Transcript Travel Demand Modeling At NCTCOG

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)
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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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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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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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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Zone Structure
~ 90 Miles
~ 120 Miles
~ 120 Miles
Number of zones :
5,303 (+83 Externals)
Coverage area :
~10,000 sq. miles
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Link Network
Link Functional Classification
F0  Centroid Connector
F1  Freeway
F2  Major Arterial
F3  Minor Arterial
F4  Collector
F6  Ramp
F7  Frontage Road
F8  HOV Lane
F9  Transit Line
Number of links :
~31,300
Number of nodes :
~20,400
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DEMOGRAPHICS
Demographics
Model Demographics
Model Year
Year 2005
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HH
2,216,167
POP
5,954,677
EMP
3,472,933
TOTAL
TRIPS
16.7x106
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ZONES
5,386
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Assignment Improvements
Item
Current
Recommended
Number of Iterations
30
Defined by the Gap
Relative Gap
0
0.0001
Number of Feedbacks
2
5
Exponential
Conical
VDF Form
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NCTCOG 4-Step Modeling
Zone Layer
Trip Generation
Demographics
Roadway
Skims
Trip Distribution
Mode Choice
Transit Network
Roadway Assignment
Stopping Criteria
Satisfied
Transit Skims
NO
YES
FEEDBACK LOOP
LOOP
Transit Assignment
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Roadway
Network
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Feedback Loop – Skim Averaging
Zone Layer
Trip Generation
Demographics
Skim Averaging (MSA, Constant Weight)
[Di] = F([Di-1] , [Ai])
Trip Distribution
[Di-1] = Average Roadway Skims (i-1)
[Ai] = Roadway Skims (i)
Mode Choice
Compare [Di] vs [Di-1]
Stopping Criteria NO
Satisfied
YES
LOOP
Roadway Assignment
[Ai]
Roadway
Skims (i)
FEEDBACK LOOP
Transit Assignment
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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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Exponential vs Conical VDFs
Conical Freeway Volume-Delay Function - Typical Form Comparison
70
CONICAL
NCTCOG ASSGN SPD
NCTCOG POST SPD
Exponential delay function
60
Speed Limit = 60 mph
Speed (mph)
50
40
30
20
10
0
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
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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
2 Dual Core
2 Quad Core
% Reduction
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Regular
2 Feedback
Model Run
5:59
4:28
25.35%
001 RG
10 Feedback
Model Run
39:24
22:23
43.19%
0001 RG
10 Feedback
Model Run
76:47
41:20
46.17%
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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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Skim Differences – Conical VDF
Total Skim Differences in Consecutive Feedbacks - PKNOHOV
Total Skim Differences in Consecutive Feedbacks - PKNOHOV
120,000,000
600,000,000
Total Difference in Skims
Skims
100,000,000
500,000,000
MSA/.0001 RG
MSA/.0001 RG
0CW/.0001 RG-Naïve
0CW/.0001 RG-Naïve
.15CW/.0001RG
.15CW/.0001RG
.25CW/.0001 RG
.25CW/.0001 RG
.35CW/.0001RG
.35CW/.0001RG
.45CW/.0001RG
.45CW/.0001RG
80,000,000
400,000,000
60,000,000
300,000,000
40,000,000
200,000,000
20,000,000
100,000,000
0
03
1
4
2
35
4
6
5
76
7 8
8
9
9
10
10
Feedback
Feedback
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Trip Differences – Conical VDF
TotalTotal
Trip Differences
in Consecutive
Feedbacks
- PADIST
Trip Differences
in Consecutive
Feedbacks
- PADIST
5,000,000
160,000
Total Trip Differences
4,500,000
140,000
4,000,000
120,000
3,500,000
MSA/.0001 RG
MSA/.0001 RG
0CW/.0001
RG-Naïve
