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![Page 1: Increasing Precision in Highway Volume through Adjustment of Stopping Criteria in Traffic Assignment and Number of Feedbacks Behruz Paschai, Kathy Yu,](https://reader036.fdocuments.in/reader036/viewer/2022070409/56649e855503460f94b87848/html5/thumbnails/1.jpg)
Increasing Precision in Highway Volume through Adjustment of Stopping Criteria in Traffic Assignment and Number of Feedbacks
Behruz Paschai, Kathy Yu, Arash Mirzaei
North Central Texas Council of Governments (NCTCOG)
![Page 2: Increasing Precision in Highway Volume through Adjustment of Stopping Criteria in Traffic Assignment and Number of Feedbacks Behruz Paschai, Kathy Yu,](https://reader036.fdocuments.in/reader036/viewer/2022070409/56649e855503460f94b87848/html5/thumbnails/2.jpg)
May 2009 TRB National Transportation Planning Applications Conference 2
Assignment Improvement Goals
1. Reduce noise level
2. Define a multi-dimensional criteria for the relative gap and number of feedbacks
3. Perform the process with the exponential and conical VDFs
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May 2009 TRB National Transportation Planning Applications Conference 3
Software Platform
1. Roadway and Transit models in TransCAD
2. Multi-modal generalized-cost user equilibrium traffic assignment
3. Microsoft® Windows® XP operating system
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May 2009 TRB National Transportation Planning Applications Conference 4
Hardware Setup
1. Intel, single dual core, 3.6 GHz, 3 GB RAM
2. Intel Xeon, two dual cores, 3.00 GHz, 3GB RAM
3. Intel Xeon, two quad cores, 3.2 GHz, 3 GB RAM
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May 2009 TRB National Transportation Planning Applications Conference 5
Model Attributes
Number of links : ~31,300
Number of nodes : ~20,400
Number of zones : 5,386 (83 Externals)
Coverage area : ~10,000 sq. miles
Counties completely covered : 13
Total daily trips : ~16.7x106
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May 2009 TRB National Transportation Planning Applications Conference 6
Zone Structure
Number of zones : 5,303 (+83 Externals)Coverage area : ~10,000 sq. miles
~ 120 Miles
~ 1
20
Mile
s
~ 9
0 M
iles
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May 2009 TRB National Transportation Planning Applications Conference 7
Link Network
Number of links : ~31,300Number of nodes : ~20,400
Link Functional ClassificationF0 Centroid ConnectorF1 FreewayF2 Major ArterialF3 Minor ArterialF4 CollectorF6 RampF7 Frontage RoadF8 HOV LaneF9 Transit Line
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May 2009 TRB National Transportation Planning Applications Conference 8
Demographics
Model Year
Model Demographics
HH POP EMPTOTAL TRIPS
ZONES
Year 2005 2,216,167 5,954,677 3,472,933 16.7x106 5,386
DEM
OG
RA
PH
ICS
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May 2009 TRB National Transportation Planning Applications Conference 9
Assignment Improvements
Item Current Recommended
Number of Iterations 30 Defined by the Gap
Relative Gap 0 0.0001
Number of Feedbacks 2 5
VDF Form Exponential Conical
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May 2009 TRB National Transportation Planning Applications Conference 10
NCTCOG 4-Step Modeling
LOOP
Demographics
Zone LayerTrip Generation
Trip Distribution
Mode Choice
Roadway Assignment
Roadway Skims
Roadway Network
Transit Network
Transit Skims
Transit Assignment
Stopping CriteriaSatisfied
YES
NO
FEEDBACK LOOP
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May 2009 TRB National Transportation Planning Applications Conference 11
Feedback Loop – Skim Averaging
LOOP
Mode Choice
Roadway Assignment
Trip Distribution
[Ai]Roadway Skims (i)
[Di] = F([Di-1] , [Ai])
[Di-1] = Average Roadway Skims (i-1) [Ai] = Roadway Skims (i)
Compare [Di] vs [Di-1]
Skim Averaging (MSA, Constant Weight)
FEEDBACK LOOP
Demographics
Zone LayerTrip Generation
Stopping CriteriaSatisfiedYES
NO
Transit Assignment
