1. Route Choice Lecture 11 Norman W. Garrick

2. By Foot, Bus, Tram, Rail, Cable Car
Route Choice
By Foot, Bus, Tram, Rail, Cable Car
From Kirche Fluntern
To ETH-Hoenggerberg

3. Route Choice or Trip Assignment
Trip assignment is the forth step of the FOUR STEP process
It is used to determining how much traffic will use each link of the transportation system
Norman W. Garrick

4. Route Choice or Trip Assignment in 4 Step Process
Example
Consider two zones
Hartford CBD
West Hartford Center
Four Steps
Trip Generation - Determines production from WH Center
Trip Distribution - Gives QIJ - Trips from WH Center attracted to Hartford CBD
Modal Split - Fraction of QIJ using different modes of travel
Trip Assignment - What roads? What bus routes?
Norman W. Garrick

5. Characterizing Road or Transit Network for Trip Assignment
In trip assignment the road network is represented by links and nodes
Links - major roads including arterials, expressways and freeways (local roads are not usually included - this can be a problem in places like in WH Center were the local road network is very dense and carry a significant portion of the traffic)
Nodes - typically intersections or interchanges but could be other points that are important to the network
Each node is numbered
Links are specified by the nodes at the end
Each link is associated with an impedance (the impedance might not be the same in each direction
Norman W. Garrick

6. Example Road Network for Trip Assignment1 2 5 5 3 6 7 8 11 4 9 10
1, 2, 3, 4, 5 are zone centroids 12 14 13
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7. Network B 2 5 1 4 3 (3) (2) (2) (4) (7) (8) (4) (6) (5) (4)
Norman W. Garrick

8. 1 2 3 4 5 Link Array Network B 2 1 5 4 3 (3) (7) (2) (5) (4) (6) (8) J
Norman W. Garrick

9. 1 2 3 4 5 ? Link Array Network B I=1 2 1 5 4 3 (3) (7) (2) (5) (4) (6)
(8) 1 2 3 4 5 ? J I
Norman W. Garrick

10. 1 2 3 4 5 ? Link Array Network B I=1 2 1 5 4 3 (3) (7) (2) (5) (4) (6)
(8) 1 2 3 4 5 ? J I
Norman W. Garrick

11. 1 2 3 4 5 2 1 5 4 3 Link Array Network B I=2 (3) (7) (2) (5) (4) (6)
(8) 1 2 3 4 5 J I
Norman W. Garrick

12. Link Array Network B All I1 4 5 3
(3)
(7) 2
(2)
(5)
(4)
(6)
(8) 1 2 3 4 5 6 7 8 J I
Norman W. Garrick

13. i j wij Link Table Network B 1 4 5 3 2 1 2 3 (3) (7) (2) (5) (4) (6)
(8) i j
wij 1 2 3
Norman W. Garrick

14. i j wij Link Table Network B 1 4 5 3 2 1 2 3 5 (3) (7) (2) (5) (4) (6)
(8) i j
wij 1 2 3 5
Norman W. Garrick

15. i j wij Link Table Network B 1 4 5 3 2 1 2 3 5 4 (3) (7) (2) (5) (4)
(6)
(8) i j
wij 1 2 3 5 4
Norman W. Garrick

16. i j wij Link Table Network B 1 4 5 3 2 1 2 3 5 4 6 7 8 (3) (7) (2) (5)
(4)
(6)
(8) i j
wij 1 2 3 5 4 6 7 8
Norman W. Garrick

17. Route Choice Behavior
Trip assignment is based on one of two assumptions about traveler's behavior
User Equilibrium
System Equilibrium
Based on the assumption that users try to minimize their individual time of travel by going along the shortest path from origin to destination
Based on the assumption that users try to minimize the TOTAL system cost - that is the cost for all users of the system, not just his or her own cost
Route assignment based on user equilibrium require that we determine the ‘minimum path’ between any two zones or the ‘minimum tree’ which is a diagram showing the minimum path from one zone to all other zones
Norman W. Garrick

18. Network B Minimum Tree from Node 1
There are two ways to go from
Node 1 to Node 5
1 to 2 to 4 to 5
1 to 3 to 4 to 5
Which has the highest impedance?
1 to 2 to 4 to 5 is the min. path from 1 to 5 2
(3)
(2)
(2)
(4)
(7) 1 5
(8) 4
(4)
(6)
There are two ways to go from
Node 1 to Node 4
1 to 2 to 4
1 to 3 to 4
Which has the highest impedance?
1 to 2 to 4 is the min. path from 1 to 4
(5)
(4) 3
Norman W. Garrick

