norman w. garrick route choice or trip assignment trip assignment is the forth step of the four step...
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Norman W. Garrick
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 Steps1. Trip Generation - Determines production from WH
Center2. Trip Distribution - Gives QIJ - Trips from WH Center
attracted to Hartford CBD3. Modal Split - Fraction of QIJ using different modes of
travel4. Trip Assignment - What roads? What bus routes?
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 numberedLinks are specified by the nodes at the endEach 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
4
3
5
687
109
11
12
13 14
5 5
1, 2, 3, 4, 5 are zone centroids
Norman W. Garrick
Network B
1
4
5
3
(3)
(7)
2
(2)
(5) (4)
(4)(2)
(4) (6)(8)
Norman W. Garrick
Link Array Network B
1 2 3 4 5
1
2
3
4
5
JI
14
5
3
(3)
(7)
2
(2)
(5)(4)
(4) (2)
(4) (6)
(8)
Norman W. Garrick
Link Array Network BI=1
1 2 3 4 5
1 3 5
2
3
4
5
JI
14
5
3
(3)
(7)
2
(2)
(5)(4)
(4) (2)
(4) (6)
(8)
Norman W. Garrick
Link Array Network BI=2
1 2 3 4 5
1 3 5
2 4 2
3
4
5
JI
14
5
3
(3)
(7)
2
(2)
(5)(4)
(4) (2)
(4) (6)
(8)
Norman W. Garrick
Link Table Network B
14
5
3
(3)
(7)
2
(2)
(5)(4)
(4) (2)
(4) (6)
(8)
i j wij
1 2 3
Norman W. Garrick
Link Table Network B
14
5
3
(3)
(7)
2
(2)
(5)(4)
(4) (2)
(4) (6)
(8)
i j wij
1 2 3
1 3 5
2 1 4
2 4 2
Norman W. Garrick
Link Table Network B
14
5
3
(3)
(7)
2
(2)
(5)(4)
(4) (2)
(4) (6)
(8)
i j wij
1 2 3
1 3 5
2 1 4
2 4 2
3 1 4
3 4 6
4 2 2
4 3 4
4 5 7
5 4 8
Norman W. Garrick
Route Choice Behavior
Trip assignment is based on one of two assumptions about traveler's behavior1. User Equilibrium2. System Equilibrium
User EquilibriumBased on the assumption that users try to minimize their individual time of
travel by going along the shortest path from origin to destination
System EquilibriumBased 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 BMinimum Tree from Node 1
1
4
5
3
(3)
(7)
2
(2)
(5)
(4)(2)
(4)(8)
(4)
(6)
Norman W. Garrick
Network BMinimum Tree from Node 4
1
4
5
3
(3)
(7)
2
(2)
(4)
(4)(2)
(6)(8)
There is an algorithm for finding the minimum tree
We will not cover the algorithm in this class
(5)
(4)
Norman W. Garrick
Network BTree Table from Node 4
14
5
3
(3)
(7)
2
(2)
(4)
(4) (2)
(6)(8)
Node ( j )
Total Impedance to Node j
Node Preceding j
1
2
3
4
5
Norman W. Garrick
Network BTree Table from Node 4
14
5
3
(3)
(7)
2
(2)
(4)
(4) (2)
(6)(8)
Node ( j )
Total Impedance to Node j
Node Preceding j
1 6 2
2
3
4
5
Norman W. Garrick
Network BTree Table from Node 4
14
5
3
(3)
(7)
2
(2)
(4)
(4) (2)
(6)(8)
Node ( j )
Total Impedance to Node j
Node Preceding j
1 6 2
2 2 4
3 4 4
4 0 -
5 7 4
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
1 2
3
4 5
6
2 2 2 3
4
4
10
6
2
3
Using Free Flow/All-or-Nothing Assignment - Example
3
2
J 1 2 3
Q1j 200 400 800
Q2j 150 200 100
Q3j 300 600 350
Trip Exchange
Norman W. Garrick
1 2
3
4 5
6
2 2 2 310
6
Minimum Tree – Zone 1
3
2
2
3
Norman W. Garrick
1 2
3
4 5
6
Free Flow/All-or-Nothing Assignment – Zone 1
J 1 2 3
Q1j 200 400 800
Q2j 150 200 100
Q3j 300 600 350
Trip Exchange
800
800
400
400
8004001200
Norman W. Garrick
1 2
3
4 5
6
2 2 2 3
4
4
2
3
Minimum Tree – Zone 2
3
2
Norman W. Garrick
1 2
3
4 5
6
2 2 2 3
4
4
2
3
Minimum Tree – Zone 3
3
2
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