1. Norman W. Garrick 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

2. Norman W. Garrick Trip Assignment in 4 Step Process Example Consider two zones Hartford CBD West Hartford Center Four Steps 1.Trip Generation - Determines production from WH Center 2.Trip Distribution - Gives Q IJ - Trips from WH Center attracted to Hartford CBD 3.Modal Split - Fraction of Q IJ using different modes of travel 4.Trip Assignment - What roads? What bus routes?

3. Norman W. Garrick 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

4. Norman W. Garrick Example Road Network for Trip Assignment 12 4 3 5 6 87 10 9 11 12 13 14 55

5. Norman W. Garrick Example Road Network for Trip Assignment 12 4 3 5 6 87 10 9 11 12 13 14 5523 65 55 77 57 5 55 4 4 4 6 8 7 8 7 8 7 8 7 8 7 8 7

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

7. Norman W. Garrick Link Array Network B 12345 1 2 3 4 5 J I 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (6) (8)

8. Norman W. Garrick Link Array Network B I=1 12345 135 2 3 4 5 J I 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (6) (8)

9. Norman W. Garrick Link Array Network B I=2 12345 135 242 3 4 5 J I 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (6) (8)

10. Norman W. Garrick Link Table Network B 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (6) (8) ijw ij 123

11. Norman W. Garrick Link Table Network B 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (6) (8) ijw ij 123 135 214 242

12. Norman W. Garrick Link Table Network B 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (6) (8) ijw ij 123 135 214 242 314 346 422 434 457 548

13. Norman W. Garrick Route Choice Behavior Trip assignment is based on one of two assumptions about traveler's behavior 1.User Equilibrium 2.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

14. Norman W. Garrick Network B Minimum Tree from Zone 1 1 4 5 3 (3) (7) 2 (2) (5) (4) (2) (4) (8) (4) (6)

15. Norman W. Garrick Network B Minimum Tree from Zone 4 1 4 5 3 (3) (7) 2 (2) (4) (2) (6) (8) The text outline an algorithm for finding the minimum tree We will not cover the algorithm in this class (5) (4)

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

17. Norman W. Garrick Network B Tree Table from Zone 4 1 4 5 3 (3) (7) 2 (2) (4) (2) (6) (8) Node ( j )Total Impedance to Node j Node Preceding j 162 2 3 4 5

18. Norman W. Garrick Network B Tree Table from Zone 4 1 4 5 3 (3) (7) 2 (2) (4) (2) (6) (8) Node ( j )Total Impedance to Node j Node Preceding j 162 224 344 40- 574

19. Norman W. Garrick 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

20. Norman W. Garrick 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.

21. Norman W. Garrick Using Free Flow/All-or-Nothing Assignment 1 4 5 3 2 Minimum Tree from Zone 4 J1235 Q 4j 200400800600 200

22. Norman W. Garrick Using Free Flow/All-or-Nothing Assignment 1 4 5 3 2 Minimum Tree from Zone 4 J1235 Q 4j 200400800600 200 400

23. Norman W. Garrick Using Free Flow/All-or-Nothing Assignment 1 4 5 3 2 Minimum Tree from Zone 4 J1235 Q 4j 200400800600 200 400 800 600