Accessibility

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Accessibility

• David Levinson

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Why Do Cities Form?

• Why does the Twin Cities exist?
• Why are the Twin Cities larger than Duluth or
  Fargo?
• Why is Chicago more important than St. Louis?
• What is inevitable, what is chance?

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Accessibility

• A measure that relates the transportation network
  to the pattern of activities that comprise land
  use.
• It measures the ease of reaching valued
  destinations.
• Accessibility is perhaps the most important
  concept in defining and explaining regional form
  and function. (Wachs and Kumagai 1973)

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The Power of Networks

• Top picture two markets A-B and B-A.
• Middle Picture six markets B-C, C-B, C-A, A-C
• Bottom Picture twelve markets D-C, C-D, D-B,
  B-D, D-A, A-D

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Mathematical Expression

• S N ( N-1)
• S Size of the Network
• N Number of Nodes (places)

• To illustrate
• With 2 nodes S 21 2
• With 3 nodes S 32 6
• With 4 nodes S 43 12. And so on.

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Relative vs. Absolute Change

• Do people value the absolute increase (each
  person I am connected to adds the same value)?
• Or do people value the relative change (I will
  pay twice as much for a network that is twice the
  size)?

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Measuring Point Accessibility

• Where
• Pj some measure of activity at point j (for
  example jobs)
• Cij the cost to travel between i and j (for
  example travel time by auto).

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Measuring Metropolitan Accessibility

• where
• A Accessibility
• Wi Workers at origin i
• Ej Employment at destination j
• f(Cij) function of the travel cost (time and
  money) between i and j.

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Network Size vs. Accessibility

• Network Size
• All nodes valued equally
• Independent of type of node
• Independent of spatial separation of nodes

• Accessibilty
• Places are not equal
• Places (i, j) are weighted according to size
• Considers spatial separation of places.

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Absolute vs. Relative Accessibility

• A transportation improvement reduces the travel
  time between two places. What happens?
• The absolute accessibility of the entire region
  increases. The pie increases
• The relative accessibility of the two places
  increases at a greater rate than the rest of the
  region. The slice of the pie going to those two
  places increases even more.
• Why does this matter?

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Feedback Positive and Negative

• Positive Feedback Systems
• More begets more
• Less begets less.
• Examples?

• Negative Feedback Systems
• More begets less
• Less begets more.
• Examples?

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Accessibility and Land Use
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Coruscant
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Constraints

• If the model is correct, why dont we live on
  coruscant?
• Time - we just dont live there yet
• We do, visit New York, Tokyo, Hong Kong
• Congestion and related costs to density limit the
  accessibility machine
• Population, food, energy are constraints

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Network Externalities
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Multi-Modal Multi-Purpose Accessibility
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Access By Mode Distance
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Journey to Work Time and Home Value by Ring
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Gravity Model

• Hypothesis The interaction between two places
  decreases with distance, but increases with the
  size of the two places.
• There is more interaction between Minneapolis and
  St. Paul than Minneapolis and Chicago, despite
  the fact that Chicago is bigger.
• Similarly there is more interaction between
  Minneapolis and Chicago than Minneapolis and Los
  Angeles.
• However, there is more interaction between
  Minneapolis and Los Angeles than Minneapolis and
  Las Vegas, despite the fact that Las Vegas is
  closer.

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Gravity Math

• Tij    KiKj Oi Dj f(Cij)

• Where
• Tij Trips from i to j
• Oi Productions of trips at origin i
• Dj Productions of trips at destination j
• Ki, Kj balancing factors solved iteratively

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f(Cij)

• For auto
• For transit
• Where
• Cija peak hour auto travel time between zones i
  and j and
• Cijt peak hour transit travel time between
  zones i and j.

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Illustration of Gravity Model
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Testing the Gravity Model

• It is hypothesized that living in an area with
  relatively high jobs accessibility is associated
  with shorter trips, as is working in an area of
  relatively high housing accessibility.
• (the doubly-constrained gravity model)

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Data

• MWCOG Household Travel Survey (1987-88)
• 8,000 households and 55,000 trips
• Accessibility Measures

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Jobs and Housing Accessibility and Commuting
Duration

• In the gravity model implicitly being tested
  here, average commute to work time is determined
  by three factors
• 1) a propensity (choices) function which relates
  willingness to travel with travel cost or time,
  (individual demand)
• 2) the opportunities (chances) available at any
  given distance or time from the origin, (market
  supply) and
• 3) the number of competing workers. (market
  demand)
• Propensity f ( tij , Income, Mode, Gender... )
• It is hypothesized that this underlying
  preference is relatively undifferentiated based
  solely on location.

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Geographic Factors

• 1) distance between the home and the center of
  the region (Di0) (the zero mile marker at the
  ellipse in front of the White House),
• 2) distance between workplace and the center
  (Dj0),
• 3) accessibility to jobs from the home (AiE),
• 4) accessibility to other houses from the home
  (AiR),
• 5) accessibility to other jobs from the workplace
  (AjE),
• 6) and accessibility to houses from workplace
  (AjR).

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Chart 1 Summary Hypotheses

• Trip-End
• Home-End Work-End
• (Origin) (Destination)
• 
  --------------------------------------------------
  ----------
• Accessibility AiE AjE
• to Jobs negative positive
• Accessibility AiR AjR
• to Houses positive negative
• Distance Di0 Dj0
• from Center positive negative

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Elasticities of Travel Time with respect to
Accessibility
AUTO COMMUTERS AUTO COMMUTERS TRANSIT COMMUTERS TRANSIT COMMUTERS
VARIABLE ELASTICITY VARIABLE ELASTICITY
AiEa -0.22 AiEt -0.12
AiRa 0.19 AiRt 0.05
AjEa 0.24 AjEt -0.25
AjRa -0.25 AjRt 0.07
Di0 0.25 Di0 0.31
Dj0 -0.16 Dj0 -0.09
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Dependent Variable Travel Time to Work
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Accessibility and Housing Value

• Urban Economics suggests trade-off time money
• - finding supported for auto accessibility
• - not for transit accessibility

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Conclusions

• The City is the Network.
• Location matters, important explanatory variable,
  but
• Density and J/H Balance (Accessibility) weak
  policy variables to influence commuting. ...
• Ignores self-selection process - creating more
  high density housing wont create more young or
  old who wish to live in those high density urban
  areas.

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