Traffic Assignment
Convergence and its
Effects on Selecting
Network Improvements
By
Chris Blaschuk, City of Calgary
and
JD Hunt, University of Calgary
October 20, 2004
18th Annual International EMME/2 User’s Conference
Mexico City, Mexico
Outline
•
•
•
•
About the Calgary Regional Transportation Model
Multiclass Assignment Process and Algorithms
Project Evaluation Process and Issues
Project Evaluation Measures
– Mobility Benefits
– Vehicle Hours Traveled (VHT)
• Empirical Testing
– Candidate Projects
– Observations
• Results of Testing
• Conclusions
City of Calgary
• Population just over 1 million people
Calgary RTM
• Both city and surrounding
region modeled
• Consists of 1447 zones
and over 14000 links
• 24-Hour model broken
into five time periods
• System of logit choice
models
• 25 trip purposes
• 5 person types
75km
24 Hour Trip Destination Choice:
o rig in z o n e i
j (1 )
j (2 )
....
j (n )
d e s ti n a ti o n z o n e j
ò
Time of Day Choice:
d a i l y i -j
am
o ff
pm
ò
Mode Choice:
t i m e o f d a y i -j
m e ta b o l i c
m echanical
a u to
tr a n s i t
car
ca r1
ca r2
w alk
cy cle
p&r
ca r3
ò
Peak Crown vs Peak Shoulder Choice:
c a r m o d e i -j
p e a k cro w n
peak s houlder
Figure 2: Concept ual nested log it model struct ure
Calgary RTM
• Steep VDF Curves used
– Links not overloaded
– Forces changes in generation, distribution and mode split
Multiclass Assignment in RTM
• Generalized cost multiclass
assignment is used in the
Calgary RTM.
• Five classes assigned
simultaneously.
• Truck penalty on non-truck
routes for medium and heavy
trucks.
• Stored as extra attribute of fixed
link costs for these classes.
• Originally was 1000 min / 250
meters for skimming -- now is 5
min / 100 meters.
Using RTM in Project Evaluation
• 34 separate projects to be tested for network benefits
• These included
–
–
–
–
–
Road Widenings
Interchanges
Lane Reversal Systems
New Roadways
Some Bundles of the above
• Goal was to determine the benefit each improvement
on the network in order to decide where money should
be invested.
• Wanted to use ‘Mobility Benefits’
Mobility Benefits
Generalized Cost of
• Change in daily
Travel
composite utility by
model segment
• Equal to change in
traveler consumer
surplus
C1
Consumer
• Indicates benefits of
Surplus
changes to person types
C2
and trip types
• Useful for analyzing
transit and other mode
improvements as well as
0
network changes.
Demand Curve for
Network Links
V1
V2
Link Volumes
Problem with Results
• Got confusing results
– Lots of unexpected negative benefits
– Results were not intuitive
– Unacceptable - clearly something wrong
• Needed to investigate
– decided on assignment convergence
• Approach: isolate problem
–
–
–
–
fixed trip table
considered just VHT
examine assignment process
experiment with convergence criteria
Reasons for Approach
•
•
•
•
•
•
Simplify to auto network
Eliminated ‘induced demand’
Simple to understand
Results more certain, more predictable
Smaller, so quick to produce and process
Observe assignment convergence effects
Empirical Testing
• Two projects were tested at various levels of
convergence
• Effects observed included
– Fluctuation of volumes on links
– Time taken to conduct assignment
– VHT of network at said level of convergence
Empirical Testing
• Project 1: John Laurie Boulevard widening from
Sarcee Trail to 53 ST NW (4 to 6 Lanes):
– Simple widening, impact generally limited to peak periods
only.
– Network effects are more local than far-reaching.
Empirical Testing
• Project 2: Glenmore Trail widening from Crowchild
Trail to 14 ST SW (7 to 10 Lanes):
– Major East-West corridor, important link in network.
– Network effects are far-reaching with no close alternative
routes.
Empirical Testing Observations
• Volume Fluctuation on Links would occur in areas
where travel times were very close.
– “Flip-Flopping” would occur -- case when two scenarios are
compared, an amount of volume takes path A in one scenario
and path B in another.
– More of a concern in the offpeak period than peak periods.
Empirical Testing Observations
• Fixed Link Costs affect
assignment convergence
and time.
– Used in Commercial Vehicle
Model to represent non-truck
routes (penalty applied to links)
– Increased fixed link costs
cause the multiclass
assignment to think it has
converged quickly when it has
not.
Number of Iterations for Various
Truck Penalty Costs
Relative Gap (%)
Truck Penalty
0.01
0
per 100 meters
1
48
2
49
3
48
577
5
44
414
10
41
211
40
32
80
28
200
20
450
19
39
- Not Tested
Results
John Laurie Boulevard Widening Project
TABLE 2: Assignment Statistics for John Laurie Boulevard Widening, AM Crown Case1
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
212
315
358
428
580
Iterations
1.25
1.85
2.11
2.52
3.40
Computing Time (h)
18.54
13.38
7.69
7.08
4.47
Maximum/Minimum
-15.59
-9.31
-6.28
-5.43
-3.08
Volume Difference3
82917
82897
82895
82895
82897
Vehicle Hours Traveled
1
For a truck trip penalty of 5 minutes per 100 meters.
