Chapter 5 Principles of Spatial
Interaction
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•
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•
•
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Introduction
The Interaction Matrix
The Bases for Spatial Interaction
Transportation Networks
Flows on Networks
Transport Impacts on Economic Activities
The Interaction Matrix
A
1
0
1
0
0
A
B
C
D
E
B
0
1
0
1
1
C
1
0
1
0
1
D
1
1
1
1
0
Direction of flow?
Connectivity Matrix
O
B
O
D
O
A
O
C
E
0
1
0
1
1
O
E
Measures of connectivity
Ratio: actual/potential links
In this example:
10 links of 20 potential:
Ratio = .5
Flow Matrices
• Example Fig. 5.2 (p. 78)
• Also our i/o table
• Why are patterns of flow organized as they
are around:
– Flows originating at particular places
– Flows terminating at particular places
– The routing structure used to move from origin
to destination
The Bases of Spatial Interaction
• Ullman’s three-part framework:
– Complementarity (place utility; alternative
scales in Figure 5.3)
– Transferability (cost re: distance)
– Intervening Opportunities (competing sources
of supplies)
• Ullman’s Research on railroad flows,
passenger flows, for data in the 1950’s,
and railroad flows for 1929.
Ullman’s Famous Railroad Map
Wheeler & Mitchelson’s Research
on Information Flows
• P. 82. (1) Information genesis, (2) hierarchy
of control, and (3) distance independence
- Information genesis – determined by center
corporate control points, not by a market
that demands the information
- Hierarchy of control – size mediates volume
- Distance has little impact the volume of
information flow
- Used to explain realignment of U.S. urban
hierarchy
City Systems and Relations With
Surrounding Territory
• Functional areas versus uniform regions:
the umland concept
• Figure 5.4 – distance decay in interaction
• Spreading of commuter fields: Figure 5.6
• The formalization of this concept by the
BEA – The system of BEA Economic Areas
(The dead idea of the Concorde on page 83:
Illustrates how forecasts of technology
are risky)
Transport Networks
• Influence of physical and political
geography on their configuration
Another Boundary Impact on
Transport Networks
See also Figure 5.8 in text
Taafee/Morrill/Gould Model of
Transport Development
• Figure 5.9 in text
• A development sequence similar to the
Vance model
–
–
–
–
Weak initial linkages
Penetration of remote territory
Development of more complex transport routes
Development of highly interconnected systems
The Location of Transport Routes
& Networks
From the isotropic plain to “real” landscapes:
water bodies & river corridors, hills,
mountains, swamps, oceans & the poles
• Seattle - impact of glaciation: water, hills
The underlying principle of complementarity
Cost components: fixed & variable
Configuration into networks
The Location of Transport Routes
& Networks
From the isotropic plain to “real” landscapes:
water bodies & river corridors, hills,
mountains, swamps, oceans & the poles
• Seattle - impact of glaciation: water, hills
The underlying principle of complementarity
Cost components: fixed & variable
Configuration into networks
Fixed & Variable (Operating) Costs
Mode
Rail or Highway
Fixed/Capital Costs
Land, Construction,
Rolling Stock
Pipeline
Land, Construction
Air
Land, Field & Terminal
Construction, Aircraft
Sea
Land for Port Terminals,
Cargo Handling
Equipment, Ships
Pedestrian/Bikeway Land, Construction
Operating Costs
Maintenance, Labor, Fuel
Maintenance, Energy
Maintenance, Fuel, Labor
Maintenance, Labor, Fuel
Maintenance
Network Options
Hybrid
Least Cost to Use
B
A
A
B
A
B
D
C
D
C
D
C
Maximum
Connectivity
Least Cost to Build
High Travel
Costs AC, BD
Benefit-Cost Evaluation of Network Choice:
- Benefits: relative travel cost (savings), interaction
- Costs: investment, operations
Evaluating Networks for
Maximum Net Benefits
(a)
(b)
(c)
(d)
5
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

4
3


7




Cost = 14, R = 25
Net Benefit 11


Cost = 19, R = 29
Net Benefit = 10




 10

Cost = 10
Revenue = 15
Net Benefit = 5
Cost = 12, R = 18
Net Benefit = 6
Impact of Multiple Transport
Modes on Routes
X

Water
10
Land
Costs: Land = $2/ton-mile
Sea = $1/ton mile
15
12
A B  C
7
6
10
Land
Y
XAY = 10*$1+10*$2 = $30
XCY = 15*$1+6*$2 = $27
XBY = 12*$1 +7*$2 = $26
Other Impacts on Network
Structure
• Construction costs of given mode in different
types of environments
• Impact of borders - political boundaries • Impact of politics (transcontinental RR;
current battle over RTA line)
• Impact of technology - mail flows; telephone
calls (flat long distance rates), the WEB,
“The End of Geography?”
Factors Influencing Transport Rates
1. Grouping freight rates into zones
2. Variations due to commodity characteristics
(a) Differences in cost of service related to:
(1) Loading characteristics
(2) Size of shipment
(3) Perishability and risk of damage
(b) Elasticity of Demand for Transportation
3. Variations due to traffic characteristics
(a) intermodal competition
pp. 91-96
(b) traffic density
(c) direction of haul
Desire Lines – Impact of Distance
on Interaction
The Gravity Model:
“Social Physics”
Iij = k * PiPj
Dijb
where I is interaction between place i and j,
p(i) and p(j) are populations of places I and j,
k is an empirically derived constant,
and D(i,j) is the distance between i and j,
raised to an empirically derived constant, b.
• Stewart, Ravenstein, Ullman
Example of Gravity Model: Visitors
to Olympic National Park
Olympic National Park, Continued
Olympic National Park, Cont.
Transport Impact on Development
• Punt here, to take up this topic later
(Janelle)
• Key point: transport (and communications)
improvements have reshaped the geography
of production
• Janelle’s argument
• The long-run reduction in the cost of the
friction of space