Route Choice

1

• Route Choice
• Lecture 11
• Norman W. Garrick

2
Route Choice By Foot, Bus, Tram, Rail, Cable Car
From Kirche Fluntern To ETH-Hoenggerberg
3
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
4
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?

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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
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Example Road Network for Trip Assignment
1
2
5
5
3
6
8
7
11
4
9
10
1, 2, 3, 4, 5 are zone centroids
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14
13
5
7
Example Road Network for Trip Assignment
1
2
5
5
2
3
4
4
8
3
6
8
7
4
6
7
6
5
5
5
7
8
8
8
11
4
9
10
7
7
7
5
5
7
7
8
8
12
14
13
7
7
5
5
5
8
Network B
2
(3)
(2)
(2)
(4)
(7)
5
1
(8)
4
(6)
(4)
(4)
(5)
3
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Link Array Network B
J
1 2 3 4 5
1
2
3
4
5
I
10
Link Array Network BI1
J
1 2 3 4 5
1 ? ?
2
3
4
5
I
11
Link Array Network BI1
J
1 2 3 4 5
1 3 5
2 ? ?
3
4
5
I
12
Link Array Network BI2
J
1 2 3 4 5
1 3 5
2 4 2
3
4
5
I
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Link Array Network BAll I
J
1 2 3 4 5
1 3 5
2 4 2
3 4 6
4 2 4 7
5 8
I
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Link Table Network B
i j wij
1 2 3









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Link Table Network B
i j wij
1 2 3
1 3 5








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Link Table Network B
i j wij
1 2 3
1 3 5
2 1 4
2 4 2






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Link Table Network B
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
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Route Choice Behavior

• Trip assignment is based on one of two
  assumptions about traveler's behavior
• User Equilibrium
• 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

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Network BMinimum 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)
5
1
(8)
4
(6)
(4)

• 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

(4)
(5)
3
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Network BMinimum 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)
5
1
(8)
4
(6)
(4)
(4)
(5)
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
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Network BMinimum Tree from Node 1
2
(3)
(2)
(2)
(4)
(7)
5
1
(8)
4
(6)
(4)
(4)
(5)
3
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Network BMinimum Tree from Node 4
2
(3)
(2)
(2)
(4)
(7)
5
1
(8)
4
(6)
(4)
(4)
(5)
3
There is an algorithm for finding the minimum
tree We will not cover the algorithm in this
class
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Network BTree Table from Node 4
2
(3)
(2)
(2)
(7)
(4)
5
1
(6)
4
(8)
Node ( j ) Total Impedance to Node j Node Preceding j
1
2
3
4
5
(4)
3
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Network BTree Table from Node 4
2
(3)
(2)
(2)
(7)
(4)
5
1
(6)
4
(8)
Node ( j ) Total Impedance to Node j Node Preceding j
1 6 2
2
3
4
5
(4)
3
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Network BTree Table from Node 4
2
(3)
(2)
(2)
(7)
(4)
5
1
(6)
4
(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
(4)
3
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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
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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.
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Using Free Flow/All-or-Nothing Assignment -
Example
Trip Exchange
1
2
J 1 2 3
Q1j 200 400 800
Q2j 150 200 100
Q3j 300 600 350
2
2
2
3
10
5
4
6
2
4
4
3
3
3
2
6
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Minimum Tree Zone 1
1
2
2
2
2
3
10
5
4
6
2
3
3
3
2
6
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Free Flow/All-or-Nothing Assignment Zone 1
Trip Exchange
1
2
J 1 2 3
Q1j 200 400 800
Q2j 150 200 100
Q3j 300 600 350
1200
800
400
400
5
4
400
800
3
6
800
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Minimum Tree Zone 2
1
2
2
2
2
3
5
4
2
4
4
3
3
3
2
6
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Minimum Tree Zone 3
1
2
2
2
2
3
5
4
2
4
4
3
3
3
2
6