Time and Space David Levinson Accessibility David Levinson.

Time and Space

David Levinson

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)

LeCorbusier• LeCorbusier, the controversial twentieth century Swiss architect and planner once said

“A house is a machine for living in”

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Villa Savoye, 1928



Machine for Access

• Transportation is “The Machine for Mobility”

• Our legs, our wheels, our tracks, our roads, our wings help us move.

• We know that since the buildout of the Interstate, mobility has been decreasing (due to congestion)

• But we cannot assess the system as a whole unless we know what we are moving to.

• The City is “The Machine for Access”

• The formation of the city allows us to reach more things in less time.

• Transportation is necessary, but so are the activities,(located at places) to be reached.

• Change in land use may mean that despite increasing congestion, we still have rising accessibility





Mobility vs. Accessibility

Manitoba• High Speeds• Few Destinations

• High Mobility

Manhattan• Low Speeds• Many Destinations• High Accessibility

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 = 2

With 3 nodes: S = 3*2 = 6

With 4 nodes: S = 4*3 =12. And so on.

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(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.

€

f Cija( ) = e−0.97−0.08Cija

€

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

Isochron: How Far Can You Go in a Given Time

• Multiply by number of things in each ring

• See how it changes over time.

• Works for individual points.

• Need to see region as a whole.



Measuring Accessibility

€

Ai = Pj f Cij( )j

∑Where:

• Ai = accessibility at point i

• 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).

• A = Overall Accessibility

• Wi = Workers at origin i

A = WiAi( )i∑

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.

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

Relative vs. Absolute Change

Or do people value the relative change (I will pay twice as much for a network that is twice the size)?

Do people value the absolute increase (each person I am connected to adds the same value)?

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.




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

Or maybe it is just this guy

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

Access By Mode & Distance (DC 1988)

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)

Journey to Work Time and Home Value by Ring

(DC 1988, 1991)

Ultimate Aim: Multi-Modal & Multi-Purpose Accessibility

Over Time

Jobs Labor Shops Play Other

Auto

Transit

Walk

Bike

Requirements

• Point to Point travel times for all points– On limited access freeways (and ramp meters),

– linking roads (signalized arterials) and

– local roads, – by transit, walking, biking



Land uses / Activities for all points in region



Questions

• Is congestion rising?• Are commutes getting longer?

• Are people spending more time commuting?

• Are people spending more time traveling?

• How do the declining trip times and increasing speeds reconcile with the general perception of worsening congestion?

• What do travel and activity depend on?

• Is spatial determinism correct?

• Does income matter?• Does location matter?

• Does demographics matter?

Is Sprawl the Problem or the Solution

• If Sprawl is the Solution … what is the problem? [ …. ]

Rational Locator Hypothesis

• “Rational Locators,” including both individual households and firms, respond to changes in transportation supply by siting themselves to reduce commuting times … The key policy implication we see is that over the long term, individual Locators act rationally to balance total costs as measured in dollars and minutes, and total benefits, as measured in proximity, space, and other preferences. These individual calculations result in the polycentric, and dispersing, urban form that exists today throughout the United States. (Levinson and Kumar 1994).

Restating

• The Rational Locator Hypothesis thus posits that individuals can, if they choose, maintain approximately steady journey-to-work travel times in the face of rising congestion and increasing distance between home and work by adjusting their home and workplace.

• Dispersion and decentralization are conscious choices that enable rational locators to achieve their goals.

• Consistent with, but not implying travel time budget hypothesis.

Evidence

• Large number of studies have shown consistency in gross travel budgets.

• However, average travel times in many metropolitan areas seem to be rising (Census data)

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.

Illustration of Gravity Model

Model of Willingness to Travel and Opportunities

0.001

0.01

0.1

1

0 10 20 30 40 50 60 70

Travel Time (Minutes)

Probability

0

2000000

4000000

6000000

8000000

10000000

12000000

Willingness To Travel Probability of Making a Trip Cumulative Jobs

Cumulative Jobs

=e-0.08*Time

=1000*3.14*Time 2

Results of Model for Different City Sizes

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90

City Size (minutes)

Mean Travel time

Mean Travel Time (alpha=-0.08, density=1000)

Jobs

Implications of Gravity Model

• As city size increases, mean commuting time increases (we have a left-truncated distribution, so as the right branch extends outward, the average must increase).

• Travel time, is largely independent of density – except to the extent that density changes network speed.

• If preferences shift, mean travel time will change inward or outward.

• If congestion rises, more opportunities will be farther away in terms of time, and fewer nearby – implying that average commuting time rises.

Actual Data

• Travel to Work Times for Albany and Anchorage (vertical line is the mean)

0.00

0.05

0.10

0.15

0.20

0.25

0 30 60 90

Travel Time (minutes)

Frequency

Census Data

Poisson Model

0.00

0.05

0.10

0.15

0.20

0.25

0 30 60 90

Travel Time (minutes)

Frequency

Census Data

Poisson Model

Inter-Metropolitan Data Summary

Variable Mean Std. Dev. Minimum MaximumMean Commute(minutes)

25.7 3.7 19.1 41.0

Congestion Index 1.00 0.17 0.69 1.52

Population 2,088,800 1,922,507 291,288 9,519,338

Population Density(persons/sq. mi.)

730.6 1,046.8 39.7 8,158.7

Housing Units 828,115 724,601 119,654 3,680,360

Housing Density(units/sq. mi.)

