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

Norman W. Garrick

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 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

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 Zone 1

1

4

5

3

(3)

(7)

2

(2)

(5)

(4)(2)

(4)(8)

(4)

(6)

Norman W. Garrick

Network BMinimum Tree from Zone 4

1

4

5

3

(3)

(7)

2

(2)

(4)

(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)

Norman W. Garrick

Network BTree Table from Zone 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 Zone 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 Zone 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

Using Free Flow/All-or-Nothing Assignment

14

5

3

2Minimum Tree from Zone 4

J 1 2 3 5

Q4j 200 400 800 600

200 200

Norman W. Garrick

Using Free Flow/All-or-Nothing Assignment

14

5

3

2Minimum Tree from Zone 4

J 1 2 3 5

Q4j 200 400 800 600

200 200

400

Norman W. Garrick

Using Free Flow/All-or-Nothing Assignment

14

5

3

2Minimum Tree from Zone 4

J 1 2 3 5

Q4j 200 400 800 600

200 200

400

800

600