Route Choice Lecture 11 Norman W. Garrick

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

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

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

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

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 Norman W. Garrick 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Network B Minimum Tree from Node 4 2 (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

Network B Tree Table from Node 4 2 (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

Network B Tree Table from Node 4 2 (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

Network B Tree Table from Node 4 2 (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

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

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

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

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

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

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

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