system that simplified in road
and joint form
Road segment or railway network, etc.
The segment must have information of road
conditions
Node intersection, station, city, etc.
Activity and Network systems was
connected with central zone
Central Zone Link virtual segment that
connected to the central zone (activity
system) by a node (network system)
Combined Cost Concept
Combining three main components of route choice (Distance, cost, time)
Combined cost of private cars
Gcp = yD + uTv + C
Where :
Gcp = Combined cost for PC (Rp)
y = Operating vehicle cost per unit distance
(Rp/km)
C = parking cost, toll, etc.
Combined cost for public transport:
Gcu = fD + u Ta + u Tw + u Tv + d
Where :
Gcu = Combined cost for PT (Rp)
D = Distance (distance unit, e.g : km)
Ta = walking time (time unit, e.g: minutes)
Tw = waiting time PT (time unit, e.g: minutes)
Tv = time in public transportation (time unit, e.g: minutes)
f = cost per distance (Rp/km)
u = time value per unit time (Rp/minutes)
d = surcharge unmeasured
A Simple Model of Land Use / Transport System
Objectives:
Help to understand how the transportation system works
Predict the changes in traffic flows which will result from changes to land use or to the transport system
Variables:
Land Use System : population and employment
Transport system : Distance, Travel time
Traffic System
Notasi:
LA,B = Land Use in Zone A, B
PA = Traffic Generation from zone A
AB = Traffic Attraction to zone B
QAB(1) = Traffic from zone A to zone B using route 1
TQAB(1) = Travel time from zone A to zone B using in
traffic condition is Q
T0 = Travel time in free-flow traffic = 0
C = Road capacity
a = Level of Service index
Traffic Generation
PA = f (LA)
AB = f (LB)
Traffic Distribution
QAB = PA.AB.k
TQAB
Mode and Route Choice
TQAB(1) = TQAB(2)
Activity system : Zone Land Use Population Information
A Residential 35.000 90% working age
B Employment area
12.000
Transport characteristic:
Route Length (km)
To (min.)
Los Index (a)
Capacity (veh/h)
1 17 25 0,4 3.000
2 20 40 1,0 2.000
3 14 20 0,25 4.000
Traffic Distribution
QAB = PA.AB.0,001
TQAB
1. The amount of traffic from zone A to zone B if only route 1 that operated?
2. The amount of traffic from zone A to zone B if only route 2 that operated?
3. The amount of traffic from zone A to zone B if route 1 and 2 operating together?
4. The amount of traffic if adding a new road 3 and route 1,2, and 3 are operated together?
5. The amount of traffic if there are changes in residential population become 40.000 and employment population 20.000?
‘Supply’ Equation:
Route 1:
TQAB(1) = 25 x (3.000 – 0.6 QAB(1))
3.000 – QAB(1)
Route 2:
TQAB(2) = 40 x 2.000
2.000 – QAB(2)
Route 3:
TQAB(3) = 20 x (4.000 – 0.75 QAB(3))
4.000 – QAB(3)
Analytical method
If only route 1 that operated:
Then:
TQAB(1) = 378.000
QAB(1)
( 75.000 – 15 QAB(1)) x QAB(1) = (3.000 – QAB(1)) x 378.000
15 QAB(1)2 – 453.000QAB(1) + 1.134.000.000 = 0
QAB(1) = 2.755 veh/h TQAB(1) = 137,2 minutes
QAB(1) = 2.755 QAB(1) = 27.445 (>>C1)
If only route 2 that operated:
TQAB(2) = 378.000
QAB(2)
80.000 x QAB(2) = (2.000 – QAB(2)) x 378.000
458.000QAB(2) + 756.000.000 = 0
QAB(2) = 1.651 veh/h TQAB(2) = 229 minutes
If route 1+2 operating together:
(1)
Equal condition 1 and 2:
TQAB = 378.000 = 378.000
QAB QAB(1) +QAB(2)
Limit 1: QAB = QAB(1) + QAB(2)
Limit 2: TQAB = TQAB(1) = TQAB(2)
Equ.(1) Limit 2:
TQAB = TQAB(2)
378.000 = 80.000
QAB(1) +QAB(2) 2.000 – QAB(2)
756.000.000 – 378.000QAB(2) = 80.000 QAB(1) + 80.000QAB(2)
QAB(1) = 9.450 – 5,725 QAB(2) (2)
75.000 – 15 QAB(1) = 80.000
3.000 – QAB(1) 2.000 – QAB(2)
150.000.000 – 75.000QAB(2) – 30.000QAB(1) – 15QAB(1)QAB(2) = 240.000.000 – 80.000QAB(1)
50.000QAB(1) – 15QAB(1) QAB(2) – 75.000QAB(2) = 90.000.000
(2)
Limit 2: TQAB(1) = TQAB(2)
Substitution (1) to (2):
50.000 (9.450 – 5,725 QAB(2)) – 15 (9.450 – 5,725 QAB(2)) QAB(2) –
75.000QAB(2) = 90.000.000
Obtainable:
Then :
85,875QAB(2) 2 + 219.500 QAB(2) – 382.500.000 = 0
(3)
QAB(2) = 1.189 veh/h TQAB(2) = 98,675 mins.
