Chapter 5 - International and Regional Transportation

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Transcript Chapter 5 - International and Regional Transportation

Transport Geography

Chapter 5 – International and Regional Transportation

Methods

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Method 1

Spatial Interactions

Conditions for the Realization of a Spatial Interaction

Complementarity Demand Supply A Alternative Opportunity A C B Supply B Demand Transferability A B

Representation of a Movement as a Spatial Interaction

i j

Movement Spatial Interaction Centroid

i j

Centroid

Constructing an O/D Matrix

A D Spatial Interactions B C E A B C D E Tj A

0 0 0 20 0 20 0 0

0 0 0 0

O/D Matrix C

50 60 0 80 90 280

0 0 30 0 10 40

0 30 0 20 0 50

50 90 30 120 100

390

Relationship between Distance and Interactions

T(B-A)

T(C-A)

T(D-A)

A B C D A B C D Distance (friction of)

• The basic assumption concerning many spatial interaction models is that spatial interactions are a function of the attributes of the places of origin, the attributes of the places of destination and the friction of distance interaction model is as follows: between the origins and the destinations. The general formulation of the spatial

T ij





V i

W j

S ij

 • Tij = Interaction between location i (origin) and location j (destination). Its units of measurement are varied and can involve people, tons of freight, traffic volume, etc. It also concerns a time period such as interactions by the hour, day, month, or year. • Vi = Attributes of the location of origin i. Variables often used to express these attributes are socio-economic in nature, such as population, number of jobs available, industrial output or gross domestic product. • Wj = Attributes of the location of destination j. • Sij = Attributes of separation between the location of origin i and the location of destination j. Also known as transport friction. Variables often used to express these attributes are distance, transport costs, or travel time. • The attributes of V and W tend to be paired to express complementarity in the best possible way. For instance, measuring commuting flows (work-related movements) between different locations would likely consider a variable such as working age population as V and total employment as W.

• From this general formulation, three basic types of interaction models can be constructed: – Gravity model. Measures interactions between all the possible location pairs. – Potential model. Measures interactions between one location and every other locations. – Retail model. Measure the boundary of the market areas between two locations competing over the same market.

Three Basic Types of Interaction Models

General Formulation:

T ij



V i



S ij

W j

T ij = 10.9

i 35 T ji = 10.9

S ij = 8 j 20

Gravity Model

T ij





V i

W j

S ij



T i

 

j W S ij

k 35 T i = 3.8

1.0

6 2.2

i j 20 3 0.6

5 l 15

Potential Model

V i T ij S ij j W

B ij



S ij

1 

W j V i

B ij = 4.9

j 15 7 i 35 B ik = 2.8

6 k 40

Retail Model

Method 2

The Gravity Model

Application of an Elementary Spatial Interaction Equation 2,000,000

400 km

2,000,000

Centroid (i) Weight (P)

k = 0.00001

(people per week)

Distance (D) Constant (k) Z

1,000,000

Interaction (T)

2,000,000

Y W X Y Z Tj W Elementary Formulation

T ij



k P i



P j D ij

X Y Z Ti

100,000 100,000 50,000 25,000 100,000 175,000 50,000 25,000 100,000 175,000 50,000 50,000 25,000 25,000 350,000

Application of a Simple Spatial Interaction Equation 2,000,000   = 0.95

= 1.05

2,000,000

  = 1.03

= 0.96

400 km   = 1.0

= 0.95

2,000,000 k = 0.00001

(people per week)

Centroid (i) Weight (P) Distance (D) Constant (k) Z

1,000,000   = 1.2

= 0.4

Interaction (T) Exponent W X Y Z Tj W

6,059

Simple Formulation

T ij



k P i

 

D ij



P j



X Y Z

71,378 2,203 1 6,059 19,420 153,893 244,692 2,203 1

71,378 8,263 19,420 153,893 252,954

Effects of beta, alpha and lambda on Spatial Interactions

100 90 80 70 60 50 40 30 20 10 0 0 Beta 5 10 Distance 15 0.25

0.5

1 1.5

2 20 40 30 20 10 0 100 90 80 70 60 50 0 Alpha and Lambda 0.25

0.5

1 1.5

2 5 10 Population 15 20

Chicago’s beta values for air transportation, 1949 1989 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990