Route Choice
Lecture 11
Norman W. Garrick
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
1. Trip Generation - Determines production from WH
Center
2. Trip Distribution - Gives QIJ - Trips from WH Center
attracted to Hartford CBD
3. Modal Split - Fraction of QIJ using different modes of
travel
4. 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
5
2
5
3
6
7
8
11
9
10
12
13
5
Norman W. Garrick
4
14
1, 2, 3, 4, 5
are zone
centroids
Network B
2
(3)
(2)
(2)
(4)
(7)
5
1
(6)
(4)
(4)
(5)
3
Norman W. Garrick
4
(8)
Link Array
Network B
2
(3)
(2)
1
(4)
I
1
1
2
3
4
5
Norman W. Garrick
2
3
4
5
5
(6)
4
(4)
(5)
J
(7)
(2)
(4)
3
(8)
Link Array
Network B
I=1
2
(3)
(2)
1
(4)
I
1
1
2
3
4
5
Norman W. Garrick
2
?
3
?
4
5
5
(6)
4
(4)
(5)
J
(7)
(2)
(4)
3
(8)
Link Array
Network B
I=1
2
(3)
(2)
1
(4)
I
1
1
2
2
3
?
3
4
5
Norman W. Garrick
3
4
5
?
5
5
(6)
4
(4)
(5)
J
(7)
(2)
(4)
3
(8)
Link Array
Network B
I=2
2
(3)
(2)
1
(4)
I
1
1
2
2
3
4
3
4
5
Norman W. Garrick
3
4
5
2
5
5
(6)
4
(4)
(5)
J
(7)
(2)
(4)
3
(8)
Link Array
Network B
All I
2
(3)
(2)
1
(4)
I
1
1
2
3
3
4
5
2
4
2
3
4
6
4
5
Norman W. Garrick
2
5
4
7
8
5
(6)
4
(4)
(5)
J
(7)
(2)
(4)
3
(8)
Link Table
Network B
2
i
j
wij
1
2
3
(3)
(2)
1
(4)
5
(6)
4
(4)
(5)
3
Norman W. Garrick
(7)
(2)
(4)
(8)
Link Table
Network B
2
i
j
wij
1
2
3
1
3
5
(3)
(2)
1
(4)
5
(6)
4
(4)
(5)
3
Norman W. Garrick
(7)
(2)
(4)
(8)
Link Table
Network B
2
i
j
wij
1
2
3
1
3
5
2
1
4
2
4
2
(3)
(2)
1
(4)
5
(6)
4
(4)
(5)
3
Norman W. Garrick
(7)
(2)
(4)
(8)
Link Table
Network B
2
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
(3)
(2)
1
(7)
(2)
(4)
(4)
5
(6)
4
(4)
(5)
3
(8)
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
Norman W. Garrick
Network B
Minimum Tree from Node 1
There are two ways to go from
Node 1 to Node 5
2
(3)
(2)
1.
1 to 2 to 4 to 5
2.
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)
(4)
(7)
5
1
(6)
(4)
(4)
(5)
3
(8)
4
There are two ways to go from
Node 1 to Node 4
1.
1 to 2 to 4
2.
1 to 3 to 4
Which has the highest impedance?
1 to 2 to 4 is the min. path from 1 to 4
Norman W. Garrick
Network B
Minimum Tree from Node 1
There is one way to go from
Node 1 to Node 2
2
1 to 2
1 to 2 is the min. path from 1 to 2
(3)
(2)
(2)
(4)
(7)
5
1
(6)
(4)
(8)
4
(4)
(5)
There is one way to go from
Node 1 to Node 3
3
1 to 3
1 to 3 is the min. path from 1 to 3
Norman W. Garrick
Network B
Minimum Tree from Node 1
2
(3)
(2)
(2)
(4)
(7)
5
1
(6)
(4)
(4)
(5)
3
Norman W. Garrick
4
(8)
Network B
Minimum Tree from Node 4
2
(3)
(2)
(2)
(4)
(7)
5
1
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
(8)
Network B
Tree Table from Node 4
2
(3)
(2)
(4)
1
2
3
4
5 W. Garrick
Norman
Total
Impedance
to Node j
(7)
5
1
Node ( j )
(2)
(6)
Node
Preceding j
4
(4)
3
(8)
Network B
Tree Table from Node 4
2
(3)
(2)
(4)
1
2
3
4
5 W. Garrick
Norman
Total
Impedance
to Node j
6
(6)
Node
Preceding j
2
(7)
5
1
Node ( j )
(2)
4
(4)
3
(8)
Network B
Tree Table from Node 4
2
(3)
(2)
(4)
Total
Impedance
to Node j
(6)
Node
Preceding j
1
2
6
2
2
4
3
4
5 W. Garrick
Norman
4
0
7
4
4
(7)
5
1
Node ( j )
(2)
4
(4)
3
(8)
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
Q1j
Q2j
Q3j
2
2
2
3
10
5
4
6
2
4
4
3
3
3
6
Norman W. Garrick
2
1
200
150
2
400
200
3
800
100
300
600
350
Minimum Tree – Zone 1
1
2
2
2
2
3
10
5
4
6
2
3
3
3
6
Norman W. Garrick
2
Free Flow/All-or-Nothing Assignment – Zone 1
Trip Exchange
1
J
Q1j
Q2j
Q3j
2
1200
400 800
400
5
4
400
800
3
6
Norman W. Garrick
800
1
200
150
2
400
200
3
800
100
300
600
350
Minimum Tree – Zone 2
1
2
2
2
2
3
5
4
2
4
4
3
3
3
6
Norman W. Garrick
2
Minimum Tree – Zone 3
1
2
2
2
2
3
5
4
2
4
4
3
3
3
6
Norman W. Garrick
2