QAB(1) = 2.641 veh/h TQAB(1) = 98,675 mins.
QAB = 3.830 veh/h TQAB = 98,675 mins.
QAB(2) = 1.189 QAB(2) = -3.745(-, impossible)
If route 1+2+3 operating together:
TQAB = 378.000 = 378.000
QAB QAB(1) +QAB(2) +QAB(3)
(1)
Limit 1:
Limit 1: QAB = QAB(1) + QAB(2)+ QAB(3)
Limit 2: TQAB = TQAB(1) = TQAB(2) = TQAB(3)
Graphical method
From the equation demand and supply, input value of QAB to obtain value of TQAB, TQAB(1), TQAB(2) or TQAB(3)
Plot the value of QAB and TQAB, to obtain the demand curve
Plot the value of QAB and TQAB(1), TQAB(2) or TQAB(3) to obtain supply curve route 1, 2 and 3
Cutting point between demand and supply curve is a equilibrium point
QAB TQAB
0 ~
500 756.00
1000 378.00
1500 252.00
2000 189.00
2500 151.20
3000 126.00
3500 108.00
4000 94.50
4500 84.00
5000 75.60
5500 68.73
6000 63.00
6500 58.15
7000 54.00
7500 50.40
8000 47.25
8500 44.47
9000 42.00
QAB TQAB(1) TQAB(2) TQAB(3)
0 25.00 40.00 20.00
500 27.00 53.33 20.71
1000 30.00 80.00 21.67
1500 35.00 160.00 23.00
2000 45.00 ~ 25.00
2500 75.00 28.33
3000 ~ 35.00
3500 55.00
4000 ~
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
Demand Supply
0
50
100
150
200
250
300
350
400
450
5000
500
100
0
150
0
20
00
250
0
300
0
350
0
40
00
450
0
500
0
550
0
60
00
650
0
700
0
750
0
80
00
850
0
90
00
950
0
100
00
T (
Tra
vel t
ime
- m
inu
tes)
Q (Vehicle per hour)
Relationship between QAB and TQAB
Demand
Supply 1
Supply 2
Supply 3
0
50
100
150
200
250
300
350
400
450
500
0
500
100
0
150
0
20
00
250
0
300
0
350
0
40
00
450
0
500
0
550
0
60
00
650
0
700
0
750
0
80
00
850
0
90
00
950
0
100
00
T (
Tra
vel t
ime
, m
inu
tes)
Q (Vehicle per hour)
Relationship between QAB and TQAB
Demand
Supply 1
Supply 2
Supply 3
Supply 1+2
Supply 1+2+3
0
50
100
150
200
250
300
350
400
450
500
0
500
100
0
150
0
20
00
250
0
300
0
350
0
40
00
450
0
500
0
550
0
60
00
650
0
700
0
750
0
80
00
850
0
90
00
950
0
100
00
T (
Tra
vel t
ime
, m
inu
tes)
Q (vehicle per hour)
Relationship between QAB and TQAB
Demand
Supply 1
Supply 2
Supply 3
Supply 1+2
Supply 1+2+3
Demand Baru
Transportation Characteristic:
Another data same with example before
Route Length (km)
To (minutes)
LoS index (a)
Capacity (veh/h)
1 15 20 0,5 3.000
2 25 45 0,9 2.000
Assignment