increasing precision in highway volume through adjustment of stopping criteria in traffic assignment...

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)

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


Software Platform

1. Roadway and Transit models in TransCAD

2. Multi-modal generalized-cost user equilibrium traffic assignment

3. Microsoft® Windows® XP operating system


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


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


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


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


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


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


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


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


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)


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


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%


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


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


.15CW/.0001RG .25CW/.0001 RG

.35CW/.0001RG .45CW/.0001RG

Skim Differences – Conical VDF


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


.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


.15CW/.0001RG .25CW/.0001 RG

.35CW/.0001RG .45CW/.0001RG


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


.15CW/.0001RG .25CW/.0001 RG

.35CW/.0001RG .45CW/.0001RG

Note : PADIST is the sum of the HBW, HNW, and NHB person trips


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


.15CW/.0001RG .25CW/.0001 RG

.35CW/.0001RG .45CW/.0001RG


• 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


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)


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)


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


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


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


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


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


Acknowledgment

NCTCOG Model Development Group staff for

development of macros, and presentation review: Kathy Yu Arash Mirzaei


Contact Info

Behruz Paschai [email protected] Kathy Yu [email protected] Arash Mirzaei [email protected]

North Central Texas Council of Governments (NCTCOG)

increasing precision in highway volume through adjustment of stopping criteria in traffic assignment...

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