Transcript Lowry Model - University of Utah

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
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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
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Directly related to the size of the destinations
(gravitational pull)
Inversely related to travel time
 Gravity models are used to
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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
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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
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Sell their goods and services to non-locals
Exogenous (Determined outside the model)
 Non-basic or Residentiary or Retail Sector
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Sell their goods and services to locals
Includes government – schools, etc.
Endogenous (Determined by the model)
 Household Sector
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Size and residential location are endogenously
determined
Specification of the Model
 Basic is given (exogenous)
 Forecast is derived from regional projections
 Retail sector
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Size and location are determined by size and
location of the population
 Household sector
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Size is determined by employment
opportunities (including basic and nonbasic)
Location is determined by accessibility,
particularly to employment
Model Logic
Basic Sector
Demand for
Labor
Size of
Population
Distribution of basic jobs across
zones is given
Travel time (network) is given
Model generates population and
non-basic employment by zone
Demand for NonBasic
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
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Provides the basis of residential location decisions
based on employment locations and travel times
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
Lowry Model Structure
Basic Employment by
Zone - Exogenous
Residential Location of
Non-Basic Employees
Population Associated with
Non-Basic Employees
Residential Location of
Non-Basic Employees
Service Workers
(Non-Basic) by
Zone
Residential Location
of Basic Employees
Population Associated with
Non-Basic Employees
Converge to
Solution
Service Workers
(Non-Basic) by
Zone
Population Associated
with Basic Employees
Technical Notes: W
 Willingness to travel = W
 Travel time = 2
 F = friction factor
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F = 0  all sectors equally
attractive regardless of
travel time
Increase F  shorter travel
times become very attractive
1
W f
T
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
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Same Logic
Initial conditions in Cartwright = Baseline
Scenario is the first scenario on Project 4
 Two tabs
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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 1
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