290.1 411.3 16.7 3,223.8

Area (sq. mi.) 4,490.4 5,760.6 751.4 39,719.1

Median Income ($) 42,714 8,313 23,992 76,752

Regression Results for Mean Commuting Time

Variable Norm. Coeff. Coefficient t-stat Prob.

[Constant] 0.560 1.44 x 101 7.37 0.000Congestion Index 0.236 6.08 x 100 2.88 0.006Population 0.038 4.65 x 10-7 1.96 0.055Population Density 0.044 1.54 x 10-3 4.19 0.000Area 0.018 9.13 x 10-5 1.84 0.071Income 0.106 6.38 x 10-5 1.87 0.067

Sample Distribution (Survey Size in Parenthesis)

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Metropolitan WashingtonDC - 1988 (10350)

Metropolitan WashingtonDC - 1994 (8509)

Metropolitan Twin Cities -1990 (12884)

Metropolitan Twin Cities -2000 (7705)

Male WorkersFemale WorkersMale Non-workersFemale Non-Workers

Rational Allocator Hypothesis

• Changes in Time Allocation due to rising female labor force participation can be understood in context of Bounded Rationality

• “Allocators” - shape temporal activity patterns within household, spending time and money to produce household goods, maximizing utility.

• Technology, rising per capita income, and labor force participation create substitution of in-house activities by out-of-home activities. E.g. eating out, day care.

Activity Duration Calculation

Activity durations

per day, in minutes, for 1968, 1988 and 1994, Washington D.C. adults

18-65

Work outside home Non-workers

Male Female Male Female

Mean S.D. Mean S.D. Mean S.D. Mean S.D.Activity Year Home 1968 786 143 831 135 1120 229 1225 164

1988 799 150 826 153 1143 196 1165 1871994 761 131 795 129 1093 219 1155 190

1994(full) 760 133 797 132 1104 219 1158 194

Work 1968 515 143 487 116 0 0 1988 472 173 447 165 0 0 1994 499 145 476 133 0 0

1994(full) 498 149 473 133 0 0

Work-related 1968 0 0 0 0 1988 0 0 0 0 1994 20 72 10 49 0 0

1994(full) 21 75 10 48 0 0

Shop 1968 7 24 10 32 27 62 52 771988 10 41 13 41 31 62 50 901994 8 28 13 28 33 75 47 77

1994(full) 8 27 13 28 34 75 47 76

Other 1968 44 100 29 76 217 214 101 1431988 61 118 62 112 187 187 140 1561994 47 78 47 75 220 204 154 165

1994(full) 46 77 48 76 207 197 149 163

Travel 1968 88 51 82 48 76 58 62 501988 99 63 92 61 80 64 85 731994 104 57 99 56 93 69 85 67

1994(full) 108 60 100 57 95 73 86 72

Activity duration per day,

in minutes, for 1990 and 2000,

Twin Cities, adults 18-65

Workers Non-workers

Male Female Male Female

Mean S.D. Mean S.D. Mean S.D. Mean S.D.Activity Year Home 1990 777 127 816 137 1092 227 1176 182

2000(7county) 777 128 802 131 1044 248 1122 200

2000(full) 775 130 805 132 1045 248 1124 202

Work 1990 485 143 466 129 0 0

2000(7county) 494 133 476 127 0 0

2000(full) 497 136 476 125 0 0

Work-related 1990 29 81 11 45 83 168 14 68

2000(7county) 14 58 9 43 96 188 33 112

2000(full) 14 57 9 43 91 185 32 112

Shop 1990 7 22 15 32 21 43 41 61

2000(7county) 8 20 14 32 26 53 36 57

2000(full) 8 20 14 30 25 52 38 64

Other 1990 53 85 55 79 144 167 131 144

2000(7county) 56 87 56 83 168 189 161 157

2000(full) 55 90 54 82 171 191 158 156Travel 1990 88 53 77 43 101 82 78 59

2000(7county) 90 53 84 45 106 95 87 57

2000(full) 90 55 83 46 107 95 88 60

Change in Travel Times

-5% 0% 5% 10% 15% 20% 25% 30%

Twin Cities (2000 - 1990):Geographical Control - Home

Based Work

Twin Cities (2000 - 1990):No Geographical Control -

Home Based Work

Washington DC (1994-1988): Geographical Control

- Home To Work

Washington DC (1994-1988): No GeographicalControl - Home To Work

TransitAuto-3Auto-2Auto-1

Intra-County Trips

0 5 10 15 20 25 30

Anoka

Carver

Dakota

Hennepin

Ramsey

Scott

Washington

Home Based Work Trip Travel Time (minutes)

2000

1990

Resolving the Paradox

Suburban Arterial

Urban Radial

1968 Speed 55 MPH 25 MPH

1988 Speed 40 MPH 20 MPH

1968 Traffic

10% 90%

1988 Traffic

50% 50%

Weighted Averages

• While Speed drops on both facilities, Average Speed rises from 28 MPH to 30 MPH.

• More generally, speed can drop on every facility from the day it opens as traffic increases, but if people increasingly use higher speed facilities, that use will outweight the speed drop.

• This may be of little comfort to the commuter whose work trip becomes worse every year until he relocates.

Myths?

1. The long commute is commonplace2. Jobs Housing Balance doesn’t

matter3. ‘Sprawl’ makes congestion worse4. Travel times are rising5. Transit investment will lower

travel times6. Most travel is work trips

For More Knowledge

• PA8202 - Networks and Places• PA5202 - American Cities 2

Questions

Time and Space David Levinson Accessibility David Levinson.

Documents

Transcript of Time and Space David Levinson Accessibility David Levinson.