Source: NHI course on Traffic
Travel Demand Forecasting
(152054A) Session 10
(Trip) Assignment
Trip Generation
Trip Distribution
Transit Estimation & Mode Split
Time-of-Day & Directional Factoring
Transit Person Trip Table
(O&D)
Vehicle Trip Table
(O&D)
Trip Assignment
Loaded Transit
Network
Loaded
Highway
Network
Review
Trip Assignment
Objectives:
• Explain the concept of an all-or-nothing assignment
• Explain the concept of an equilibrium assignment
• Identify the BPR formula
• Identify the source of the input data to the BPR formula
• Explain the application of the BPR formula in an equilibrium
assignment
• Explain the meaning of the volumes from an all-or-nothing
assignment
• Explain the meaning of the volumes from an equilibrium
assignment
Terminology
• Highway/trip
assignment
• Transit trip assignment
• All-or-nothing
assignment
• Equilibrium
assignment
• Freeflow speed
•
•
•
•
•
Path finding
Impedance
Path loading
Level of service
Capacity restraint
Inputs and Outputs
Inputs
• O&D trip table
• Coded network
Outputs
• Link flows as per coded network
• Link travel times/speeds
• VMT
• Vehicle hours of travel
Trip Assignment Methods
•All-or-nothing assignment
•Equilibrium assignment (approximation!)
•Transit assignment
All-or-Nothing Assignment
Step 1:
Find Shortest
route between
the TAZs
Step 2:
Assign all trips to
links
compromising
shortest route
Advantages
•Simple
•Inexpensive
•Results easy to understand
Disadvantages
•Assumes all traffic will travel on shortest path
•Creates unrealistic flow patterns
Step 3:
Continue until
trips between all
TAZ pairs have
been assigned
(7)
(8)
(9)
These results
From this specification
Logit model
Can set Ui = -tti
Can set Ui = 1/tti, but if you do, will need a
calibration coefficient
67
24
9
Capacity Restraint
• Volume-delay relationship
• Average travel speed decreases
with increased flow (volume)
• Average travel time increases as
the volume-to-capacity ratio on a
link increases
• The Bureau of Public Roads
(BPR) formula, used as default in
most model packages
shows this relationship:
Travel time depends on
the loading, but the
loading depends on the
travel time – it’s an
iterative process
Alpha and beta can be
calibrated for various
link types and assumed
LOS for capacity
Source: Virginia Travel Demand Modeling Policies and Procedures Manual
Equilibrium Assignment
Step 1:
Find shortest
routes
Step 2:
Assign trips to
shortest routes
Step 3:
Update link travel
times using capacity
restraint function
Step 6: Average
trips for last two
assignments
Step 5:
Assign trips to
shortest route
Step 4: Compute
now shortest routes
using new travel
times
Step 7: Update link
travel times using
average trips assigned
and capacity restraint
function.
Step 8 :
Go back to
Step 1.
Step 9: Continue
until volumes and
travel times on links
are in equilibrium
•Utilizes the concept of capacity restraint (link impedance depends on link flow levels)
•Assign traffic in congested networks so that no individual trip maker can reduce path costs by
switching routes
•Assumes trip makers know conditions on all routes.
10
100
12
16
13
12
100
16
11
14
Note: it is difficult to demonstrate the usefulness of this
process in such a simplified network. Imagine thousands
of links and OD pairs, and you could see how running this
multiple times could produce various loads on the many
links. In this and some other examples in this lecture, the
loading pattern would simply repeat itself.
50
50
16
Average of the first two iteration’s loads, and resulting
travel times
Speed
volume
Why? Because speed
doesn’t change much
until you get close to
capacity … the times
and loads here are
for demonstration
purposes only.
Note: 40% refers to
40% of the traffic
between all OD pairs
that use that link
along their path. It
may well be more or
less than 40% of the
capacity of the link
itself.
Re-compute these times with 67 and 33 trips, respectively
Using Damping Factors to Control Oscillations
By incorporating a damping factor you don't let the change in
travel time between each iteration change so quickly. If the
factor is, D = .5, then...
instead of travel time changing from 7 to 12 minutes (change =
5), multiply change by .5, 5*.5 = 2.5, change travel time from 7
to 9.5 minutes.
instead of travel time changing from 9.5 to 12 minutes (change =
2.5), multiply change by .5, 2.5*.5 = 1.25, change travel time
from 9.5 to 10.75 minutes.
100
9.5
10.75
100
10
instead of travel time changing from 10 to 15 minutes (change =
5), multiply change by .5, 5*.5 = 2.5, change travel time from 10
to 12.5 minutes.
10.75
100
12.5
16
10 or 20 iterations or more may be needed in a real network
10.75
300/4=75
12.5
16
Re-compute these times with 75 and 25 trips, respectively
100/4=25
Older pseudo-equilibrium method (equilibrium approximation)
This is not a true
equilibrium
method. It is a
methods that
was
implemented in
early models.
TransCAD can
do it, but it is
not
recommended
Transit Assignment
• Links include different services running between
stops or stations.
• Involves movement of passengers, not vehicles
• Complex interchange patterns associated with
passengers
• Impedance functions includes fare structure
• Some paths offer more than one parallel service
with complex associated choices (e.g., express bus
versus local bus service)
Error Checking and Validation
• Examine plotted trees
• Compare counted VMT with modeled VMT
• Compare external station counted volumes with
modeled volumes.
• Compare counted and modeled screen line
volumes
• Compare assigned volumes to ground counts for
links grouped by facility type and by volume
groups
Some discussion on TransCAD
• True EU and SUE assignment methods
• Select Link Analysis
– Zone/node based
– Link based
• Flow maps and v/c maps
• Accounting for and optimizing signal operations
• Combined trip dist/assignment method
– feedback
– Simultaneous modeling
• Question: what would happen if we tested the shortest path from an O
to a D following various types of assignments
– All or nothing? Approximate methods?
– Stochasting or SUE? (for this, need to know all used flow paths between
the O and D … how to get?)