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Lowry Model

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Lowry Model

Pam Perlich

URBPL 5/6020

University of Utah

- “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

- 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

- 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

- 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

- 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

- 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

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

- 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

- 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

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

- 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

- 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

- Basic Jobs
- Service worker: Population
- Worker: Population
- Friction Factor
- Travel times

- 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:

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

- 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