Geographic Information Systems
Path Analysis and Network Applications

Mark Foley
mark.foley@dit.ie

Path Analysis

Network

Path Analysis

Cost distance measures follow the node-link representation: a lateral link connects two direct neighbours, and a diagonal link connects two diagonal neighbours.

Cost distance measures follow the node-link representation: a lateral link connects two direct neighbours, and a diagonal link connects two diagonal neighbours.

The cost distance of a lateral link is the average of the costs in the linked cells, for example, (1 + 2) / 2 = 1.5. The cost distance of a diagonal link is the average cost times 1.4142, for example, 1.4142 x ((1 + 5) / 2) = 4.2.

The cost distance of a lateral link is the average of the costs in the linked cells, for example, (1 + 2) / 2 = 1.5. The cost distance of a diagonal link is the average cost times 1.4142, for example, 1.4142 x ((1 + 5) / 2) = 4.2.

The cumulative cost from cell a to cell b is the sum of 1.0 and 3.5, the costs of two lateral links. The cumulative cost from cell a to cell c is the sum of 4.2 and 2.5, the costs of a diagonal link and a lateral link.

The cumulative cost from cell a to cell b is the sum of 1.0 and 3.5, the costs of two lateral links. The cumulative cost from cell a to cell c is the sum of 4.2 and 2.5, the costs of a diagonal link and a lateral link.

The cost distance for each link (c) and the least accumulative cost distance from each cell (d) are derived using the source cells (a) and the cost raster (b). See Box 17.2 for the derivation.

The cost distance for each link (c) and the least accumulative cost distance from each cell (d) are derived using the source cells (a) and the cost raster (b). See Box 17.2 for the derivation.

The least cost path (a) and the allocation raster (b) are derived using the same input data as in Figure above.

The least cost path (a) and the allocation raster (b) are derived using the same input data as in Figure above.

Network

First Ave. crosses Oak St. with an overpass. A nonplanar representation with no nodes is used at the intersection of Oak St. and First Ave.
First Ave. crosses Oak St. with an overpass. A planar representation with two nodes is used at the intersection: one for First Ave., and the other for Oak St. First Ave has 1 for the T-elev and F-elev values, indicating that the overpass is on First Ave.

First Ave. crosses Oak St. with an overpass. A planar representation with two nodes is used at the intersection: one for First Ave., and the other for Oak St. First Ave has 1 for the T-elev and F-elev values, indicating that the overpass is on First Ave.

Possible turns at node 341.

Possible turns at node 341.

Node 265 has stop signs for the east–west traffic. Turn impedance applies only to turns in the shaded rows.

Node 265 has stop signs for the east–west traffic. Turn impedance applies only to turns in the shaded rows.

Node 339 is an intersection between a southbound one-way street and an east–west two-way street. Notice –1 (no turn) in the shaded rows.

Node 339 is an intersection between a southbound one-way street and an east–west two-way street. Notice –1 (no turn) in the shaded rows.

Shortest Path Analysis

Link impedance values between cities on a road network.

Link impedance values between cities on a road network.

The Impedance Matrix among Six Nodes in Figure above

-1

-2

-3

-4

-5

-6

-1

20

53

58

-2

20

39

-3

53

39

25

19

-4

58

25

13

-5

13

13

-6

19

13

Shortest Paths from Node 1 to All Other Nodes in Figure above

From-node

To-node

Shortest Path

Minimum Cumulative impedance

1

2

p12

20

1

3

p13

53

1

4

p14

58

1

5

p14 + p45

71

1

6

p13 + p36

72