# Accessibility by langkunxg

VIEWS: 0 PAGES: 38

• pg 1
```									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%
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)

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
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.

```
To top