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Unformatted text preview: Lecture 4 Lecture 4 Introduction to Network Models Introduction to Network Models and and Shortest Paths Shortest Paths Profs. Profs. Ismail Chabini Ismail Chabini and and Amedeo Odoni Amedeo Odoni 1.225 1.225 J (ESD 225) Transportation Flow Systems J (ESD 225) Transportation Flow Systems 1.225, 11/07/02 Lecture 4, Page 2 Lecture 4 Outline Lecture 4 Outline Conceptual Networks: Definitions Representation of an Urban Road Network (Supply) Shortest Paths (Reading: pp. 359367, 6.2.3 and 6.2.4 of R6) Introduction Dijkstras algorithm: example Dijkstras algorithm: statement Observations Extensions to Classical Shortest Path Problems Allornothing traffic assignment Zoning and Analysis Periods (Demand) Motivation for more advanced traffic assignment models Summary 1.225, 11/07/02 Lecture 4, Page 3 Conceptual Networks: Definitions Conceptual Networks: Definitions A network is: a set of nodes N and a set of links A nodes are also called vertices or points links are also called arcs or edges Directed networks : all links are directed Path : a sequence of links from one node to another node (i.e., (5,4)(4,3)(3,2)) A network is connected if there is at least one path from one node to another node (Net1 is connected whereas Net2 is not) Examples: 2 3 4 5 1 Net 1 2 1 4 3 Net 2 1.225, 11/07/02 Lecture 4, Page 4 Representation of an Urban Road Network Representation of an Urban Road Network Physical Conceptual Intersections Nodes Streets Links Zones Centroids Simple node representation 1.225, 11/07/02 Lecture 4, Page 5 Intersection Representations Intersection Representations Simple node representation: no direction differenciation no conflicting movement Subnetwork representation: explicit direction representation conflicting turns in an intersection are captured by internal links and their impedances Conceptual representation is not unique and depends on: type of analysis data availability to build, validate, and apply model accuracy vs. computation time tradeoff 1.225, 11/07/02 Lecture 4, Page 6 Shortest Path Problems Shortest Path Problems Basic problem: find a shortest path and the shortest distance between two nodes Basic problem is called the onetoone shortest path problem Types of shortest path problems: Onetoone Onetoall: find shortest paths from one node to all nodes...
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This note was uploaded on 12/06/2011 for the course ESD 1.225j taught by Professor Ismailchabini during the Fall '02 term at MIT.
 Fall '02
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