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May 2009 TRB National Transportation Planning Applications Conference 12
Assignment Tests
1. Relative gap : 0.001, and 0.0001
2. Number of iterations : defined by the relative gap
3. Number of feedbacks : 10
4. VDF : exponential, conical
5. Averaging methods:
a. Method of Successive Averages (MSA)
b. Constant weight (0, .15, .25, .35, .45, .55)
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May 2009 TRB National Transportation Planning Applications Conference 13
Exponential vs Conical VDFsConical Freeway Volume-Delay Function - Typical Form Comparison
0
10
20
30
40
50
60
70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
V/C
Sp
ee
d (
mp
h)
CONICALNCTCOG ASSGN SPDNCTCOG POST SPD
Speed Limit = 60 mph
Exponential delay function
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May 2009 TRB National Transportation Planning Applications Conference 16
Conclusion 1 – Exponential VDF
1. Relative gap : 0.0001
2. Feedback loops : 5 (run time ~ 20 hrs)
3. Constant weight : 0.25/0.75
4. Model run time reduction : mostly contributed to the core-distributed traffic assignment step
Machine
Regular2 FeedbackModel Run
001 RG 10 FeedbackModel Run
0001 RG 10 FeedbackModel Run
2 Dual Core 5:59 39:24 76:472 Quad Core 4:28 22:23 41:20
% Reduction 25.35% 43.19% 46.17%
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May 2009 TRB National Transportation Planning Applications Conference 17
Comparison of Trip and Skim Matrices – Conical VDF
• Total Difference
Sum of the absolute value of the cell-by-cell differences in two consecutive feedback loops
• Root Square Error
The root square error of the cell-by-cell differences in two consecutive feedback loops
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May 2009 TRB National Transportation Planning Applications Conference 18
Total Skim Differences in Consecutive Feedbacks - PKNOHOV
0
100,000,000
200,000,000
300,000,000
400,000,000
500,000,000
600,000,000
0 1 2 3 4 5 6 7 8 9 10
Feedback
To
tal
Dif
fere
nce
in
Ski
ms
MSA/.0001 RG 0CW/.0001 RG-Naïve
.15CW/.0001RG .25CW/.0001 RG
.35CW/.0001RG .45CW/.0001RG
Total Skim Differences in Consecutive Feedbacks - PKNOHOV
0
20,000,000
40,000,000
60,000,000
80,000,000
100,000,000
120,000,000
3 4 5 6 7 8 9 10
Feedback
To
tal
Dif
fere
nce
in
Ski
ms
MSA/.0001 RG 0CW/.0001 RG-Naïve
.15CW/.0001RG .25CW/.0001 RG
.35CW/.0001RG .45CW/.0001RG
Skim Differences – Conical VDF
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May 2009 TRB National Transportation Planning Applications Conference 19
Total Trip Differences in Consecutive Feedbacks - PADIST
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
4,000,000
4,500,000
5,000,000
1 2 3 4 5 6 7 8 9 10
Feedback
To
tal
Tri
p D
iffe
ren
ces
MSA/.0001 RG 0CW/.0001 RG-Naïve
.15CW/.0001RG .25CW/.0001 RG
.35CW/.0001RG .45CW/.0001RG
Trip Differences – Conical VDF
Note : PADIST is the sum of the HBW, HNW, and NHB person trips
Total Trip Differences in Consecutive Feedbacks - PADIST
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
160,000
6 7 8 9 10
Feedback
To
tal
Tri
p D
iffe
ren
ces
MSA/.0001 RG 0CW/.0001 RG-Naïve
.15CW/.0001RG .25CW/.0001 RG
.35CW/.0001RG .45CW/.0001RG
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May 2009 TRB National Transportation Planning Applications Conference 20
Skim Error – Conical VDF
Root Square Error of Skims in Consecutive Feedbacks - PKNOHOV
0
20,000
40,000
60,000
80,000
100,000
120,000
1 2 3 4 5 6 7 8 9 10
Feedback
Ro
ot
Sq
uar
e E
rro
r
MSA/.0001 RG 0CW/.0001 RG-Naïve
.15CW/.0001RG .25CW/.0001 RG
.35CW/.0001RG .45CW/.0001RG
Note : PADIST is the sum of the HBW, HNW, and NHB person trips
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May 2009 TRB National Transportation Planning Applications Conference 21
Trip Error – Conical VDF
Root Square Error of Trips in Consecutive Feedbacks - PADIST
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
1 2 3 4 5 6 7 8 9 10
Feedback
Ro
ot
Sq
uar
e E
rro
r
MSA/.0001 RG 0CW/.0001 RG-Naïve
.15CW/.0001RG .25CW/.0001 RG
.35CW/.0001RG .45CW/.0001RG
