Transportation Planning Models

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Transportation Planning Models

• I. GENERAL EQUILIBRIUM APPROACH
• Transportation is a part of the Urban Economic
  Activities
• T Urban Activities
• II. PARTIAL EQUILIBRIUM APPROACH
• Urban Activities T
• Aggregated Disaggregated
• Sequential I II
• Simultaneous III IV

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Integrated Model of OD, Mode and Route Choice
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Schoon, John G. (1996), p.37
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Trip Generation (1)

• To estimate daily trips from readily available
  socio-economic data such as
• land-use, dwelling units and employment.
• Trip generation composed of trip production
  (amount of trips originated) and trip attraction
  (amount of trips ended).
• Trip Production Ti f (population, automobile
  ownership, dwelling unit, etc)
• Dwelling units and land use are generally
  considered
• Trip Attraction Tj f (employment, retail sales
  volume, etc)
• Employment related variables are generally used

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Trip Generation (2)

• Assumptions
• different land uses and socio-economic conditions
  affect different amount and type of trips
  generated and/or attracted.
• How to estimate
• Statistical techniques such as regression
  analysis
• Simple method use trip production factors and/or
  trip attraction factors (1.17 trips per dwelling
  unit per day for middle income family or 1.70
  trip per day per high income household)
• The most frequently used method for trip
  generation is the multiple linear regression model

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Trip Purpose

• There are several trip purposes frequently
  defined in the trip generation. The usual
  classifications are
• Home Based Work Trip HBW
• Home Based Other Trip HBO
• Non-home Based Trip NHB

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Trip Distribution

• Where the trips will go
• Estimate the number of trips from each zone going
  to each of the other zones
• Predict how people decide on their possible
  destinations.
• Analysis methods
• Gravity model
• Entropy maximization model

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Matrix
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Matrix
Column Vector (Origin Matrix)
Row Vector (Destination Matrix)
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Trip Distribution (2)
Result from Trip Generation - Trip production
Tij
Ti
Tj
Result from Trip Generation - Trip Attraction
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Gravity Model (1)

• The gravity model was adapted from Newtons Law
  of Gravitation
• The amount of gravitational force b/w masses is a
  function of the mass of the bodies and distance
  b/w them
• Apply the gravity model to determine where trips
  go.
• The gravitational force in the gravity model
  become the amount of travel b/w TAZs
• To convert the gravity model equation to
  represent the travel or number of trips as
  opposed to gravitational force, two modifications
  must be made
• Accessibility is used instead of distance
• Number of attractions is used instead of mass

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Gravity Model (2)
Definition of Newtons Law of Gravity The force
of attraction is proportional to the product of
the two masses, and inversely proportional to the
square of their mutual distance.
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Gravity Model (2)
Let
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T1,1 (124/434)11132
T2,1 (124/434)7321
T3,1 (124/434)5917
T4,1 (124/434)4312
T5,1 (124/434)14842
If the first round calculation is
B1 124/127 B1,3 (124/127)1817
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Iterative Balancing Methods
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How to solve

• Iterative balancing method
• In this operation, calculating Ai and Bj is
  iterative process. (Note first value of Bj is 1)

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Lab Exercise 3

• Trip distribution by using MS Excel
• Trip distribution by using Cube Voyager

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Using MS Excel

• Doubly constrained gravity model
• Iterative balancing method

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Using Cube Voyager

• MATRIX step
• Convert ASCII matrix to Voyager matrix
• DISTRIBUTION step
• Perform trip distribution

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MATRIX

• MATRIX is a module that processes zonal data and
  matrices according to user specified expressions.
  
• Zonal data and matrices can be input, and
  matrices and reports can be output.
• Various file formats for both input and output
  are supported.

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MATRIX

• Input
• Cost.txt
• Output
• Cost.mat

Zone number
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MATRIX script
Number of zones
Store Data from ASCII file to Voyager matrix
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MATRIX script
I
J
V
Cost.txt
variable width
J is implied
I
V
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DISTRIBUTION

• Usually the process uses the number of trip ends
  in each zone as the starting point.
• These margin totals are distributed to the rows
  and column of a generated matrix.
• Usually, additional information about some
  measure of travel between each zone pair should
  be included in the process.
• The most commonly used distribution process is
  the "gravity" model, but other processes are also
  employed.

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DISTRIBUTION

• Input
• Cost.mat (Impedance matrix)
• Tripends.txt (Trip Ends matrix)
• Lookup.txt (lookup table for friction factors)
• Output
• Odmatrix.mat

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DISTRIBUTION
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DISTRIBUTION
First column is named Z Second column is
P Third column is A
Set Production Matrix (P1) to Column P
Set Attraction Matrix (A1) to Column A
Maximum Iteration
Maximum RMS Error
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DISTRIBUTION
Lookup table file
Lookup file is 1 Name is FF
Curve Definition 1 (yf(x)) X value column 1 Y
value column 2
1 0.9512294245007 2 1.2796333483291
3 1.4907899456480 4 1.6374615061560
5 1.7414514918777 6 1.8146266328268
7 1.8644294372649 8 1.8959514004683
9 1.9128844548653 10 1.9180183554165
11 1.9135260438988 12 1.9011392749997
13 1.8822628162513 14 1.8580520700945
15 1.8294677920714 16 1.7973158564689
17 1.7622769103908 18 1.7249289805637
19 1.6857650385597 20 1.6452068759680
Interpolate the value which is not in the table
(i.e. x1.5)
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DISTRIBUTION
Impedance Matrix
Impedance matrix
Lookup table for Friction factor
Gravity model uses P1 and A1 as trip ends
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Lab Homework 2

• Trip distribution by using MS Excel
• You need to show the process to get the result
• Submit Excel file
• Trip distribution by using Cube Voyager
• You need to download the data (lab-hw02-data.zip)
• Submit a zip that contains your working folder