Lowry Model

1
Lowry Model

• Pam Perlich
• URBPL 5/6020
• University of Utah

2
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
3
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

4
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

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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

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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

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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

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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
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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

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Computation Sequence

1. Basic job locations by zone (assumed)
2. Location probability matrix ? residential zones
   of basic workers
3. workers per zone ? population x zone
4. Population x zone ? number of service jobs x zone
5. Location probability matrix ? residential zones
   of service sector workers

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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
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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

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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

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Inputs Changes to Analyze

• Basic Jobs
• Service worker Population
• Worker Population
• Friction Factor
• Travel times

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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

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Model Operation
Model Operation Tab 1 Model and Inputs
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Model Operation
Model Operation Tab 1 Model and Inputs

• 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

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Output Page 1
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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 gt baseline
• Orange ? scenario lt baseline
• No shading ? scenario baseline