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May 2009 TRB National Transportation Planning Applications Conference 22
• Total Difference
Sum of the absolute value of the differences in two consecutive feedback loops for each functional classification and the whole network
• Root Mean Square Error
The root mean square error (RMSE) of the differences in two consecutive feedback loops per functional classification and the whole network
Comparison of Volumes – Conical VDF
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May 2009 TRB National Transportation Planning Applications Conference 23
Volume Differences – Conical VDF
AM Peak Period Volume Difference in Consecutive Feedbacksper Functional Classification (SC29 - CW25)
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
14,000,000
1 2 3 4 5 6 7 8 9 10
AM
Pea
k P
erio
d V
olu
me
Dif
fere
nce
FUNCL 0
FUNCL 1
FUNCL 2
FUNCL 3
FUNCL 4
FUNCL 6
FUNCL 7
FUNCL 8
ALL
Note : ALL graph excludes the centroid connectors (FUNCL = 0)
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May 2009 TRB National Transportation Planning Applications Conference 24
Volume RMSEs – Conical VDF
AM Peak Period Volume RMSEs in Consecutive Feedbacksper Functional Classification (SC29 - CW25)
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10
AM
Pea
k P
erio
d V
olu
me
RM
SE
(%
)
FUNCL 0
FUNCL 1
FUNCL 2
FUNCL 3
FUNCL 4
FUNCL 6
FUNCL 7
FUNCL 8
ALL
Note : ALL graph excludes the centroid connectors (FUNCL = 0)
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May 2009 TRB National Transportation Planning Applications Conference 25
Volume Change – Conical VDF
Number of Links with Volume Change Less than 1/2 Capacity of a Single Lane in Consecutive Feedbacks (SC29 - CW25)
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
1 2 3 4 5 6
Feedback
Nu
mb
er o
f L
inks
(%
)
FUNCL 4 FUNCL 3
FUNCL 2 FUNCL 1
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May 2009 TRB National Transportation Planning Applications Conference 26
Max Volume Differences – Conical VDF
AM Peak Period MAX Volume Difference in Consecutive Feedbacks(SC29)
0
500
1,000
1,500
2,000
2,500
3,000
1 2 3 4 5 6 7 8 9 10
AM
Pea
k P
erio
d M
AX
Vo
lum
e D
iffe
ren
ce
.45CW/.0001 RG .15CW/.0001 RG
.25CW/.0001 RG 0CW/.0001 RG-Naïve
MSA/.0001 RG .35CW/.0001 RG
.55CW/.0001 RG
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May 2009 TRB National Transportation Planning Applications Conference 27
Min Volume Differences – Conical VDF
AM Peak Period MIN Volume Difference in Consecutive Feedbacks(SC29)
-7,000
-6,000
-5,000
-4,000
-3,000
-2,000
-1,000
0
1 2 3 4 5 6 7 8 9 10
AM
Pea
k P
erio
d M
IN V
olu
me
Dif
fere
nce
.45CW/.0001 RG .15CW/.0001 RG
.25CW/.0001 RG 0CW/.0001 RG-Naïve
MSA/.0001 RG .35CW/.0001 RG
.55CW/.0001 RG
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May 2009 TRB National Transportation Planning Applications Conference 28
Run Times – Conical VDF
Cumulative Run Times
0:00:00
0:04:48
0:09:36
0:14:24
0:19:12
1:00:00
1:04:48
1:09:36
0 1 2 3 4 5 6 7 8 9 10
Feedback
Cu
mu
lati
ve R
un
Tim
e (d
d:h
h:m
m)
MSA/.0001 RG 0CW/.0001 RG
15CW/.0001 RG 25CW/.0001 RG
35CW/.0001 RG 45CW/.0001 RG
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May 2009 TRB National Transportation Planning Applications Conference 29
Conclusion 2 – Conical VDF
1. Relative gap : 0.0001
2. Feedback loops : 5 (run time ~ 15 hrs)
3. Constant weight : 0.25/0.75
4. Total link RMSE : < 1.2%
5. Solution accuracy : ½ one lane capacity for each functional classification
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May 2009 TRB National Transportation Planning Applications Conference 30
Acknowledgment
NCTCOG Model Development Group staff for
development of macros, and presentation review: Kathy Yu Arash Mirzaei
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May 2009 TRB National Transportation Planning Applications Conference 31
Contact Info
Behruz Paschai [email protected] Kathy Yu [email protected] Arash Mirzaei [email protected]
North Central Texas Council of Governments (NCTCOG)