2
A maximum of 2000 iterations was used as a stopping criteria.
3
Difference in volume links from previous iteration for the last iteration in the assignment.
TABLE 3: Assignment Statistics for John Laurie Boulevard Widening, AM Shoulder Case
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
90
131
150
180
216
Iterations
0.54
0.78
0.90
1.08
1.29
Computing Time (h)
61.68
27.49
31.55
15.29
10.05
Maximum/Minimum
-36.96
-23.79
-15.60
-11.60
-11.57
Volume Difference
62269
62242
62224
62228
62229
Vehicle Hours Traveled
0.01
907
5.35
2.94
-2.66
82896
~0 2
2000
11.72
1.11
-0.81
82896
0.01
341
2.03
6.06
-3.80
62217
~0
2000
11.84
0.72
-0.61
62214
Results
John Laurie Boulevard Widening Project
TABLE 2: Assignment Statistics for John Laurie Boulevard Widening, AM Crown Case1
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
212
315
358
428
580
Iterations
1.25
1.85
2.11
2.52
3.40
Computing Time (h)
18.54
13.38
7.69
7.08
4.47
Maximum/Minimum
-15.59
-9.31
-6.28
-5.43
-3.08
Volume Difference3
82917
82897
82895
82895
82897
Vehicle Hours Traveled
1
For a truck trip penalty of 5 minutes per 100 meters.
2
A maximum of 2000 iterations was used as a stopping criteria.
3
Difference in volume links from previous iteration for the last iteration in the assignment.
TABLE 3: Assignment Statistics for John Laurie Boulevard Widening, AM Shoulder Case
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
90
131
150
180
216
Iterations
0.54
0.78
0.90
1.08
1.29
Computing Time (h)
61.68
27.49
31.55
15.29
10.05
Maximum/Minimum
-36.96
-23.79
-15.60
-11.60
-11.57
Volume Difference
62269
62242
62224
62228
62229
Vehicle Hours Traveled
0.01
907
5.35
2.94
-2.66
82896
~0 2
2000
11.72
1.11
-0.81
82896
0.01
341
2.03
6.06
-3.80
62217
~0
2000
11.84
0.72
-0.61
62214
Results
Glenmore Trail Widening Project
TABLE 4: Assignment Statistics for Glenmore Trail Widening, AM Crown Case
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
209
308
347
406
547
Iterations
1.25
1.82
2.05
2.39
3.22
Computing Time (h)
19.38
9.61
10.86
4.67
6.03
Maximum/Minimum
-14.07
-11.25
-10.27
-4.85
-3.11
Volume Difference
82397
82389
82387
82381
82378
Vehicle Hours Traveled
0.01
865
5.09
2.81
-2.34
82380
~0
2000
11.77
1.01
-0.86
82375
TABLE 5: Assignment Statistics for Glenmore Trail Widening, AM Shoulder Case
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
85
124
141
164
212
Iterations
0.51
0.75
0.85
0.98
1.27
Computing Time (h)
47.20
19.52
17.08
13.95
11.49
Maximum/Minimum
-30.48
-30.66
-16.88
-13.02
-8.42
Volume Difference
61894
61862
61853
61856
61852
Vehicle Hours Traveled
0.01
331
1.97
4.49
-5.07
61849
~0
2000
11.87
0.66
-0.59
61846
Results
Glenmore Trail Widening Project
TABLE 4: Assignment Statistics for Glenmore Trail Widening, AM Crown Case
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
209
308
347
406
547
Iterations
1.25
1.82
2.05
2.39
3.22
Computing Time (h)
19.38
9.61
10.86
4.67
6.03
Maximum/Minimum
-14.07
-11.25
-10.27
-4.85
-3.11
Volume Difference
82397
82389
82387
82381
82378
Vehicle Hours Traveled
0.01
865
5.09
2.81
-2.34
82380
~0
2000
11.77
1.01
-0.86
82375
TABLE 5: Assignment Statistics for Glenmore Trail Widening, AM Shoulder Case
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
85
124
141
164
212
Iterations
0.51
0.75
0.85
0.98
1.27
Computing Time (h)
47.20
19.52
17.08
13.95
11.49
Maximum/Minimum
-30.48
-30.66
-16.88
-13.02
-8.42
Volume Difference
61894
61862
61853
61856
61852
Vehicle Hours Traveled
0.01
331
1.97
4.49
-5.07
61849
~0
2000
11.87
0.66
-0.59
61846
Results
• Computer time increases drastically as relative gap is
decreased (more iterations required).
• Link fluctuations decreased with increased
convergence.
• Large VHT differences from 0% RG value at 0.1% RG.
• VHT stabilizes as relative gap is decreased.
