Route Choice or Trip Assignment

1. 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

2. 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

3. Characterizing Road 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

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

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

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

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

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

9. 2 (3) (2) (7) (2) (4) 5 1 (6) (4) 4 (8) (4) (5) 3 Link Table Network B Norman W. Garrick

10. 2 (3) (2) (7) (2) (4) 5 1 (6) (4) 4 (8) (4) (5) 3 Link Table Network B Norman W. Garrick

11. 2 (3) (2) (7) (2) (4) 5 1 (6) (4) 4 (8) (4) (5) 3 Link Table Network B Norman W. Garrick

12. Route Choice Behavior • Trip assignment is based on one of two assumptions about traveler's behavior • User Equilibrium • System Equilibrium • User 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 • System Equilibrium • 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

13. Network BMinimum Tree from Node 1 2 (3) (2) (2) (4) (7) 5 1 (8) 4 (6) (4) (4) (5) 3 Norman W. Garrick

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

15. Network BTree Table from Node 4 2 (3) (2) (2) (7) (4) 5 1 (6) 4 (8) (4) 3 Norman W. Garrick

16. Network BTree Table from Node 4 2 (3) (2) (2) (7) (4) 5 1 (6) 4 (8) (4) 3 Norman W. Garrick

17. Network BTree Table from Node 4 2 (3) (2) (2) (7) (4) 5 1 (6) 4 (8) (4) 3 Norman W. Garrick

18. 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

19. 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

20. Using Free Flow/All-or-Nothing Assignment - Example Trip Exchange 1 2 2 2 2 3 10 5 4 6 2 4 4 3 3 3 2 6 Norman W. Garrick

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

22. Free Flow/All-or-Nothing Assignment – Zone 1 Trip Exchange 1 2 1200 400 800 400 5 4 400 800 3 6 800 Norman W. Garrick

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

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