Transcript Slide 1
Feedback Loops
Guy Rousseau
Atlanta Regional Commission
ARC Historical Perspective
Old feedback model iterated with simple iteration
(“naïve approach”)
Looked at the Suzanne Evans’ algorithm of optimal
convex combination formulation
Looked at the MSA (method of successive averages).
Included the inter-relationship between model
formulation, system-wide convergence statistics, link
volume convergence and output accuracy as
determined by traffic counts.
Results were quantified by looking at link volume
differences using GIS plots and statistical indicators.
ARC Historical Perspective
Allowed to estimate relationship between system and
link level convergence.
System-wide criteria estimated the degree of
convergence to the optimal/equilibrium solution for
purposes of validating the output.
Relationships between system statistics and
convergence for individual links were established,
and system level convergence (or relative gap).
Inclusion of trip table estimation into the equilibrium
process was investigated, and looked at the elasticity
of trip tables with respect to congestion, in
establishing the accuracy of the assignment.
ARC Background and Findings
Common method for doing feedback is to average
link flows (using weighted successive averages)
rather than averaging times.
Nothing technically wrong with using averaged times,
as long as the closure checks are achieved, but one
could get slightly different answers using averaged
link flows.
Averaging times may not always lead to
convergence, but ARC has not had problems
reaching closure using averaged times based on the
criteria set.
ARC Feedback Loop Definition
Skims are calculated using congested travel times
Gravity model uses “gamma” functions for 4 income
groups.
Iteratively executes the primary steps in the travel
demand model to insure that trip generation, trip
distribution and mode choice are based on
accurate input speeds and travel times, then
creates the person and vehicle trip tables to be
used in the assignment process.
Congested speeds and travel times from each
iteration serve as inputs to the next iteration.
1st loop begins with fixed “seed” AM trip table, and
each successive loop is a feedback from the
preceding run.
Method of Successive Averages
MSA built into equilibrium highway assignment procedures
Travel times on each link from the previous iteration are
averaged with the travel times from the most recent assignment
based on the number of the current iteration, and new input
speeds are determined for the next iteration.
The process uses 2 criteria to test for closure / convergence.
Travel times are within +/- 5% for 95% of the network links
between each iteration.
Link volumes are within +/-5% for 95% of the network links
between each iteration.
Travel times and volumes are within 5% between the last 2
iterations for 95% of the network links.
Convergence occurs if less than 5% of O-D pairs have peak
hour travel times that change by more than 5% & average
change in peak hour link volumes is less than 5%.
ARC Feedback Loop Description
Run AM Peak Assignment
Input Files
Skims
1st loop – Built from Lookup Table of Congested Skims
2-+ Loops – Built from Congested Highway Times from
assignment
Check for Method of Successive Averages
Check between iteration
Travel times within +/-5% for 95% of network
Link volumes within +/-5% for 95% of network
Number of Feedback Loops
This prescribes the number of iterative loops the
model will go through during the Feedback Loop
Module, for instance 15.
The first loop begins with a fixed “seed” AM trip table,
and each successive loop is a feedback from the
preceding run.
Build peak skims creates matrices of toll, distance
and time for every zone-to-zone combination within
the peak network.
Initially the peak travel time skims are based on
lookup tables, but they are updated during the
feedback loop.
ARC Feedback Loop Closure
The feedback loop closure criteria were modified.
Previously, there were cases where the closure
check for difference in O-D volumes would produce
slightly erroneous results.
An additional midday highway assignment has been
incorporated within the feedback loop.
Two midday highway assignments are now
performed within the feedback loop regardless of the
number of assignments or loops required for the AM
peak period assignment.
ARC Feedback Loop Module
This module runs an AM peak period
assignment and builds congested highway
travel time skims.
The module includes functions that build
transit support links, calculate TAZ transit
walk accessibility, and estimates transit walk
times.
It also runs trip generation, trip distribution
and mode choice and then creates the
person and vehicle trip tables to be used in
the assignment process.
Feedback Loop & Trip Tables
While merging trip tables, we combine the
output trip tables from the mode choice model
into a final trip table containing truck, SOV,
and HOV trips.
This trip table is used in the highway
assignment procedure.
It creates a new AM trip table that is fed back
into the AM assignment procedure in the
feedback loop process.
Miscellaneous Pre-Processors
(Network Preparation, Data Formatting, etc.)