Results
Savings in VHT from Network Improvements
TABLE 8: Difference in VHT from Starting Point AM Crown Scenario (Savings in VHT from Project)
VHT
Relative Gap (%)
0.10
0.05
0.02
0.01
~0
135
138
131
135
134
John Laurie Boulevard Widening
655
646
650
651
655
Glenmore Trail Widening
TABLE 9: Difference in VHT from Starting Point AM Shoulder Scenario (Savings in VHT from Project)
VHT
Relative Gap (%)
0.10
0.05
0.02
0.01
~0
1
0
0
12
11
John Laurie Boulevard Widening
376
380
377
380
379
Glenmore Trail Widening
Results
• Effect of convergence on savings unclear in AM Crown
scenario
• Increased convergence lead to increased savings in
AM Shoulder scenario
• Important to obtain stable values, particularly in
projects that may not have much benefit in some time
periods.
• Most stable VHT results again near 0% RG
Results
Stability of Network
TABLE 10: Maximum Link Volume Differences from Starting Point Scenario Observed, John Laurie
Boulevard Widening Project, Truck Penalty of 5 minutes / 100 m
Scenario
Relative Gap (%)
0.10
0.05
0.04
0.03
0.02
0.01
~0
AM Crown
509
493
489
485
480
477
474
AM Shoulder
146
138
136
138
138
138
141
Numbers in Italics indicate largest change was in an area not associated with the improvement.
• At 0.1 % RG, Volume differences from link instability
begin to outshadow that of the improvement.
• Volumes more refined with increased convergence.
Results
Difference in Link Volumes from Volume at 0 Relative Gap
70
McKnight BV W of McCall Way EB
60
McKnight BV W of McCall Way WB
Sarcee RD N of 44 AV SW NB
40
30
20
10
0
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Sarcee RD N of 44 AV SW SB
Difference in Link Volumes (Vehicles)
50
162 AV SW W of Shawinigan Dr SW EB
162 AV SW W of Shawinigan Dr SW WB
Berkshire BV S of Country Hills BV NB
Berkshire BV S of Country Hills BV SB
Deerfoot TR S of Peigan TR SB
Deerfoot TR S of Peigan TR NB
Anderson RD E of 14 ST SW EB
Anderson RD E of 14 ST SW WB
Rundlehorn DR E of 36 ST NE EB
Rundlehorn DR E of 36 ST NE WB
Nose Hill DR N of Crowchild Trail SB
Nose Hill DR N of Crowchild Trail NB
Fairmount DR N of 86 AV SE NB
Fairmount DR N of 86 AV SE SB
5 AV SW E of Centre ST S EB
-10
-20
Relative Gap (%)
9 AV SW E of 9 ST SW EB
Results
Difference in Link Volumes from Volume at 0 Relative Gap (Excluding Anderson Road)
10
McKnight BV W of McCall Way EB
5
McKnight BV W of McCall Way WB
0
-5
Difference in Link Volumes (Vehicles)
Sarcee RD N of 44 AV SW NB
Sarcee RD N of 44 AV SW SB
162 AV SW W of Shawinigan Dr SW EB
162 AV SW W of Shawinigan Dr SW WB
Berkshire BV S of Country Hills BV NB
Berkshire BV S of Country Hills BV SB
Deerfoot TR S of Peigan TR SB
Deerfoot TR S of Peigan TR NB
Rundlehorn DR E of 36 ST NE EB
Rundlehorn DR E of 36 ST NE WB
Nose Hill DR N of Crowchild Trail SB
Nose Hill DR N of Crowchild Trail NB
Fairmount DR N of 86 AV SE NB
Fairmount DR N of 86 AV SE SB
-10
-15
0.1
0.09
0.08
0.07
0.06
0.05
0.04
Relative Gap (%)
0.03
0.02
0.01
0
5 AV SW E of Centre ST S EB
9 AV SW E of 9 ST SW EB
Results
• Links approach 0% RG value with increased
assignment.
• Anderson Road link has most dramatic change - this is
a link where flip-flopping occurs.
• Remaining links are more or less stable around 0.05
% RG (differences are 10 or less)
• With Anderson Road included, differences are about
30 or less vehicles at 0.05 % RG
Results
• Assignments below 0.01% RG may stop for a variety
of reasons:
– RG or Normalized Gap may go negative and stop assignment.
– Unsure if assignments are then equally converged (same
distance from the optimum objective function)
– Differences in assignment should be small, but practitioners
should be aware
– EMME/2 will only allow assignment of up to two decimals for
RG -- Must use iterations to get between 0.01 % or 0 % RG.
Conclusions
• Small differences in large numbers
– Tighter convergence needed to see benefits
• Important tradeoffs to be made
– More converged assignment vs. increased
computing time
– End criteria depends on use of data and
needs
Conclusions
• For comparing VHT values between
scenarios, RG of 0.01 % recommended
• RG of 0.01 % also recommended for link
volumes
• If volumes are to be rounded, and practitioners
are aware of areas with link fluctuations, an
RG of 0.05 % can be used to save time.
• Knowledge of the importance of convergence
will be used in refining mobility benefits
process.