Trip distribution lecture 9 norman w garrick
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Trip Distribution Lecture 9 Norman W. Garrick. 1. 3. 2. 5. 4. 8. 7. 6. Trip Generation. Socioeconomic Data Land Use Data. Input:. Output:. Trip Ends by trip purpose. Trip Generation Trip Distribution.

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Trip Distribution Lecture 9 Norman W. Garrick

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Trip distribution lecture 9 norman w garrick

Trip Distribution

Lecture 9

Norman W. Garrick


Trip generation

1

3

2

5

4

8

7

6

Trip Generation

Socioeconomic Data

Land Use Data

Input:

Output:

Trip Ends by trip purpose


Trip generation trip distribution

Trip Generation Trip Distribution

The question is… how do we allocate all the trips among all the potential destinations?

Trip MatrixorTrip Table

Zone 1


Trip distribution

Trip Distribution


Trip distribution1

Trip Distribution

  • We link production or origin zones to attraction or destination zones

  • A trip matrix is produced

    • The cells within the trip matrix are the “trip interchanges” between zones


Basic assumptions of trip distribution

Basic Assumptions of Trip Distribution

  • Number of trips decrease with COST between zones

  • Number of trips increase with zone “attractiveness”


Methods of trip distribution

Methods of Trip Distribution

  • Growth Factor Models

  • Gravity Model


Growth factor models

Growth Factor Models

  • Growth Factor Models assume that we already have a basic trip matrix

    • Usually obtained from a previous study or recent survey data


Growth factor models1

Growth Factor Models

  • The goal is then to estimate the matrix at some point in the future

    • For example, what would the trip matrix look like in 2 years time?

  • Trip Matrix, T (2018)

  • Trip Matrix, t(2008)


Some of the more popular growth factor models

Some of the More Popular Growth Factor Models

  • Uniform Growth Factor

  • Singly-Constrained Growth Factor

  • Average Factor

  • Detroit Factor

  • Fratar Method


Uniform growth factor model

Uniform Growth Factor Model


Uniform growth factor

Uniform Growth Factor

i= I = Production Zone

j= J = Attraction Zone

Tij = τ tij for each pair i and j

Tij =Future Trip Matrix

tij = Base-year Trip Matrix

τ = General Growth Rate


Uniform growth factor1

Uniform Growth Factor

If we assume τ = 1.2 (growth rate), then…

  • Trip Matrix, t(2013)

Tij = τ tij

= (1.2)(5)

= 6

  • Trip Matrix, T (2018)


Uniform growth factor2

Uniform Growth Factor

The Uniform Growth Factor is typically used for over a 1 or 2 year horizon

However, assuming that trips growat a standard uniform rate is a fundamentally flawed concept


The gravity model

The Gravity Model


The inspiration for the gravity model

The Inspiration for the Gravity Model

The big idea behind the gravity model is Newton’s law of gravitation…

The force of attraction between 2 bodies is directly proportional to the product of masses between the two bodies and inversely proportional to the square of the distance

M1 M2

F = k

r2


Some of the variables

Some of the Variables

Tij = Qij= Trips Volume between i & j

Fij=1/Wcij = Friction Factor

Wij= Generalized Cost (including travel time, cost)

c= Calibration Constant

pij= Probability that trip i will be attracted to zone j

kij= Socioeconomic Adjustment Factor

Tij = Trips between i & j

i = production zone

j = attraction zone

Tij = f (Pi, Aj, Cij)

Cij = Generalized cost of trip from i to j


The gravity model1

The Gravity Model

The bigger the friction factor, the more trips that are encouraged

Pi Aj FijKij

Tij =Qij =

= Pipij

ΣAjFijKij

(Productions)(Attractions)(Friction Factor)

=

Sum of the (Attractions x Friction Factors) of the Zones

Fij = 1 / Wcij

or ln F = - c ln W


To apply the gravity model

To Apply the Gravity Model

What we need…

  • Productions, {Pi}

  • Attractions, {Aj}

  • Skim Tables {Wij)

