Why Do Cities Form?
• Why does the Twin Cities exist?
• Why are the Twin Cities larger than Duluth
• Why is Chicago more important than St.
• What is inevitable, what is chance?
• A measure that relates the transportation network
to the pattern of activities that comprise land use.
• It measures the ease of reaching valued
• Accessibility “is perhaps the most important
concept in defining and explaining regional form
and function.” (Wachs and Kumagai 1973)
The Power of
• Top picture: two
“markets”: A-B and B-
• Middle Picture: six
A B C
markets: B-C, C-B, C-
A B C D
• Bottom Picture: twelve
markets: D-C, C-D, D-
B, B-D, D-A, A-D
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
• Do people value the
Law of the Network: Increasing or Decreasing Returns
absolute increase (each
S - Size of the
% Increase in S
person I am connected
to adds the same
• Or do people value the
relative change (I will
0 20 40 60
N - Number of Nodes
80 100 120
pay twice as much for a
S % Increase in S
network that is twice
• 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
• 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.
Network Size: Accessibilty:
• All nodes valued • Places are not equal
equally • Places (i, j) are
• Independent of type of weighted according to
• Independent of spatial • Considers spatial
separation of nodes separation of places.
Absolute vs. Relative
• 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
• Why does this matter?
Feedback: Positive and
Positive Feedback Systems Negative Feedback Systems
• More begets more • More begets less
• Less begets less. • Less begets more.
• Examples? • Examples?
Positive Feedback Positive Feedback
(A Vicious Circle) (A Virtuous circle)
- + -
Accessibility and Land
Network Access Development
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• If the model is correct, why don’t we live on
– Time - we just don’t live there yet
– We do, visit New York, Tokyo, Hong Kong
– Congestion and related costs to density limit the
– Population, food, energy are constraints
0 1 2 3 4 5 6
Number of Network Members (Quantity Demanded)
Multi-Modal & Multi-
Mode Jobs Workers Shops Other
Access By Mode &
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
($, 000) Average Journey to Work Time (minutes)
0 5 10 15 20 25 30 35
Distance from Center (miles)
Single Family Home Price ($, 000) Journey to Work Time (minutes)
• 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.
Tij = KiKj Oi Dj f(Cij) • Where
• Tij = Trips from i to j
O i Tij
• Oi = Productions of
trips at origin i
D j Tij
i • Dj = Productions of
1 trips at destination j
K j Dj f (Cijm ) • Ki, Kj = balancing
K iOi f Cijm
f Cija e
• For auto:
• For transit: f Cijt e
• Cija = peak hour auto travel
0.2 time between zones i and j;
0.05 • Cijt = peak hour transit
0 10 20 30 40
50 60 70 80 90
travel time between zones i
Illustration of Gravity
Testing the Gravity
• 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)
• MWCOG Household Travel Survey
– 8,000 households and 55,000 trips
• Accessibility Measures
Jobs and Housing
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.
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
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
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
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
Urban Economics suggests trade-off time &
- finding supported for auto accessibility
- not for transit accessibility
• 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.