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.

• 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

A B

A B

A B DC

C

Mathematical Expression

S = N ( N-1)S = Size of the

Network:N = Number of

Nodes (places)

• To illustrateWith 2 nodes: S = 2*1

= 2With 3 nodes: S = 3*2

= 6With 4 nodes: S = 4*3

=12. And so on.

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)?

Law of the Network: Increasing or Decreasing Returns

0

2000

4000

6000

8000

10000

12000

0 20 40 60 80 100 120

N - Number of Nodes

S - Size of the Network

0%

50%

100%

150%

200%

250%

% Increase in S

S % Increase in S

Measuring Point Accessibility

€

Ai = Pj f Cij( )j

∑

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).

Measuring Metropolitan Accessibility

€

A = Wi Ej f Cij( )( )j

∑ ⎛

⎝ ⎜

⎞

⎠ ⎟

i

∑

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.

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.

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

• More begets more• Less begets less.• Examples?

+

+

Positive Feedback(A Virtuous circle)

-

+

Negative Feedback

Negative Feedback Systems

• More begets less• Less begets more.• Examples?

-

-

Positive Feedback(A Vicious Circle)

Accessibility and Land Use

Ne t wo r k Acc e s s Deve l op m en t+ +

+

+

Coruscant

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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 ExternalitiesNetwork Externalities

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Number of Network Members (Quantity Demanded)

Price, Cost

Demand:n=1

Demand:n=2

Demand:n=3

Demand:n=4

Demand:n=*

Revealed Demand

Multi-Modal & Multi-Purpose Accessibility

Mode Jobs Workers Shops OtherAutoTransitWalkBike

Access By Mode & Distance

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 5 10 15 20 25 30 35

Distance from the center (miles)

Accessibility Index

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

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35

Distance from Center (miles)

Average Home Price ($, 000)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

Single Family Home Price ($, 000) Journey to Work Time (minutes)

Average 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• Oi = Productions of

trips at origin i • Dj = Productions of

trips at destination j• Ki, Kj = balancing

factors solved iteratively€

Oi = Tijj

∑

Dj = Tiji

∑

€

K i =1

K jDj f (Cijm )∑

€

K j =1

K iOi f Cijm( )∑

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.

Friction Factors

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40 50 60 70 80 90

Travel Time

Friction Factor

Friction-Auto Friction-Transit

€

f Cija( ) = e−0.97−0.08Cija

€

f Cijt( ) = e−1.91−0.08Cijt+ 0.265 Cijt

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-EndHome-End Work-End(Origin)

(Destination)

------------------------------------------------------------Accessibility AiE AjEto Jobs negative

positive

Accessibility AiR AjRto Houses positive negative

Distance Di0 Dj0from Center positive negative

Elasticities of Travel Time with respect to

AccessibilityAUTO

COMMUTERS

AUTO COMMUTER

S

TRANSIT COMMUTER

S

TRANSIT COMMUTER

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 AUTOAiEt, 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 1950Adj. r-squared 0.38 0.17F 12.96 22.79Significance 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.