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,  Ereserve:

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 Basic Sector Demand for Labor Size of Population Demand for Non- Basic Distribution of basic jobs across zones is given Travel time (network) is given Model generates population and non-basic employment by zone

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 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 Basic Employees Population Associated with Non-Basic Employees Service Workers (Non-Basic) by Zone Residential Location of Non-Basic Employees Population Associated with Basic Employees Service Workers (Non-Basic) by Zone Residential Location of Non-Basic Employees Population Associated with Non-Basic Employees Converge to Solution

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 Model Operation: Tab 1: Model and Inputs

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

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