    • Target-Year Interzonal Impedances


Gravity model example 8 2

Gravity Model Example 8.2

  • Given:

    • Target-year Productions, {Pi}

    • Relative Attractiveness of Zones, {Aj}

    • Skim Table, {Wij}

    • Calibration Factor, c = 2.0

    • Socioeconomic Adjustment Factor, K = 1.0

  • Find:

    • Trip Interchanges, {Qij}


Given

Find Trip Interchanges, {Qij}

Find Denominator of Gravity Model Equation {AjFijKij}

Calculate Friction Factors, {Fij}

Find Probability that Trip i will be attracted to Zone j, {pij}

Given…

1

F11=

=

0.04

52

A2F12K12

Calibration Factorc = 2.0 Socioeconomic Adj. FactorK = 1.0

Target-Year Inter-zonal Impedances, {Wij}

Given…

Calculate Friction Factors, {Fij}

1

Fij =

=

Wcij

Find AjFijKij

AjFijKij=A2F12K12

(3)(0.01)(1.0) = 0.03

Find Probability that Trip from i will be attracted to Zone j, {pij}

0.03

p12 =

= 0.5838

=

Σ(AjFijKij)

0.0514

Find Trip Interchanges, {Qij}

Q12 = P1p12 = (1500)(0.5838) = 876


Given1

Find Trip Interchanges, {Qij}

Find Denominator of Gravity Model Equation {AjFijKij}

Calculate Friction Factors, {Fij}

Find Probability that Trip i will be attracted to Zone j, {pij}

Given…

1

F23=

=

0.01

102

A3F23K23

Calibration Factorc = 2.0 Socioeconomic Adj. FactorK = 1.0

Target-Year Inter-zonal Impedances, {Wij}

Given…

Calculate Friction Factors, {Fij}

1

Fij =

=

Wcij

Find AjFijKij

AjFijKij=A3F23K23

(2)(0.01)(1.0) = 0.02

Find Probability that Trip from i will be attracted to Zone j, {pij}

0.02

p23 =

= 0.1233

=

Σ(AjFijKij)

0.1622

Find Trip Interchanges, {Qij}

Q12 = P2p23 = (0)(0.1233) = 2


Given2

Find Trip Interchanges, {Qij}

Find Denominator of Gravity Model Equation {AjFijKij}

Calculate Friction Factors, {Fij}

Find Probability that Trip i will be attracted to Zone j, {pij}

Given…

1

F23=

=

0.01

102

A3F23K23

Calibration Factorc = 2.0 Socioeconomic Adj. FactorK = 1.0

Target-Year Inter-zonal Impedances, {Wij}

Given…

Calculate Friction Factors, {Fij}

1

Fij =

=

Wcij

Find AjFijKij

AjFijKij=A3F23K23

(2)(0.01)(1.0) = 0.02

Find Probability that Trip from i will be attracted to Zone j, {pij}

0.02

p23 =

= 0.1233

=

Σ(AjFijKij)

0.1622

Find Trip Interchanges, {Qij}

Q12 = P2p23 = (0)(0.1233) = 2


Trip distribution lecture 9 norman w garrick

Keep in mind that the socioeconomic factor, K, can be a matrix of values rather than just one value


The problem with k factors

The Problem with K-Factors

  • Although K-Factors may improve the model in the base year, they assume that these special conditions will carry over to future years and scenarios

    • This limits model sensitivity and undermines the model’s ability to predict future travel behavior

  • The need for K-factors often is a symptom of other model problems.

    • Additionally, the use of K-factors makes it more difficult to figure out the real problems


Limitations of the gravity model

Limitations of the Gravity Model

  • Too much of a reliance on K-Factors in calibration

  • External trips and intrazonal trips cause difficulties

  • The skim table impedance factors are often too simplistic to be realistic

    • Typically based solely upon vehicle travel times

      • At most, this might include tolls and parking costs

    • Almost always fails to take into account how things such as good transit and walkable neighborhoods affect trip distribution

    • No obvious connection to behavioral decision-making


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