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					Accessibility


       David Levinson
   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?
            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)
        The Power of
         Networks
                 • Top picture: two
                   “markets”: A-B and B-
                   A.
A   B

                 • Middle Picture: six
A   B    C
                   markets: B-C, C-B, C-
A   B    C   D
                   A, A-C
                 • Bottom Picture: twelve
                   markets: D-C, C-D, D-
                   B, B-D, D-A, A-D
           Mathematical
            Expression
       S = N ( N-1)        • To illustrate
S = Size of the Network:   With 2 nodes: S = 2*1 = 2
N = Number of Nodes        With 3 nodes: S = 3*2 = 6
  (places)                 With 4 nodes: S = 4*3 =12.
                            And so on.
              Relative vs. Absolute
                     Change
                                                                                           • Do people value the
                  Law of the Network: Increasing or Decreasing Returns
                                                                                             absolute increase (each
S - Size of the
  Network
 12000
                                                                         % Increase in S

                                                                               250%
                                                                                             person I am connected
 10000
                                                                               200%
                                                                                             to adds the same
  8000

                                                                               150%
                                                                                             value)?
  6000




  4000
                                                                               100%
                                                                                           • Or do people value the
  2000
                                                                               50%
                                                                                             relative change (I will
      0
          0         20         40           60
                                    N - Number of Nodes
                                                             80   100       120
                                                                               0%
                                                                                             pay twice as much for a
                                      S    % Increase in S
                                                                                             network that is twice
                                                                                             the size)?
     Measuring Point
      Accessibility
                     Where:
                     • Pj = some measure of
                       activity at point j (for

Ai   Pj f Cij      example jobs)
                     • Cij = the cost to travel
      j                between i and j (for
                       example travel time by
                       auto).
            Measuring
           Metropolitan
           Accessibility
                 where:
                             • A = Accessibility
                             • Wi = Workers at origin i
                         • Ej = Employment at
A   i Ej f Cij 
       W                       destination j
    i   j                • f(Cij) = function of the
                               travel cost (time and
                               money) between i and j.
       Network Size vs.
        Accessibility
Network Size:              Accessibilty:
• All nodes valued         • Places are not equal
  equally                  • Places (i, j) are
• Independent of type of     weighted according to
  node                       size
• Independent of spatial   • Considers spatial
  separation of nodes        separation of places.
  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?
      Feedback: Positive and
            Negative
    Positive Feedback Systems              Negative Feedback Systems
    • More begets more                     • More begets less
    • Less begets less.                    • Less begets more.
    • Examples?                            • Examples?
Positive Feedback    Positive Feedback
                                                 Negative Feedback
(A Vicious Circle)   (A Virtuous circle)
         -                    +
                                                         +




         -                    +                          -
Accessibility and Land
         Use


   +
                +

          +            +
Network       Access       Development
       Coruscant                                                                            QuickTime™ an d a TIFF (Uncomp ressed) decompre ssor are need ed to see this p icture .




      QuickTime™ and a TIFF (Uncompressed ) decompressor are needed to se e this picture.




QuickTime™ an d a TIFF (Uncomp ressed) decompre ssor are need ed to see this p icture .
           Constraints
• If the model is correct, why don’t we live on
  coruscant?
  – Time - we just don’t 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
  Network Externalities
                                    Network Externalities
Price, Cost

  6




  5




  4

                                                                          Demand:n=1
                                                                          Demand:n=2
  3                                                                       Demand:n=3
                                                                          Demand:n=4
                                                                          Demand:n=*
                                                                          Revealed Demand
  2




  1




  0
      0       1            2           3            4             5   6
                  Number of Network Members (Quantity Demanded)
    Multi-Modal & Multi-
   Purpose Accessibility


Mode      Jobs   Workers   Shops   Other
Auto
Transit
Walk
Bike
                 Access By Mode &
Accessibility Index

  90000
                    Distance
  80000



  70000



  60000



  50000



  40000



  30000



  20000



  10000



      0
          0                 5            10              15            20               25            30              35
                                                 Distance from the center (miles)

              Access to Jobs by Auto   Access to Housing by Auto   Access to Jobs by Transit   Access to Housing by Transit
  Journey to Work Time
 and Home Value by Ring
Average Home Price
     ($, 000)                                                    Average Journey to Work Time (minutes)

350                                                                                                   50.0


                                                                                                      45.0
300

                                                                                                      40.0


250
                                                                                                      35.0


                                                                                                      30.0
200

                                                                                                      25.0

150
                                                                                                      20.0


                                                                                                      15.0
100


                                                                                                      10.0

50
                                                                                                      5.0


 0                                                                                                    0.0
      0          5   10               15               20           25              30           35
                                Distance from Center (miles)

                          Single Family Home Price ($, 000)    Journey to Work Time (minutes)
            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.
              Gravity Math
Tij = KiKj Oi Dj f(Cij)   • Where
                          • Tij = Trips from i to j
O i   Tij
      j
                          • Oi = Productions of
                            trips at origin i
D j   Tij
       i                  • Dj = Productions of
            1               trips at destination j
Ki 
      K j Dj f (Cijm )   • Ki, Kj = balancing
                            factors solved
           1                iteratively
Kj 
      K iOi f Cijm 
                                                                                f(Cij)
                                                                                                             f Cija   e
                                                                                                                             0.970.08C ija
                                                                                          • For auto:
                                                                                          • For transit: f Cijt   e
                                                                                                                       1.910.08C  0.265
                                                                                                                                      ijt      Cijt
                                 Friction Factors
Friction Factor
   0.4

                                                                                          Where:
                                                                                             
 0.35



   0.3
                                                                                          • Cija = peak hour auto travel
 0.25
                                                                                                
   0.2                                                                                      time between zones i and j;
 0.15
                                                                                            and
   0.1



 0.05                                                                                     • Cijt = peak hour transit
    0
         0        10   20   30       40
                                      Travel Time
                                                   50          60          70   80   90
                                                                                            travel time between zones i
                                                                                            and j.
                                       Friction-Auto    Friction-Transit
Illustration of Gravity
        Model
    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)
                     Data
•      MWCOG Household Travel Survey
    (1987-88)
    –        8,000 households and 55,000 trips
•       Accessibility Measures
       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.
    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).
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
Elasticities of Travel
 Time with respect to
    Accessibility
  AUTO     AUTO    TRANSIT  TRANSIT
COMMUTER COMMUTER COMMUTER COMMUTER
    S        S        S        S

 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
Dependent Variable:
Travel Time to Work
  VARIABLES         TRANSIT              AUTO
  AiEt, AiEa       -1.15E-03        -8.68E-05
                      (-2.27) **       (-4.86)   ***
  AiRt , AiRa       1.12E-03         1.18E-04
                       (0.85)           (2.75)   ***
  AjEt , AjEa      -1.14E-03         7.13E-05
                      (-2.56) **        (4.21)   ***
  AjRt , AjRa       1.05E-03        -1.47E-04
                       (0.75)          (-3.26)   ***
  Di0                    1.71             0.63
                       (9.71) ***       (5.82)   ***
  Dj0                   -1.67            -0.55
                      (-5.63) ***      (-3.77)   ***
  CONSTANT             44.12            23.29
                       (9.21) ***       (4.61)   ***
  Sample Size            346             1950
  Adj. r-squared        0.38             0.17
  F                    12.96            22.79
  Significance F           0                0
      Accessibility and
       Housing Value
Urban Economics suggests trade-off time &
   money
- finding supported for auto accessibility
- not for transit accessibility
              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 won’t create more young or old who wish to live in
  those high density urban areas.

				
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posted:2/22/2013
language:English
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