Synthesizing Agents and Relationships for Land Use / Transportation Modelling

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Synthesizing Agents and Relationships for Land
Use / TransportationModelling
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Lecture Outline

• Introduction
• Previous Work
• Data
• New Methods
• Results

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Introduction

• How would land use, transportation patterns and
  emissions react to...
• High congestion charge?
• Greenbelt policy?
• Do nothing while population grows
• Major transportation projects
• Major extrapolations from current behaviour
• Too hard to predict conventionally

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Introduction

• Traditional 4-stage

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Introduction

• Integrated Land Use/Transportation Environment
  (ILUTE) model

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Introduction

• We cant build such a complicated model using
  conventional methods
• Instead, preferred approach is microsimulation
  model
• What is microsimulation?

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Introduction

• Conventional Model

Simulation Model
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Introduction

• Microsimulation Simulation Agents
• Models the state of agents
• Combined behaviour of agents yields system state
• 1. Begin with initial population in start year
• 2. Update population, year by year
• age persons, change family structures
• change jobs, move homes
• use this to predict annual travel patterns
• 3. Obtain travel patterns in forecast year

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Introduction

• Need an initial population in the start year
• List of agents and their attributes - e.g.,
• Number of persons, and their ages
• Number of vehicles
• Type of dwelling
• etc.
• But - complete list is unknown
• Population Synthesis used instead
• Use known data to create initial agents
• Result has known statistical properties
• Best estimate from limited data

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Introduction

• My results
• Improved method for population synthesis
• Allows more attributes for each agent
• New method for relationship synthesis
• Allows correct set of agents and correct set of
  relationships
• Created a synthetic population for ILUTE
• Persons, families, households and dwellings
• Complete 1986 population for GTHA

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Previous Work

• Two representations of set of agents
• List of agents and their attributes (as
  categories)?
• Contingency table
• One cell for each combination of attributes
• Cell contains count of number of agents

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Previous Work

• Data Limitations
• Patchwork of partial data
• Mostly, we have one-way margins
• Break down of a single attribute into a few
  categories
• Example look at how we can use one-way margins

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Previous Work
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Previous Work

• Iterative Proportional Fitting

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Previous Work

• Iterative Proportional Fitting

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Previous Work

• Iterative Proportional Fitting
• e.g., Biproportional Updating of O/D tables
• Exactly satisfies target margins
• Also minimizes discrimination information
  relative to source population
• Information theory maximum entropy
• Resulting PDF satisfies the constraints without
  assuming any information we do not possess

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Previous Work

• Many options for margins in 3D

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Previous Work

• Beckman, Baggerley McKay (1996)?
• State-of-the-art application of IPF for census
• Geography attribute gets special treatment
• Due to nature of data in PUMS and census tables
• Two approaches zone-by-zone, or all zones at
  once
• Treats final table as a PMF
• Monte Carlo draws used to integerize
• Hurts fit to target margins
• Limited number of attributes

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Previous Work

• Williamson, Birkin and Rees (1998)?
• Not IPF Combinatorial Optimisation
• List-based, instead of tables
• Pros
• good fit to target margins
• may handle more attributes
• Cons
• no guarantees about relationship with source
  sample
• not entropy maximizing
• slow

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Data

• Summary Tables
• Usually one attribute, by zone (2D margin)?
• Contingency table
• Large sample 20 or 100
• Sometimes 2-3 attributes by zone
• Used as Target Margins
• Public Use Microdata Sample (PUMS)?
• List almost all attributes, except zones
• Small sample (1-2)?
• Canada defined for each large Census
  Metropolitan Area (CMA)?
• Used as Source Sample

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Data
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Data
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Data
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Data

• Canadian Census includes three PUMS
• Persons
• Census families
• Households Dwellings
• Also summary tables related to each

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New Methods Sparsity

• Beckman et al.s approach doesnt work well with
  many attributes
• Computation becomes hard
• Huge memory requirement
• Slow
• Thirteen attributes on family agent
• Beckman Zone-by-Zone needs 1.4 GB memory
• Beckman Multizone needs 1,036 GB memory

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New Methods Sparsity

• Number of cells in multiway table grows
  exponentially with number of attributes
  (dimensions)?

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New Methods Sparsity
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New Methods Sparsity

• Large number of bins
• Most bins are zero
• Number of bins is larger than sample!

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New Methods Sparsity

• Is it meaningful to use many attributes?
• Tentatively, yes
• Not a meaningful 13-way distribution
• But, a link between many statistically valid
  low-order distributions (e.g., 3-way)?
• If acceptable, can we do better than standard
  IPF?
• Yes - use a sparse data structure instead of a
  complete array to represent table
• Store only non-zero cells in table

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New Methods Sparsity

• Same representation as Williamsons
  Combinatorial Optimisation
• But, uses IPF algorithm
• Maximum entropy guarantee fast
• Can implement either zone-by-zone or multizone
  IPF using sparse data structure

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New Methods Relationships

• Land use/transportation models have more types of
  agents
• Agents Persons, families, households, business
  establishments
• Objects Vehicles, dwellings

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New Methods Relationships

• Need to synthesize correct relationships
• Examples
• Which persons are married?
• Opposite sex, similar ages - usually
• Which household owns/rents a given dwelling?
• Number of rooms and number of persons should be
  correlated
• Earlier methods could guarantee correct PDF for
  one agent type, but not all simultaneously

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New Methods Relationships

• Family PUMS contains information about persons in
  family
• husband/wife ages child ages
• Can synthesize family agent
• Include some person attributes in family

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New Methods Relationships

• Then, conditionally synthesize persons on family
  attributes
• IPF result is a joint probability mass function
  P(AGE, EDU, INCOME, OCCUP, SEX, ...)
• Can convert to a conditional PMF P(EDU,
  INCOME, OCCUP, ... AGE, SEX)
• Synthesize, repeating for husband, wife, children

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New Methods Relationships

• Guarantees good fit for both agent types
• Correct Family PDF
• Correct Person PDF
• Simple, data-driven
• No rules
• No special data sources, models
• Provided that attributes can be aligned between
  agents

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Results
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Results
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Results

• Programmed in R
• A statistical programming platform
• Dynamic language, fast prototyping
• Good support for categorical data, contingency
  tables
• Toronto CMA 1.1 million households, 1.0 million
  families, 3.3 million persons
• Run time 2 hours, 7 minutes on older 1.5GHz
  computer
• Repeated for Hamilton and Oshawa CMAs

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Results
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Results

• Experiment
• Is there value in using really rich input data?
• Or does PUMS 1D tables give enough?
• Calculated fit against all available data
• SRMSE and G2 information theoretic statistics

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Results
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Results

• Improvement of result with additional data
  evident
• However, no statistical tests possible
• Monte Carlo stage causes some error
• My conditional synthesis introduces small amount
  of additional error
• Little difference between zone-by-zone and
  multizone methods

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Questions?