1. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. THE GEOGRAPHY OF TRANSPORT SYSTEMS Chapter 2 – Transportation Systems and Networks METHODS Copyright © 1999-2007, Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University, Hempstead, NY, 11549 USA. Jean-paul.Rodrigue@hofstra.edu You may use the figures within for educational purposes only. No modification or redistribution permitted. For more information: http://people.hofstra.edu/geotrans

2. THE GEOGRAPHY OF TRANSPORT SYSTEMS Method 1 Graph Theory: Definition and Properties

3. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Graph Representation of a Real Network Real Network Graph Representation

4. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Basic Graph Representation of a Transport Network 12 34 5 Vertex (Node) Edge (Link) Buckle

5. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Planar and Non-Planar Graphs PlanarNon-Planar AB

6. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Connections and Paths 1 2 3 4 Link Connection 123 B 123 C Path (1 to 3) A

7. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Length of a Link, Connection or Path 1 23 45 6 2 km 5 km 6 km 7 km 4 km 2 km 3 km

8. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Cycles and Circuits 1 23 45 6 Circuit Cycle

9. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Connectivity in a Graph 1 23 4 56 A 1 23 4 56 B

10. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Complementary Graph 1 23 45 1 23 45 1 23 45 GXY

11. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Root Node 1 23 45 6 8 7 Root

12. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Tree Graph 1 2 3 4 5 6 8 7 Root

13. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Articulation Node 1 2 3 4 5 A 1 2 3 4 5 B (Connected) 1 2 3 4 5 C (Unconnected) Removed

14. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Isthmus Connection 1 2 345 Isthmus

15. THE GEOGRAPHY OF TRANSPORT SYSTEMS Method 2 Graph Theory: Indexes and Measures

16. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Diameter of a Graph Shimbel Distance v1234567 1 0112213 2 1021324 3 1203122 4 2130213 5 2312011 6 1221102 7 3423120 1 2 3 4 5 6 7 Diameter = 4

17. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Diameter of a Graph - 2 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 A d = 2 B d = 3 C d = 4 D d = 3

18. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Number of Cycles evpu A 3520 B 5511 C 5412 D 6712 AB C D

19. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Order of a Node 2 1 1 2 Order (o) A 4 2 3 3 2 B 5 1 1 1 1 1 C 2 3 3 22 D Perfect hub Perfect spoke

20. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Pi Index and the Shape of Transportation Networks d Highly developed (High Pi) Least developed (Low Pi)

21. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Eta Index L(G)eEta A 80 km516.0 B 80 km711.4 A B

22. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Theta Index Q(G)vTheta A 3,500 t6583.3 B 3,500 t8437.5 A B

23. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Iota Index 1 3 1 A L(G)W(G)Iota A 80233.47 B 80223.63 1 3 1 3 1 4 4 1 1 11 11 B Order (o)

24. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Beta Index AB C D evBeta A 240.5 B 340.75 C 441.0 D 541.25

25. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Alpha Index A B C D u ( e-v+p ) 2v-5 Alpha A 030.0 B 130.33 C 230.66 D 331.0

26. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Gamma Index AB CD e3(v-2) Gamma A 490.44 B 690.66 C 890.88 D 991.0

27. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Under construction

28. THE GEOGRAPHY OF TRANSPORT SYSTEMS Method 3 Network Data Models

29. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. The ArcView Shapefile Model a b c d Main file (*.shp) Index file (*.shx) dBase table (*.dbf) a b c d id geomshp_len 101 102 103 104 105... 4507.4 3491.1 2321.8 682.9 1279.1... type 2 1 3 5 4... Predefined fields surface asphalt concrete asphalt gravel asphalt... width 85.3 45.1 75.9 35.2 60.3... lanes 4 2 4 2 4... name I95 Route 4 Pinewood Ridge Main... custom fields

30. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Topology of a Network Data Model Topology Node Bi-directional Link Directional Link

31. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Cartography of a Network Data Model Cartography 74 Maple Blvd. East Ave. Oakway West Ave. Highway Main Street Street Central Park City Hall Campus One-way Traffic light

32. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Geocoding in a Network Data Model Geocoding Address 150 151 170 172 210 212 189 209 211 219220 197 East Ave. 188 East Ave. 8 915 16 Matching link and address range 191

33. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Routing in a Network Data Model Routing Warehouse Pickup Delivery Route segment Turn penalty Start End

34. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Relational Database Representation of a Simple Network A B C D E Nodes IDLatLong A40.42345-75.1245 B40.31021-75.2510 C40.41882-74.9124 D40.25908-75.0031 E40.28990-74.7893 1 2 3 4 5 6 Links IDFromToOne_Way 1ACYes 2BA 3DB 4DCNo 5DE 6CE

35. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Creation of a Connectivity Matrix with a Link Table Links IDFromToOne_Way 1CAYes 2BA 3DB 4DCNo 5DE 6CE Connectivity Matrix (C) ABCDE A00000 B10000 C10011 D01101 E00110

36. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Turn Penalties at an Intersection Turn Penalty Table – Node A FromToPenalty 122 211 130 310 141 412 232 321 240 420 34 431 A 1 2 3 4

37. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Object-Oriented Network Model Transport Network LinkNode ID Length Capacity … ID Capacity Impedance … Inheritance Connection Class Properties A B a

38. THE GEOGRAPHY OF TRANSPORT SYSTEMS Method 4 Traffic Assignment

39. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Traffic Assignment Origin Destination Generation Attraction Which path? Cost Time Number of connections

40. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. 36 28 50 i jk i j k Origin / Destination Traffic in a Network Spatial Interactions and Traffic

41. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Demand Travel time 1 Assignment Transport costs 2 Two Perspectives for Considering Traffic

42. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. a c b d e f 30 25 20 15 30 25 Possible paths between a and f a-b-d-f, a-b-e-f et a-c-e-f a-b-d-f path (possible assignment = 20) a c b d e f 10 5 0 15 30 25 20 a-b-e-f path (possible assignment = 10) a c b d e f 0 5 0 5 20 25 30 a-c-e-f path (possible assignment = 20) Maximal traffic between a and f = 50 units. a c b d e f 0 5 0 5 0 5 5 50 0 Maximal Possible Traffic between a and f 1 2 3 4 Heuristic Method for Traffic Maximization

43. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. a c b d e f 30-1 25-2 20-2 15-1 30-1 25-2 25-1 Possible paths between a and f by order of cost: 1) a-b-e-f, 2) a-c-e-f and 3) a-b-d-f Assignment on path 1 (a-b-e-f) = 15 units 0 35 Units at minimal cost 35 a c b d e f 15-1 (15) 25-2 20-2 0-1 (15) 15-1 (15) 25-2 25-1 15 20 Assignment on path 2 (a-c-e-f) = 15 units a c b d e f 15-1 (15) 25-2 20-2 0-1 (15) 0-1 (30) 10-2 (30) 10-1 (15) 30 5 Assignment on path 3 (a-b-d-f) = 5 units Minimal cost = 130. Average cost = 3.7 per unit. a c b d e f 10-1 (20) 20-2 (10) 15-2 (10) 0-1 (15) 0-1 (30) 10-2 (30) 10-1 (15) 35 0 1 2 3 4 Heuristic Method for Costs Minimization

44. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Demand Global cost a b c d Marginal cost (a-b) Marginal cost (c-d) Types of Traffic Costs

45. Copyright © 1998-2007, Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University. For personal or classroom use ONLY. This material (including graphics) is not public domain and cannot be published, in whole or in part, in ANY form (printed or electronic) and on any media without consent. This includes conference presentations. Permission MUST be requested prior to use. Traffic Q(a,b) Cost g(Q(a,b)) c = 5 Linear cost function Non-linear cost function Traffic Cost Functions