CORE MODELING SYSTEM
Module 1. Highway Network Building
Build Highway Networks and Develop Highway Skims
Module 2. Feedback Loops
Trip Generation, Transit Networks, Trip Distribution, Trip table
Manipulations, Mode Choice, AM Highway Assignment, Closure Checks
Module 3. Transit Assignments
Work & Non-Work
Walk-to-Local / Walk-to-Premium / Drive-to-Transit
Module 4. Time of Day Assignments
Trip Table Preparation, AM, MD, PM, NT Highway Assignments
Miscellaneous Post Processors
(Value Pricing, Emissions, etc.)
Recent Modifications
Modifications were made to both the highway and
transit skim building procedures.
The model feedback loop was modified to reflect bus
path building into every iteration.
For highway, a correction was made to the HOV
skims for both the AM and MD highway assignments
in the feedback loop.
Previously, the skims were calculated using uncongested travel times and have now been updated
to use the congested travel times.
Other Modifications
2 modifications to the highway assignment
Added a cost function for consistency in paths
and equilibrium
Changed the closure gap from 0.01 to 0.001
The closure gap was set to be more stringent
to try and minimize the fluctuation of
equilibrium assignments between alternatives
TP+ Implications
TP+ allows users to build paths using any variables,
but unless specifically specified in a cost function,
variables other than time will not be included in the
equilibrium closure calculations.
In the absence of a cost function, equilibrium closure
is based on time alone.
A cost function was added since we are adding a
time penalty for tolls.
By including the toll penalty in the cost function, we're
trying to make the path building and equilibrium
closure calculations more consistent.
Future Enhanements
For the time being, ARC practically lets TP+
determine when assignments "converge"
ARC will soon develop a TP+ code to
manually do assignment/equilibrium gap
closure determinations
So that ARC could base closure on multiple
vehicle class volumes & related time
penalties.
More Enhancements
Add a closure check for the maximum link
flow change.
Setup the feedback process to base feedback
loop travel times on averaged link flows
rather than averaging assignment times.
Use the maximum link flow change as the
primary feedback closure check.
Feedback Loop Criteria Scripting
Must do at least 2 assignments to determine convergence of link
volumes:
Criteria 1: TRAVEL TIME / SPEEDS
Determine new congested skims, using the highway load
function to calculate travel time skims, then calculate and add
intra zonal times, then add terminal time based on lookup table
files, then create the AM peak period highway skims for trip
distribution;
Determine before and after assignment time;
Calculate weighted average percent change in travel time for
each O-D pair;
Total percent change is calculated by weighting each O-D pair's,
travel time relative to the O-D trips, using trip table from current
iteration for weighted average.
Feedback Loop Criteria Scripting
Criteria 2: LINK VOLUMES
Calculate average total volume for all links,
comparing the previous loaded network with
the current loaded network;
Calculate weighted average percent change
in link volumes;
Total percent change is calculated by
weighting each link's % change
Convergence and Subsequent Steps
If convergence criteria not met, produce skims for the next loop,
using the average of times from the previous 2 assignments,
with the first loop using the average of free-flow and congested.
While building the peak skims, it creates matrices of toll,
distance and time for every zone-to-zone combination within the
peak network. Initially the peak travel time skims are based on
lookup tables, but they are updated during the feedback loop.
We also reflect bus path building into every iteration. An
additional midday highway assignment has been incorporated
within the feedback loop. Two midday highway assignments are
performed within the feedback loop regardless of the number of
assignments or loops required for the AM peak period
assignment.
ARC Land Use Feedback Loop
Composite Impedances: Linkage to Dram/Empal
Land Use Model
TP+ procedure uses a skim file with the HBW
composite times from the AM peak period highway
and transit assignment, the total person trip table
from the distribution, and an equivalency file to
prepare the composite impedance, by DRAM/EMPAL
district (census tracts).
This procedure is run after the model set has been
run and fully evaluated. For instance, 2005
composite impedances feed into 2010 land use
ARC Land Use Feedback Loop
HBW composite time by income group (4)
This is a matrix of composite times using the AM
peak period highway and transit assignment.
Total Person Trips, a standard trip matrix file. The file
has 7 tables, which are:
Total Home Based Work
Total Home Based Other
Total Non Home Based
Home Based Work: Income Group 1
Home Based Work: Income Group 2
Home Based Work: Income Group 3
Home Based Work: Income Group 4