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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

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:

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

### 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

• 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 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

• 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

• 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

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

• 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

• 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

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

• 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

• 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

• Basic Jobs

• Service worker: Population

• Worker: Population

• Friction Factor

• Travel times

### 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 Operation:

Tab 1: Model and Inputs

### Model Operation

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 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