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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 0.970.08C ija • For auto: • For transit: f Cijt e 1.910.08C 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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