19. Network B Minimum Tree from Node 1
There is one way to go from
Node 1 to Node 2
1 to 2
1 to 2 is the min. path from 1 to 2 2
(3)
(2)
(2)
(4)
(7) 1 5
(8) 4
(4)
(6)
(5)
(4)
There is one way to go from
Node 1 to Node 3
1 to 3
1 to 3 is the min. path from 1 to 3 3
Norman W. Garrick

20. Network B Minimum Tree from Node 12
(3)
(2)
(2)
(4)
(7) 1 5
(8) 4
(4)
(6)
(5)
(4) 3
Norman W. Garrick

21. Network B Minimum Tree from Node 42
(3)
(2)
(2)
(4)
(7) 1 5
(8) 4
(4)
(6)
(5)
(4) 3
There is an algorithm for finding the minimum tree
We will not cover the algorithm in this class
Norman W. Garrick

22. Network B Tree Table from Node 42
(3)
(2)
(2)
(7)
(4) 1 5
(6) 4
(8)
Node ( j )
Total Impedance to Node j
Node Preceding j 1 2 3 4 5
(4) 3
Norman W. Garrick

23. Network B Tree Table from Node 42
(3)
(2)
(2)
(7)
(4) 1 5
(6) 4
(8)
Node ( j )
Total Impedance to Node j
Node Preceding j 1 6 2 3 4 5
(4) 3
Norman W. Garrick

24. Network B Tree Table from Node 42
(3)
(2)
(2)
(7)
(4) 1 5
(6) 4
(8)
Node ( j )
Total Impedance to Node j
Node Preceding j 1 6 2 4 3 - 5 7
(4) 3
Norman W. Garrick

25. Allocating Traffic to Individual Routes
Once the MINIMUM PATH is determined between different zones then traffic can be allocated to the various links between the zones
One common approach is the FREE FLOW/ALL-OR-NOTHING TRAFFIC ASSIGNMENT Technique
As the name implies, the technique assumes that all traffic between any two zones will use the minimum path between those two zones. The other big assumption is that the minimum path is calculated based on FREE FLOW conditions. In other ways, it is assumed that the minimum path calculations will not be affected by the amount of traffic using that path.
This is obviously this an unreasonable assumption. Other traffic assignment techniques have been developed which tries to correct for the two big problems with Free Flow/All-or-Nothing Traffic Assignment
Norman W. Garrick

26. Allocating Traffic to Individual Routes (continued)
FREE Flow/Multipath Traffic Technique
Does not assume that all traffic will use the minimum path - instead traffic is assigned to the various paths between the two zones based on their relative impedance. So for example, the path with the minimum impedance will get the most traffic followed by paths with increasing impedance
This method is still limited by the fact that the impedance is based on free flow assumptions and the impedance value is not changed to reflex the level of traffic loading.
Capacity-Restrained Traffic Assignment Techniques
Accounts for the fact that as the traffic on a link increases, the impedance also increases. Therefore, it is based on an interactive traffic assignment process that re-calculate the impedance to account for the level of traffic assigned to each link. As you can imagine this is a complex and computer intensive process.
Norman W. Garrick

27. Using Free Flow/All-or-Nothing Assignment - Example
Trip Exchange 1 2 J 1 2 3
Q1j
200
400
800
Q2j
150
100
Q3j
300
600
350 2 2 2 3 10 4 5 6 2 4 4 3 3 3 6 2
Norman W. Garrick

28. Minimum Tree – Zone 1 1 2 2 2 2 3 10 4 5 6 2 3 3 3 6 2
Norman W. Garrick

29. Free Flow/All-or-Nothing Assignment – Zone 1
Trip Exchange 1
1200 2 J 1 2 3
Q1j
200
400
800
Q2j
150
100
Q3j
300
600
350
400
800
400 4 5
400
800 3 6
800
Norman W. Garrick

30. Minimum Tree – Zone 2 1 2 2 2 2 3 4 5 2 4 4 3 3 3 6 2
Norman W. Garrick

31. Minimum Tree – Zone 3 1 2 2 2 2 3 4 5 2 4 4 3 3 3 6 2
Norman W. Garrick