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Lowry Model. Pam Perlich URBPL 5/6020 University of Utah. Reading / Model. “Urban Form: The Lowry Model of Population Distribution” Chapter 7 from: Modeling the World in a Spreadsheet , Timothy Cartwright, John Hopkins University Press, 1993. Ereserve:.

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Lowry model

Lowry Model

Pam Perlich

URBPL 5/6020

University of Utah


Reading model

Reading / Model

  • “Urban Form: The Lowry Model of Population Distribution”

  • Chapter 7 from:

  • Modeling the World in a Spreadsheet, Timothy Cartwright, John Hopkins University Press, 1993.

  • Ereserve:

http://ereserve.lib.utah.edu/ereserve/trms/annual/URBPL/5020/Perlich/urban.pdf


Gravity models

Gravity Models

  • Planners need small area forecasts of population and employment

  • Travel models require small area forecasts

  • Transportation networks

    • Distance

    • Travel time

    • Capacity

  • Gravity models specify interactions between origins and destinations


Gravity model basics

Gravity Model Basics

  • Given a set of origins, destinations, and travel times, trips to destinations are

    • Directly related to the size of the destinations (gravitational pull)

    • Inversely related to travel time

  • Gravity models are used to

    • Analyze commuting and other travel patterns

    • Determine optimal location for facilities and services

    • Allocate regional projections to specific locations within the region


Lowry model1

Lowry Model

  • 1960s – Ira Lowry

  • Spatial interaction model

  • Modeling innovations

    • Sub-regional forecasts were generated to control to regional totals

    • Employment, population, and transportation were combined in one model

  • Many variations and extension have been subsequently developed


Sectors in lowry model

Sectors in Lowry Model

  • Basic or Export Sector

    • Sell their goods and services to non-locals

    • Exogenous (Determined outside the model)

  • Non-basic or Residentiary or Retail Sector

    • Sell their goods and services to locals

    • Includes government – schools, etc.

    • Endogenous (Determined by the model)

  • Household Sector

    • Size and residential location are endogenously determined


Specification of the model

Specification of the Model

  • Basic is given (exogenous)

    • Forecast is derived from regional projections

  • Retail sector

    • Size and location are determined by size and location of the population

  • Household sector

    • Size is determined by employment opportunities (including basic and nonbasic)

    • Location is determined by accessibility, particularly to employment


Model logic

Model Logic

Size of Population

Demand for Labor

Basic Sector

Distribution of basic jobs across zones is given

Travel time (network) is given

Model generates population and non-basic employment by zone

Demand for Non-Basic


Model inputs

Model Inputs

  • Basic jobs by zone

  • Transportation network: travel times between every pair of zones (generalized cost matrix)

  • Ratio of population to workers

  • Ratio of service (non-basic) workers to population

  • Friction factor (willingness to travel)

  • Location probability matrix

    • Provides the basis of residential location decisions based on employment locations and travel times


Computation sequence

Computation Sequence

  • Basic job locations by zone (assumed)

  • Location probability matrix  residential zones of basic workers

  • # workers per zone  population x zone

  • Population x zone  number of service jobs x zone

  • Location probability matrix  residential zones of service sector workers


Lowry model structure

Lowry Model Structure

Basic Employment by Zone - Exogenous

Residential Location of Basic Employees

Population Associated with Non-Basic Employees

Residential Location of Non-Basic Employees

Converge to Solution

Population Associated with Non-Basic Employees

Service Workers (Non-Basic) by Zone

Residential Location of Non-Basic Employees

Service Workers (Non-Basic) by Zone

Population Associated with Basic Employees


Technical notes w

Technical Notes: W

  • Willingness to travel = W

  • Travel time = 2

  • F = friction factor

    • F = 0  all sectors equally attractive regardless of travel time

    • Increase F  shorter travel times become very attractive


Technical notes probabilities

Technical Notes: Probabilities

  • Convert travel times to an index

  • Divide each component travel time in a zone by the total for the zone

  • These become probabilities

  • Location probability matrix


Inputs changes to analyze

Inputs Changes to Analyze

  • Basic Jobs

  • Service worker: Population

  • Worker: Population

  • Friction Factor

  • Travel times


Model operation

Model Operation

  • Cartwright Chapter 7

    • Same Logic

    • Initial conditions in Cartwright = Baseline

    • Scenario is the first scenario on Project 4

  • Two tabs

    • Inputs & Model – input cells are shaded yellow

    • Outputs

      • Basic assumptions as well as outputs

      • Compares scenarios to baseline


Model operation1

Model Operation:

Tab 1: Model and Inputs

Model Operation


Model operation2

Model Operation:

Tab 1: Model and Inputs

Model Operation

  • Inputs (shaded yellow):

  • Scenario Name

  • Scenario Description

  • Friction Factor

  • Population / Worker Multiplier

  • Service Worker – Population Ratio

  • By Zone:

  • Generalized Travel Costs / Time

  • Number of Basic Jobs


Output page 1

Output – Page 1


Output page 2

Output – Page 2

  • Note the comparisons to the baseline case. Scenario results minus baseline results = impact results. These three tables have conditional formatting as follows:

    • Green  scenario > baseline

    • Orange  scenario < baseline

    • No shading  scenario = baseline


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