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Lowry Model

Lowry Model

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Lowry Model

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  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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. Inputs Changes to Analyze • Basic Jobs • Service worker: Population • Worker: Population • Friction Factor • Travel times

  15. 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

  16. Model Operation: Tab 1: Model and Inputs Model Operation

  17. 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

  18. Output – Page 1

  19. 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