TRANSPORTATION MODELING

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?

Physical Model

Map Model (Desire Line)

Map Model

Chart Model

Statistic and Mathematical Models

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)

1 2 Internal Zone Central Zone 4 3 Border Study Study area 5 6

gateway Road Node Border area Study area

1 2 4 3 Zone center link Border area Study area 5 6

1 2 4 3 5 6

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: G cu = fd + u T a + u T w + u T v + d Where : Gcu D Ta Tw Tv minutes) f u d = Combined cost for PT (Rp) = Distance (distance unit, e.g : km) = walking time (time unit, e.g: minutes) = waiting time PT (time unit, e.g: minutes) = time in public transportation (time unit, e.g: = cost per distance (Rp/km) = time value per unit time (Rp/minutes) = 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: L A,B P A A B = Land Use in Zone A, B = Traffic Generation from zone A = Traffic Attraction to zone B Q AB(1) = Traffic from zone A to zone B using route 1 T Q AB(1) = Travel time from zone A to zone B using in traffic condition is Q T 0 = Travel time in free-flow traffic = 0 C = Road capacity a = Level of Service index

Traffic Generation P A = f (L A ) A B = f (L B ) Traffic Distribution Q AB = P A.A B.k T QAB Mode and Route Choice T QAB(1) = T QAB(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 Q AB = P A.A B.0,001 T QAB

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?

Solution Demand Equation: Q AB = 31.500 x 12.000 x 0,001 T QAB = 378.000 T QAB

Supply Equation: Route 1: Route 2: Route 3: T QAB(1) = 25 x (3.000 0.6 Q AB(1) ) 3.000 Q AB(1) T QAB(2) = 40 x 2.000 2.000 Q AB(2) T QAB(3) = 20 x (4.000 0.75 Q AB(3) ) 4.000 Q AB(3)

Analytical method If only route 1 that operated: T QAB(1) = 378.000 Then: Q AB(1) ( 75.000 15 Q AB(1) ) x Q AB(1) = (3.000 Q AB(1) ) x 378.000 15 Q 2 AB(1) 453.000Q AB(1) + 1.134.000.000 = 0 Q AB(1) = 2.755 Q AB(1) = 27.445 (>>C 1 ) Q AB(1) = 2.755 veh/h T QAB(1) = 137,2 minutes

If only route 2 that operated: T QAB(2) = 378.000 Q AB(2) 80.000 x Q AB(2) = (2.000 Q AB(2) ) x 378.000 458.000Q AB(2) + 756.000.000 = 0 Q AB(2) = 1.651 veh/h T QAB(2) = 229 minutes

If route 1+2 operating together: Limit 1: Q AB = Q AB(1) + Q AB(2) Limit 2: T QAB = T QAB(1) = T QAB(2) Equal condition 1 and 2: T QAB = 378.000 = 378.000 Q AB Q AB(1) +Q AB(2) (1)

Equ.(1) Limit 2: T QAB = T QAB(2) 378.000 = 80.000 Q AB(1) +Q AB(2) 2.000 Q AB(2) 756.000.000 378.000Q AB(2) = 80.000 Q AB(1) + 80.000Q AB(2) Q AB(1) = 9.450 5,725 Q AB(2) (2)

Limit 2: T QAB(1) = T QAB(2) 75.000 15 QAB(1) = 80.000 3.000 Q AB(1) 2.000 Q AB(2) 150.000.000 75.000Q AB(2) 30.000Q AB(1) 15Q AB(1) Q AB(2) = 240.000.000 80.000Q AB(1) 50.000Q AB(1) 15Q AB(1) Q AB(2) 75.000Q AB(2) = 90.000.000 (2)

Substitution (1) to (2): 50.000 (9.450 5,725 Q AB(2) ) 15 (9.450 5,725 Q AB(2) ) Q AB(2) 75.000Q AB(2) = 90.000.000 85,875Q AB(2) 2 + 219.500 Q AB(2) 382.500.000 = 0 (3) Obtainable: Q AB(2) = 1.189 Q AB(2) = -3.745(-, impossible) Then : Q AB(2) = 1.189 veh/h T QAB(2) = 98,675 mins. Q AB(1) = 2.641 veh/h T QAB(1) = 98,675 mins. Q AB = 3.830 veh/h T QAB = 98,675 mins.

If route 1+2+3 operating together: Limit 1: Q AB = Q AB(1) + Q AB(2) + Q AB(3) Limit 2: T QAB = T QAB(1) = T QAB(2) = T QAB(3) Limit 1: T QAB = 378.000 = 378.000 Q AB Q AB(1) +Q AB(2) +Q AB(3) (1)

Graphical method From the equation demand and supply, input value of Q AB to obtain value of T QAB, T QAB(1), T QAB(2) or T QAB(3) Plot the value of Q AB and T QAB, to obtain the demand curve Plot the value of Q AB and T QAB(1), T QAB(2) or T QAB(3) to obtain supply curve route 1, 2 and 3 Cutting point between demand and supply curve is a equilibrium point

QAB Demand 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 Supply 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

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 T (Travel time- minutes) 500 450 400 350 300 250 200 150 100 50 Relationship between Q AB and T QAB Demand Supply 1 Supply 2 Supply 3 0 Q (Vehicle per hour)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 T (Travel time, minutes) 500 450 400 350 300 250 200 Relationship between Q AB and T QAB Demand Supply 1 Supply 2 Supply 3 Supply 1+2 Supply 1+2+3 150 100 50 0 Q (Vehicle per hour)

Assignment Transportation Characteristic: 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 Another data same with example before

Complete with analytical method: 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?