lecture51a

lecture51a - 1.225J (ESD 205) Transportation Flow Systems...

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1 Lecture 5 Lecture 5 Assignment on Traffic Networks Prof. Prof. Ismail Chabini Ismail Chabini and Prof. and Prof. Amedeo Amedeo R. R. Odoni Odoni 1.225 1.225 J (ESD 205) Transportation Flow Systems J (ESD 205) Transportation Flow Systems 1.225, 11/14/02 Lecture 5, Page 2 Lecture 5 Outline Lecture 5 Outline ¡ Summary from previous lectures: • Assignment on non-congested networks: All-or-nothing assignment • Volume-delay functions for “congested” networks ¡ Framework for static traffic assignment models ¡ Static traffic assignment: concepts ¡ Static traffic assignment: principles ¡ User Optimal (UO) and System Optimal (SO) static traffic assignment ¡ Summary
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2 1.225, 11/14/02 Lecture 5, Page 3 Non Non -Congested Road Network and O Congested Road Network and O -D Matrix D Matrix » » » » » » ¼ º « « « « « « ¬ ª 0 0 0 0 0 40 35 30 45 40 35 30 25 20 35 40 50 10 12 15 10 15 40 35 30 To 1 2 3 4 5 1 2 3 4 5 )] , ( [ j i t From O-D Matrix 1 2 3 4 5 4 8 3 1 2 4 Directed network 1 6 2 Mixed network 1 2 3 4 5 4 8 3 1 2 4 1 6 2 •In±R7,± t ( i , j ) means demand for O-D pair ( i , j ). ( t ( i , j ) does not mean travel time of link (i,j) • Other common notation: q ( i , j ) or q ij 1.225, 11/14/02 Lecture 5, Page 4 Assign O Assign O -D Flows Originating from Node 1 D Flows Originating from Node 1 1 2 3 4 5 3 1 2 Shortest path tree from node 1 2 (0,*) + (3,1) + (6,4) + (5,3) + (8,2) + 1 2 3 4 5 Assign flows originating from node 1 30+35+ 40+15 30+40+15 30+15 15 35 40 30 15 30+35+40+15
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3 1.225, 11/14/02 Lecture 5, Page 5 Assign O Assign O -D Flows Originating from Node 2 D Flows Originating from Node 2 Shortest path tree from node 2 1 2 3 4 5 Assign flows originating from node 2 15 12 10 1 2 3 4 5 4 3 1 2 (2,4) + (7,1) + (1,2) + (2,2) + (0,*) + 10+15 10+15+12+10 12 15 10 10 1.225, 11/14/02 Lecture 5, Page 6 Assign O Assign O -D Flows Originating from Node 3 D Flows Originating from Node 3 1 2 3 4 5 Assign flows originating from node 3 50 40+35+20 40+20 20 1 2 3 4 5 3 2 2 (3,3) + (0,*) + (2,3) + (5,2) + (3,4) + Shortest path tree from node 3 1 50+40+35+20 50 35 20 40
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4 1.225, 11/14/02 Lecture 5, Page 7 Assign O Assign O -D Flows Originating from Node 4 D Flows Originating from Node 4 1 2 3 4 5 Assign flows originating from node 4 35 25+35 25+30+ 35+40 40 Shortest path tree from node 4 1 2 3 4 5 4 3 2 (5,2) + (8,1) + (0,*) + (3,2) + (1,4) + 1 25+30+35+40 30 40 25 35 1.225, 11/14/02 Lecture 5, Page 8 Assign O Assign O -D Flows Originating from Node 5 D Flows Originating from Node 5 1 2 3 4 5 Assign flows originating from node 5 45 40 45+30+40 Shortest path tree from node 5 1 2 3 4 5 4 1 1 6 (5,2) + (6,5) + (2,2) + (0,*) + (1,5) + 35 45+30+35+40 40 35 30 45
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lecture51a - 1.225J (ESD 205) Transportation Flow Systems...

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