0CW/.0001
RG-Naïve
.15CW/.0001RG
.15CW/.0001RG
.25CW/.0001
RG
.25CW/.0001
RG
.35CW/.0001RG
.35CW/.0001RG
.45CW/.0001RG
.45CW/.0001RG
100,000
3,000,000
2,500,000
80,000
2,000,000
60,000
1,500,000
40,000
1,000,000
20,000
500,000
00
1
6
2
3
7
4
5
8
6
7
9
8
9
10
10
Feedback
Feedback
Note : PADIST is the sum of the HBW, HNW, and NHB person trips
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Skim Error – Conical VDF
Root Square Error of Skims in Consecutive Feedbacks - PKNOHOV
120,000
Root Square Error
100,000
MSA/.0001 RG
0CW/.0001 RG-Naïve
.15CW/.0001RG
.25CW/.0001 RG
.35CW/.0001RG
.45CW/.0001RG
80,000
60,000
40,000
20,000
0
1
2
3
4
5
6
7
8
9
10
Feedback
Note : PADIST is the sum of the HBW, HNW, and NHB person trips
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Trip Error – Conical VDF
Root Square Error of Trips in Consecutive Feedbacks - PADIST
20,000
18,000
16,000
Root Square Error
14,000
MSA/.0001 RG
0CW/.0001 RG-Naïve
.15CW/.0001RG
.25CW/.0001 RG
.35CW/.0001RG
.45CW/.0001RG
12,000
10,000
8,000
6,000
4,000
2,000
0
1
2
3
4
5
6
7
8
9
10
Feedback
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Comparison of Volumes – Conical VDF
•
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
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Volume Differences – Conical VDF
AM Peak Period Volume Difference in Consecutive Feedbacks
per Functional Classification (SC29 - CW25)
14,000,000
12,000,000
AM Peak Period Volume Difference
FUNCL 0
FUNCL 1
10,000,000
FUNCL 2
FUNCL 3
FUNCL 4
8,000,000
FUNCL 6
FUNCL 7
6,000,000
FUNCL 8
ALL
4,000,000
2,000,000
0
1
2
3
4
5
6
7
8
9
10
Note : ALL graph excludes the centroid connectors (FUNCL = 0)
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Volume RMSEs – Conical VDF
AM Peak Period Volume RMSEs in Consecutive Feedbacks
per Functional Classification (SC29 - CW25)
45
FUNCL 0
40
FUNCL 1
AM Peak Period Volume RMSE (%)
FUNCL 2
FUNCL 3
35
FUNCL 4
FUNCL 6
30
FUNCL 7
FUNCL 8
25
ALL
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Note : ALL graph excludes the centroid connectors (FUNCL = 0)
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Volume Change – Conical VDF
Number of Links with Volume Change Less than 1/2 Capacity
of a Single Lane in Consecutive Feedbacks (SC29 - CW25)
100.00%
90.00%
80.00%
Number of Links (%)
70.00%
60.00%
FUNCL 4
FUNCL 3
FUNCL 2
FUNCL 1
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
1
2
3
4
5
6
Feedback
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Max Volume Differences – Conical VDF
AM Peak Period MAX Volume Difference in Consecutive Feedbacks
(SC29)
3,000
AM Peak Period MAX Volume Difference
2,500
.45CW/.0001 RG
.15CW/.0001 RG
.25CW/.0001 RG
0CW/.0001 RG-Naïve
MSA/.0001 RG
.35CW/.0001 RG
.55CW/.0001 RG
2,000
1,500
1,000
500
0
1
May 2009
2
3
4
5
6
7
8
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Min Volume Differences – Conical VDF
AM Peak Period MIN Volume Difference in Consecutive Feedbacks
(SC29)
1
2
3
4
5
6
7
8
9
10
0
AM Peak Period MIN Volume Difference
-1,000
-2,000
-3,000
.45CW/.0001 RG
.15CW/.0001 RG
.25CW/.0001 RG
0CW/.0001 RG-Naïve
MSA/.0001 RG
.35CW/.0001 RG
.55CW/.0001 RG
-4,000
-5,000
-6,000
-7,000
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Run Times – Conical VDF
Cumulative Run Times
1:09:36
MSA/.0001 RG
0CW/.0001 RG
15CW/.0001 RG
25CW/.0001 RG
35CW/.0001 RG
45CW/.0001 RG
Cumulative Run Time (dd:hh:mm)
1:04:48
1:00:00
0:19:12
0:14:24
0:09:36
0:04:48
0:00:00
0
1
2
3
4
5
6
7
8
9
10
Feedback
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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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Acknowledgment
NCTCOG Model Development Group staff for
development of macros, and presentation review:


May 2009
Kathy Yu
Arash Mirzaei
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Contact Info



Behruz Paschai
Kathy Yu
Arash Mirzaei
[email protected]
[email protected]
[email protected]
North Central Texas Council
of Governments (NCTCOG)
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